Abstract:
In a zoom lens consisting of a first lens group having a negative refractive power and a second lens group having a positive refractive power with the air separation between the first and second groups being variable for zooming, there are provided two non-spherical surfaces positioned respectively in the first lens group and on the image side of a diaphragm in the second lens group at optional locations to prevent deterioration of aberrations which occurs when the image angle of the zoom lens is increased.

Description:
This is a continuation of application Ser. No. 692,034, filed June 2, 1976 now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to zoom lenses with greatly increased image angle, and more particularly to a zoom lens consisting of a movable front lens group having a negative focal length and a movable rear lens group having a positive focal length, the rear lens group having a diaphragm incorporated therein, and the front and rear lens groups being axially moved in differential relation to each other to vary the focal length of the entire lens system, which zoom lens has photographic capabilities extended toward the wide angle side while still preserving good stabilization of aberrations throughout the zooming range with limitation of the overall dimensions of the zoom lens to a minimum. 
     As shown in FIG. 1, a zoom system which may be conveniently considered as comprising a negative front lens I and a positive rear lens II, both of which are moved axially but in differential relation to each other to effect variation of the focal length of the overall lens system is, because of its being of inverted telephoto type, advantageous in providing an increased extent of image angle. As the maximum axial separation between the front and rear lenses I and II occurs at the wide angle setting for the maximum image angle, however, there is a disadvantage to this zoom system such that an increase in the diameter of the front lens I must be made for the extended range of image angle toward the maximum. This problem becomes serious in designing a zoom lens with a greatly increased image angle. If the provision for increasing the maximum image angle is forced to be compatible with severe limitation of the overall dimensions of the zoom lens to a minimum, the barrel type distortion at the wide angle setting is rapidly increased and its satisfactory correction is made difficult by any means. 
     SUMMARY OF THE INVENTION 
     The present invention employs nonspherical refracting surfaces for facilitating correction of not only distortion but other various aberrations in correlation therewith and is intended to provide a compact zoom lens which is well corrected for aberrations even in the extended range of image angle at the wide angle settings. 
     A zoom lens constructed in accordance with the present invention comprises a movable front lens group having a negative focal length and a movable rear lens group having a positive focal length with the axial air separation between the movable front lens group and the movable rear lens group being varied to effect variation of the focal length of the entire system, whereby use is made of two non-spherical surfaces provided at optionally selected surfaces in the front and rear lens groups respectively while a diaphragm being positioned therebetween. 
     The present inventors have found, with this configuration of the present invention, that despite the fact that the image angle at the wide angle setting is increased to as high as 84°, it is possible to achieve a very good stabilization of distortion as well as other various aberrations throughout the entire zooming range, while still limiting the overall dimensions to a miniumum. The zoom lens of the invention in the form of a mechanically compensated varifocal lens system, as it is capable of maintaining a constant image plane while its focal length varies throughout a range of axial movement of the front and rear lens groups, is suitable either for use particularly with a still camera or for use as a super-wide angle zoom lens for a cinematographic camera, or a television camera. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG 1 is a diagram of geometry considered in performance of a two component zoom system of the inverted telephoto type. 
     FIG. 2 is a graph showing the figuring operation for a non-spherical surface. 
     FIG. 3 is a diagram of geometry considered in tracing a paraxial ray and a paraxially pupil ray to derive an equation having figuring constants for non-spherical surfaces. 
     FIG. 4 is a block diagram of a first example of a zoom lens in the preferred form of the present invention in three different operative positions, i.e., at wide angle, medium and telephoto settings respectively shown in FIGS. 4A, 4B and 4C. 
     FIGS. 5A, 5B and 5C are curves of aberration of the zoom lens of FIG. 4 at the wide angle, medium and telephoto settings respectively. 
     FIGS. 6A, 6B and 6C are curves of aberration of a second example of a zoom lens according to the invention at wide angle, medium and telephoto settings respectively. 
     FIGS. 7A, 7B and 7C are curves of aberration of a third example of a zoom lens of the invention at wide angle, medium and telephoto settings respectively. 
     FIGS. 8A, 8B and 8C are curves of aberration of a fourth example of a zoom lens of the invention at wide angle, medium and telephoto settings respectively. 
     FIG. 9 is block diagrams of a fifth example of a zoom lens according to the invention at wide angle, medium and telephoto settings respectively shown in FIGS. 9A, 9B and 9C. 
     FIGS. 10A, 10B and 10C are curves of aberration of the zoom lens of FIG. 9 at the wide angle, medium and telephoto settings respectively. 
     FIG. 11 is block diagrams of a sixth example of a zoom lens of the invention at wide angle, medium and telephoto settings respectively shown in FIGS. 11A, 11B and 11C. 
     FIGS. 12A, 12B and 12C are curves of aberration of the zoom lens of FIG. 11 at the wide angle, medium and telephoto settings respectively. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The zoom lens of the preferred embodiment of the present invention comprises a first lens group having a negative focal length and a second lens group having a positive focal length and having a diaphragm incorporated therein, whereby the axial air separation between the first and second lens groups is varied to effect variation of the focal length of the entire lens system, and wherein there are provided two non-spherical refracting surfaces respectively in the first lens group at an optionally selected surface or an i-th surface and in the second lens group behind the diaphragm at an optionally selected surface (or j-th surface) to achieve high standard of aberration correction, being characterized by the following relationships: ##EQU1## (3) ψi&gt;0 and ψj&lt;0 (4) hi hiψi+hj hj ψj&lt;-0.05 
     (5) |hi 2  hi 2  ψi+ hj 2  hj 2  ψj|&lt;0.15 
     wherein 
     f 1  : the focal length of the first lens group; 
     fw: the focal length of the entire system at the wide angle setting; 
     lw: the axial separation between the first and second lens groups at the wide angle setting; 
     ψi: the 3rd-order non-spherical coefficient at the i-th surface; 
     ψj: the 3rd-order non-spherical coefficient at the j-th surface; 
     hi: the height of the point of incidence of a paraxial ray on the i-th surface from the optical axis; 
     hj: the height of the point of incidence of a paraxial ray on the j-th surface from the optical axis; 
     hi: the height of the point of incidence of a paraxially pupil ray on the i-th surface from the optical axis; and 2 
     hj: the height of the point of incidence of a paraxially pupil ray on the j-th surface. 
     Conditions (1) and (2) concern a power distribution of the lens system. When the upper limit of condition (1) is violated, it is made more difficult to achieve satisfactory correction of distortion as well as other various aberrations. When the lower limit is violated, the size of the complete lens system is increased to contradict the above mentioned object of the invention which is to provide a compact zoom lens, though the aberration can be made more easily. The upper limit of condition (2) is also for limitation of the overall dimensions of the lens system to a minimum, while the lower limit of condition (2) is determined to secure a sufficient amount of axial movement of the zoom control lens groups, thereby it is avoided for the zoom ratio to be unduly decreased. 
     Conditions (3) to (5) concern figuring constants for the non-spherical surfaces. These quantities will be explained in detail below. The figuring of a non-spherical surface is generally expressed by use of co-ordinates X and Y, as shown in FIG. 2, where the abscissa X is parallel to the optical axis, and the ordinate is perpendicular to the optical axis, with the original point being coincident with the vertex of the non-spherical surface. Hence, the amount of deviation X of the non-spherical surface curve from the ordinate at the hight H of a point on the non-spherical surface from the optical axis may be expressed as: ##EQU2## wherein R is the radius of curvature of a paraxial part of the non-spherical surface at its vertex, and B, C and D are figuring constants. The first term on the right side of this equation (11) contains only one parameter R, namely, the radius of curvature of the paraxial part of the non-spherical surface. The second term contains a figuring constant B relates to the 3rd-order aspheric coefficient ψ as follows: 
     
         ψ=8(N&#39;-N)B                                             (12) 
    
     wherein N is the refractive index of the medium containing the incident ray, and N&#39; that of the medium containing the refracted ray. 
     The third term also contains a figuring constant C related to the 5th-order aspheric coefficient Ω as follows: 
     
         Ω=48(N&#39; -N)C                                         (13) 
    
     now assuming that a non-spherical surface in question is formed by modifying a spherical surface having a curvature of value R, the corresponding amounts of variation of 3rd-order aberration coefficients, namely, spherical aberration coefficient (I), coma aberration coefficient (II), astigmatism aberration coefficient (III), sagittal curvature of field aberration coefficient (IV) and distortion coefficient (V) are functions of aspheric coefficient ψ as follows: 
     
         ΔI=h.sup.4 ψ 
    
     
         ΔII=h.sup.3 hψ 
    
     
         ΔIII=h.sup.2 h.sup.2 ψ 
    
     
         ΔIV=h.sup.2 h.sup.2 ψ 
    
     
         ΔV=h h.sup.3 ψ 
    
     wherein h and h are the quantities selected for tracing rays with regard to the location and the aperture of the diaphragm one of the rays, namely, the ray 1, as shown in FIG. 3, goes along the optical axis and cuts the individual refracting surfaces (i, j) at respective heights, h, to intersect the optical axis at the image focus, while the other ray, namely, the ray 2 enters the system under an angle of obliquity and passes at the center 4 of the aperture of the diaphragm 3, the points of incidence on the individual surfaces (i, j) being at heights, h. 
     With the foregoing in mind, it is understandable that condition (3) assists in correction of barrel-type distortion or positive distortion due to the decrease in relative aperture of the lens system by production of a negative distortion resulting from the modification of an optionally selected surface (the i-th surface) in the first lens group and of an optionally selected surface (the j-th surface) on the image side of the diaphragm in the second lens group to the respective non-spherical ones. Of the other aberrations, I, II, III and IV with their amounts of variation caused by the introduction of the i-th and j-th non-spherical surfaces, there are two aberration variations namely, ΔIII and ΔIV which are most difficult to be compensated for by other lens surfaces. Even in this respect, condition (3) is effective for achieving good correction of astigmatism III and field curvature IV, as both non-spherical surfaces (the i-th and j-th surfaces) provide respective amounts of variation of astigmatism and field curvature which can be cancelled out with each other. Those facts constitute a reason why the diaphragm is placed between the i-th and j-th nonspherical surfaces. As is evident from FIG. 3, the sign of the quantity h is reversed at the diaphragm (hi∝ 0, hj&gt; 0), so that when ψi&gt; 0 and ψj&lt; 0, it is possible to make both of αVi and αVj negative as is understandable from the formulae (14). Formulae (14) also give ΔIIIj&gt; 0, ΔIVi&lt; 0, ΔIIIj&lt; 0, ΔIVj&lt; 0. This leads to establish the following equations (15): ##EQU3## 
     Condition (4) concerns the sum of the amounts of variation of 3rd-order distortion aberration coefficients due to the introduction of the terms only for the i-th and j-th non-spherical surfaces and operates within the framework of condition (3) to limit the acceptable range of 3rd-order non-spheric coefficients ψi and ψj or figuring constants Bi and Bj. When this limit is violated, the residual distortion becomes so large that a remarkable compactness and improvement in image quality are difficult to achieve. 
     Condition (5) concerns the sum of the amounts of variation of 3rd -order astigmatism III and curvature of image field IV aberration coefficients due to the introduction of the terms only for the i-th and j-th non-spherical surfaces, and operates within the framework of condition (3) and in combination with condition (4) to limit the acceptable range of combined ψi and ψj, or combined Bi and Bj. When this limit is violated, satisfactory correction of astigmatism and curvature of image field becomes difficult. 
     The present invention will be further illustrated in connection with six examples of a specific zoom lens of the preferred form of the present invention. In the following description and in the accompanying drawing, the focal length of the entire lens system is designated by f, the focal length of the front lens group by f 1 , the focal length of the rear lens group by f 2 , and f-number by F. The radii of curvature R, the axial separations, D, between the successive refracting surfaces are expressed with the subscripts to identity the particular surface and axial separation, numbered from front to rear. The plus and minus values of the radii, R, indicates surfaces convex and concave toward the front respectively. The refractive indices of the materials from which the various lens elements are made are designated by N, and their Abbe numbers are designated by Vd. 
     FIGS. 4A, 4B and 4C show a first example of the preferred embodiment of the zoom lens according to the present invention at the wide angle setting, a medium setting and the telephoto setting respectively. In this example, a number of lens elements with their surfaces R 1  to R 9  constitute a first lens group having a negative refractive power, and a number of lens elements with their surface R 10  to R 19  constitute a second lens group having a positive refractive power. The surfaces R 1  and R 19  are non-spherical. The diaphragm aperture is located between the surfaces R 13  and R 14 . With this zoom lens, it is possible to vary the focal length of the entire lens system by varying the axial separation D 9  between the surfaces R 9  and R 10 . The states of correction of spherical aberrations, astigmatism and distortion of the zoom lens of FIG. 4 when adjusted to the wide angle, medium and telephoto settings are shown in FIGS. 5A, 5B and 5C respectively. 
     EXAMPLE 1 
     The first example of the zoom lens may be constructed in accordance with the numerical data given below. 
     
         f= 1.0- 1.5 F/3.5 Image angle: 84°-62° 
    
     
         ______________________________________  No.  R         D         N      Vd______________________________________         1     4.0814  0.0958  1.72342                                      38.0         2     1.1436  0.4972         3     6.0310  0.2488  1.61293                                      37.0         4     -3.5394 0.0667         5     -3.7009 0.0833  1.77250                                      49.6f.sub.1 =     6     1.0459  0.2012  1.71736                                      29.5-1.6667       7     1.2405  0.2432         8     1.5182  0.1963  1.64769                                      33.8         9     13.2818  0.8346˜                       0.0096        10     5.0197  0.1027  1.60729                                      59.4        11     -4.4345 0.0042        12     1.1150  0.1763  1.60311                                      60.7        13     2.9677  0.2698f.sub.2 =    14     1.4990  0.2062  1.60311                                      60.71.4844       15     -6.7547 0.1079        16     -1.1877 0.0625  1.80518                                      25.4        17     1.883   0.1025        18     8.9553  0.1257  1.70154                                      41.1        19     -0.8623______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________f                D.sub.9______________________________________1.0              0.83461.2              0.42211.5              0.0096______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 1  and R 19  ##EQU4## The diaphragm aperture is located at a distance of 0.2073 rearwardly from surface R 13   
     
         ______________________________________α      h         -α   -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.175291 2     0.177250  9.990144  -1.208320                               -1.108100 3    -0.449092  1.213420  -0.507362                               -0.855854 4    -0.325772  1.263665  -0.594342                               -0.764187 5    -0.106940  1.270802  -0.726678                               -0.715687 6    -0.372195  1.288301  -0.577293                               -0.688546 7    -0.440112  1.339872  -0.540994                               -0.625154 8    -1.214912  1.635324  -0.179490                               -0.581504 9    -0.517247  1.696958  -0.427572                               -0.53055510    -0.600000  2.197729  -0.401699                               -0.19529011    -0.334114  2.219084  -0.425326                               -0.16810512    -0.030217  2.219210  -0.448347                               -0.16623713     1.170211  2.090534  -0.538269                               -0.107050 AP*   0.745367  1.936054  -0.516514                                0.00000014     0.745367  1.889469  -0.516514                                0.03228215     1.505554  1.695841  -0.503526                                0.09704016     1.656971  1.517007  -0.494862                                0.15045017     0.628501  1.495247  -0.596861                                0.17111418    -0.384705  1.534695  -0.712811                                0.24420719    -0.264480  1.554234  -0.693680                                0.295453  1.000000            -0.453308______________________________________ *Aperture plane 
    
     wherein the initial values for α, h and α when f= 1.0 with object at infinity are taken as α=0, h= 1, and α=-1. α and α are the values of tangent of angles under which respective paraxial rays intersect the optical axis. The angle has the positive sign when a clockwise turn will bring a ruler from the direction of the optical axis into that of the ray, and the negative sign if the turn is counter-clockwise. The value h, h has the positive sign when the measure is upward from the optical axis, and it is negative when the measure is downward. 
     The aberration coefficients of the zoom lens in Example 1 are as follows: 
     
         ______________________________________Wide Angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.002202    0.000167    -0.003443T       -0.000004   0.000091    0.000210LS      -0.017420   -0.011356   -0.006668I       1.57312     1.91693     2.28809II      -0.00553    0.04974     0.12004III     -0.03306    -0.02839    -0.02100P       0.11474     0.11474     0.11474V       0.22816     0.11046     0.03829I.sup.s -0.09097    -0.07174    -0.04226I*      -134.26523  -190.19276  -217.32985II*     -18.41178   -19.58180   -7.22936I.sub.F -2.53966    -2.03001    0.51001II.sub.P   0.67436     0.62257     0.74373I       -7.81431    -8.73541    -8.83642II      0.01116     -0.27105    -0.37760III     0.31518     0.20588     0.10551IV      -0.32360    -0.31193    -0.31474V       -1.11302    -0.47120    -0.17670IIz*    0.28456     0.33372     0.38746Iz      3.28758     3.68991     4.33780IIz     -0.00456    0.06309     0.10428______________________________________ 
    
     wherein 
     I: 3rd-order spherical aberration 
     Ii: 3rd-order coma 
     Iii: 3rd-order astigmatism 
     P: 3rd-order petzval sum 
     V: 3rd-order distortion 
     I s  : Pupil spherical aberration 
     I*: 5th-order zonal spherical aberration 
     Ii*: 5th-order zonal coma 
     If: 5th-order oblique meridional spherical aberration 
     Iip: 5th-order oblique arrowlike coma 
     I: 5th-order oblique spherical aberration 
     Ii: 5th-order oblique coma 
     Iii: 5th-order oblique astigmatism 
     Iv: 5th-order oblique field curvature 
     V: 5th-order oblique distortion 
     Iiz: 5th-order additional zonal coma 
     Iz: 5th-order additional spherical aberration 
     Iiz: 5th-order additional coma 
     EXAMPLE 2 
     The second example of the zoom lens though not shown in the drawings may be constructed in accordance with the numerical data given below. In this example, the 2nd and 19th surfaces are non-spherical. The states of correction of aberrations achieved in this example at the wide angle setting, a medium setting and the telephoto setting are shown in FIGS. 6A, 6B and 6C respectively. 
     
         f= 1.0-1.5 F/3.5 Image angle: 84°-62° 
    
     
         ______________________________________  No.  R         D         N      Vd______________________________________         1     2.6666  0.0958  1.72342                                      38.0         2     1.1655  0.519         3     -14.0131                       0.2392  1.61293                                      37.0f.sub.1 =     4     -2.7236 0.026-1.6667       5     -7.8433 0.8333  1.77250                                      49.6         6     0.9109  0.1842  1.71736                                      29.5         7     1.1010  0.2706         8     1.3436  0.1776  1.64769                                      33.8         9     4.6958   0.9471˜                       0.1221        10     3.3854  0.1266  1.60729                                      59.4        11     -2.6890 0.0417        12     0.9884  0.1731  1.60311                                      60.7f.sub.2 =    13     1.4550  0.25581.4844       14     1.4432  0.1890  1.60311                                      60.7        15     -6.6610 0.0753        16     -1.1519 0.0625  1.80518                                      25.4        17     1.2869  0.1295        18     -21.6055                       0.1308  1.70154                                      41.1        19     -0.8144______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________f                D.sub.9______________________________________1.0              0.94711.2              0.53461.5              0.1221______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 2  and R 19  ##EQU5## 
     The diaphragm aperture is located at a distance of 0.1932 rearwardly from surface R13. 
     
         ______________________________________No.   α    h         -α -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.272124 2     0.271904  0.984880  -1.345895                               -1.197283 3    -0.339407  1.161021  -0.602747                               -0.884477 4    -0.390190  1.218877  -0.564060                               -0.800840 5    -0.115886  1.221886  -0.744286                               -0.781515 6    -0.236233  1.232993  -0.667313                               -0.750141 7    -0.310867  1.266329  -0.621906                               -0.683451 8    -0.135959  1.573700  -0.176595                               -0.635667 9    -0.377330  1.614374  -0.483030                               -0.58359910    -0.600000  2.182661  -0.402534                               -0.20234211    -0.208465  2.199075  -0.438831                               -0.16778812     0.288175  2.197875  &lt;0.476724                               -0.16580113     1.629246  2.021940  -0.577891                               -0.10339814     0.791107  1.819610  -0.535030                                0.03343915     1.551492  1.636677  -0.521056                                0.09487616     1.699683  1.508719  -0.512466                                0.13345617     0.645121  1.486383  -0.605749                                0.15442918    -0.284842  1.523271  -0.702368                                0.24538819    -0.334303  1.548970  -0.710336                                0.299994  1.000000            -0.451917______________________________________ 
    
     Aberration Coefficient in Example 2 
     
         ______________________________________Wide Angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.002021    -0.000101   -0.003909T       0.000926    0.000949    0.000977LS      -0.016530   -0.010700   -0.006223I       1.44684     1.66650     1.75991II      -0.16516    -0.15192    -0.16364III     -0.01736    -0.03049    -0.04492P       0.10872     0.10872     0.10872V       0.20219     0.08917     0.02057I.sup.s -0.06088    -0.05659    -0.03560I*      -130.38641  -167.71822  -118.14091II*     -14.80253   -13.53817   5.25466I.sub.F -1.04452    -0.46237    2.17340II.sub.P   1.57484     1.49856     1.53195I       -6.69176    -7.56540    -7.63811II      1.12728     0.79455     0.57939III     0.19348     0.25959     0.22388IV      -0.44489    -0.25315    -0.19174V       -0.66883    -0.30425    -0.12162IIz*    0.26209     0.32896     0.40301Iz      4.06200     4.62270     5.55208IIz     -0.25678    -0.18014    -0.13746______________________________________ 
    
     EXAMPLE 3 
     The third examples of the zoom lens though not shown in the drawings may be constructed in accordance with the numerical data given below. In this example, the 1st and 18th surfaces are non-spherical. The states of correction of aberrations achieved in this example at the wide angle setting, a medium setting and the telephoto setting are shown in FIGS. 7A, 7B and 7C respectively. 
     
         f=1.0-1.5 f/3.5 Image Angle: 84°-62° 
    
     
         ______________________________________  No.  R         D         N      Vd______________________________________         1     4.3842  0.0958  1.72342                                      38.0         2     1.2118  0.5087         3     10.0526 0.2553  1.61293                                      37.0f.sub.1 =     4     -4.0175 0.0772-1.6667       5     -4.4334 0.0833  1.77250                                      49.6         6     1.0323  0.2002  1.71736                                      29.5         7     1.2096  0.2483         8     1.5448  0.1931  1.64769                                      33.8         9     25.0021  0.8279˜                       0.0042        10     3.8104  0.1032  1.60729                                      59.4        11     -4.5371 0.0042        12     1.0844  0.1760  1.60311                                      60.7        13     2.3253  0.2681f.sub.2 =    14     1.4084  0.2059  1.60311                                      60.71.4844       15     -5.2219 0.0976        16     -1.2283 0.0625  1.80518                                      25.4        17     1.1653  0.1039        18     93.5756 0.1327  1.70154                                      41.1        19     -0.8593______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________f                D.sub.9______________________________________1.0              0.82791.2              0.41541.5              0.0042______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 1  and R 18  ##EQU6## 
     The diaphragm aperture is located at a distance of 0.2056 rearwardly from the surface R 13 . 
     
         ______________________________________No.   α    h         -α -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.185217 2     0.165005  0.990825  -1.195567                               -1.118736 3    -0.426483  1.207762  -0.527720                               -0.850303 4    -0.352843  1.263618  -0.579565                               -0.758556 5    -0.160061  1.275977  -0.695293                               -0.705868 6    -0.382396  1.293955  -0.572472                               -0.677954 7    -0.451509  1.346599  -0.536261                               -0.615428 8    -1.250101  1.656994  -0.171285                               -0.572899 9    -0.555389  1.722085  -0.41179 -0.52467410    -0.600000  2.218835  -0.397887                               -0.19525711    -0.246366  2.234648  -0.429007                               -0.16772012     0.052738  2.234429  -0.451456                               -9.16583913     1.395504  2.092178  -0.543694                               -0.10614014     0.752864  1.890312  -0.516165                                0.03226015     1.562341  1.689696  -0.502350                                0.09676616     1.757495  1.518240  -0.491174                                0.14468317     0.762249  1.491849  -0.586018                                0.16497218    -0.268576  1.519767  -0.700009                                0.23773519    -0.257183  1.539828  -0.698226                                0.292200  1.000000            -0.459662______________________________________ 
    
     
         ______________________________________Aberration Coefficient in Example 3Wide Angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.001922    -0.000174   -0.003887T       0.000219    0.000328    0.000465LS      -0.017853   -0.011629   -0.006820I       1.67604     2.08229     2.54863II      0.11397     0.19546     0.30451III     -0.00703    0.00066     0.01044P       0.10439     0.10439     0.10439V       0.22980     0.11307     0.04138I.sup.s -0.14296    -0.09539    -0.05104I*      -125.41069  -183.72966  -229.24836II*     -21.85615   -25.97799   -21.00143I.sub.F -4.41582    -4.57400    -3.20459II.sub.P   -0.05957    -0.15126    -0.07310I       -9.71252    -11.37773   -12.79016II      -0.94936    -1.23477    -1.35560III     0.07081     -0.00426    -0.06138IV      -0.57903    -0.54439    -0.50422V       -1.12452    -0.49746    -0.20039II*.sub.Z   0.22451     0.29104     0.39829I.sub.Z 2.11750     2.22490     2.35043II.sub.Z   0.18435     0.23832     0.25974______________________________________ 
    
     EXAMPLE 4 
     The fourth example of the zoom lens of the invention though not shown in the drawings may be constructed in accordance with the numerical data given below. In this example, the 3rd and 19th surfaces are non-spherical. The states of correction of aberrations achieved in this example at the wide angle setting, a medium setting and the telephoto setting are shown in FIGS. 8A, 8B and 8C respectively. 
     
         f=1.0-1.5 F/3.5 Image angle: 84°-62° 
    
     
         ______________________________________No.        R          D         N      Vd______________________________________        1     2.6858   0.0958  1.72342                                      38.0        2     1.1649   0.5093        3     -3718.6930                       0.2570  1.61293                                      37.0f.sub.1 =    4     -3.4243  0.0804-1.6667      5     -4.6422  0.0833  1.77250                                      49.6        6     0.9940   0.2019  1.71736                                      29.5        7     1.1146   0.2637        8     1.4576   0.1927  1.64769                                      33.8        9     12.0696   0.8728˜                       0.0478       10     3.6804   0.1053  1.60729                                      59.4       11     -3.4655  0.0042       12     1.1405   0.1761  1.60311                                      60.7f.sub.2 =   13     2.0668   0.26881.4844      14     1.4127   0.2058  1.60311                                      60.7       15     -5.6582  0.994       16     1.1910   0.0625  1.80518                                      25.4       17     1.2267   0.1072       18     859.5100 0.1367  1.70154                                      41.1       19     -0.8310______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________f                D.sub.9______________________________________1.0              0.87281.2              0.46031.5              0.0478______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 3  and R 19  ##EQU7## 
     The diaphragm aperture is located at a distance of 0.2063 rearwardly from the surface R 13 . 
     
         ______________________________________No.   α    h         -α -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.274484 2     0.269350  0.985022  -1.343282                               -1.199789 3    -0.342378  1.159379  -0.598178                               -0.895166 4    -0.342569  1.213963  -0.598030                               -0.799877 5    -0.125276  1.224037  -0.741204                               -0.740275 6    -0.328968  1.239503  -0.618015                               -0.711219 7    -0.397725  1.286271  -0.578563                               -0.643186 8    -1.225590  1.609446  -0.164597                               -0.599784 9    -0.510430  1.669129  -0.431113                               -0.54937610    -0.600000  2.192809  -0.401631                               -0.19883211    -0.238175  2.208418  -0.434440                               -0.17036012     0.148829  2.207798  -0.464294                               -0.16842613     1.316306  2.063228  -0.553357                               -0.10765114     0.714236  1.871277  -0.521943                                0.03262115     1.513127  1.676991  -0.508016                                0.09785116     1.691877  1.508769  -0.497587                                0.14732617     0.671863  1.485508  -0.597187                                0.16800218    -0.303223  1.518019  -0.707463                                0.24385419    -0.301984  1.542288  -0.707264                                0.300694  1.000000            -0.453421______________________________________ 
    
     Aberration Coefficient in Example 4 
     
         ______________________________________Wide Angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.001936    -0.000395   -0.004580T       0.000587    0.000599    0.000614LS      -0.017518   -0.011383   -0.006659I       1.51579     1.81878     2.16232II      -0.14942    -0.11142    -0.06800III     -0.02710    -0.03299    -0.03721P       0.10785     0.10785     0.10785V       0.22994     0.10708     -0.03159I.sup.s -0.11241    -0.07953    -0.04441I*      -120.96575  -167.28250  -161.40807II*     -19.21069   -19.54677   -3.58358I.sub.F -2.63640    -2.07626    0.77706II.sub.p   1.36698     1.20133     1.23430I       -8.04652    -8.94594    -8.80755II      0.71884     0.31677     0.09582III     0.29632     0.26716     0.18138IV      -0.29792    -0.22409    -0.22902V       -0.94590    -0.40465    -0.15325IIz*    0.29027     0.34099     0.40337Iz      3.50262     3.96119     4.77284IIz     -0.22580    -0.12772    -0.05376______________________________________ 
    
     EXAMPLE 5 
     The fifth example of the zoom lens of the invention is shown in FIGS. 9A, 9B and 9C for the wide angle setting, a medium setting and the telephoto setting respectively, and may be constructed in accordance with the numerical data given below. In this example, the 4th and 19th surfaces are non-spherical. The states of correction of aberrations achieved in this example at the wide angle, medium and telephoto settings are shown in FIGS. 10A, 10B and 10C respectively. 
     
         f=1.0-1.5 F/3.5 Image Angle: 84°-62° 
    
     
         ______________________________________  No.  R         D         N      Vd______________________________________         1     2.7390  0.0958  1.72342                                      38.0         2     1.1330  0.5131         3     -60.3069                       0.2554  1.61293                                      37.0f.sub.1 =     4     -3.6505 0.0758-1.6667       5     -9.5261 0.0833  1.77250                                      49.6         6     0.9232  0.2016  1.71736                                      29.5         7     1.1096  0.2632         8     1.3978  0.1924  1.64769                                      33.8         9     6.6991   0.8818˜                       0.0568        10     3.8212  0.1054  1.60729                                      59.4        11     -3.0792 0.0042        12     1.1753  0.1753  1.60311                                      60.7f.sub.2 =    13     2.0520  0.26871.4844       14     1.3874  0.2052  1.60311                                      60.7        15     -5.2075 0.1019        16     -1.1647 0.0625  1.80518                                      25.4        17     1.2412  0.1104        18     -21.5094                       0.1369  1.70514                                      41.1        19     0.8107______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________F                D.sub.9______________________________________1.0              0.88181.2              0.46931.5              0.0568______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 4  and R 19  ##EQU8## The diaphragm aperture is located at a distance of 0.2062 rearwardly from surface R 13 . 
     
         ______________________________________No.   α    h         -α -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.263681 2     0.264119  0.985313  -1.333762                               -1.189515 3    -0.364988  1.172579  -0.574276                               -0.894870 4    -0.376905  1.232257  -0.565181                               -0.805380 5    -0.170007  1.245142  -1.700405                               -0.752299 6    -0.270979  1.257882  -0.639399                               -0.722238 7    -0.346109  1.298518  -0.596262                               -0.652231 8    -1.185583  1.610558  -0.174604                               -0.606276 9    -0.439325  1.661869  -0.455524                               -0.55307310    -0.600000  2.190924  -0.402051                               -0.19856111    -0.251801  2.207442  -0.433608                               -0.17011712     0.183557  2.206677  -0.467159                               -0.16817113     1.315921  2.062661  -0.553456                               -0.10760014     0.709692  1.871970  -0.521832                                0.03261515     1.523472  1.676981  -0.507654                                0.09758916     1.717694  1.501969  -0.496352                                0.14816117     0.679379  1.478447  -0.588776                                0.16889218    -0.279731  1.509320  -0.708341                                0.24706819    -0.328958  1.535790  -0.716399                                0.304714  1.000000            -0.452722______________________________________ 
    
     Aberration Coefficient in Example 5 
     
         ______________________________________Wide Angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.002116    -0.000153   -0.004222T       0.000281    0.000307    0.000340LS      -0.017483   -0.011373   -0.006677I       1.60791     1.86955     2.07581II      -0.12658    -0.06544    0.01007III     -0.03435    -0.03794    -0.04084P       0.11012     0.11012     0.11012V       0.24614     0.11086     0.02848I.sup.s -0.12370    -0.08247    -0.04504I*      -106.37290  -145.00256  -120.53203II*     -21.69655   -23.63549   -11.29596I.sub.F -3.25061    -3.00289    -0.65495II.sub.P   1.17628     1.03580     1.07509I       -8.50560    -0.67127    -9.98235II      0.57483     0.19246     -0.02389III     0.31269     0.27550     0.18842IV      -0.27989    -0.21640    -0.22544V       -0.95939    -0.40540    -0.15349IIz*    0.31958     0.35631     0.39836Iz      3.14172     3.45302     3.93935IIz     -0.18771    -0.07389    0.01034______________________________________ 
    
     EXAMPLE 6 
     The sixth example of the zoom lens of the invention is shown in FIGS. 11A, 11B and 11C for the wide angle setting, a medium setting and the telephoto setting respectively, and may be constructed in accordance with the numerical data given below. In this example, the 1st and 19th surfaces are non-spherical. The states of correction of aberrations achieved in this example at the wide angle, medium and telephoto settings are shown in FIGS. 12A, 12B and 12C respectively. 
     
         f=1.0-1.5 F/3.5 Image Angle: 84°-62° 
    
     
         ______________________________________  No.  R         D         N      V______________________________________         1     3.1283  0.0958  1.72342                                      38.0         2     1.0992  0.4335         3     8.8270  0.2063  1.61293                                      37.0f.sub.1 =     4     -3.2427 0.0143-1.6667       5     -4.4405 0.0833  1.77250                                      49.6         6     0.9477  0.1864  1.71736                                      29.5         7     1.2002  0.2500         8     1.4672  0.1921  1.64769                                      33.8         9     7.5714   0.8851˜                       0.0601        10     -10.5053                       0.0995  1.60311                                      60.7        11     -2.5645 0.0042        12     1.0342  0.1920  1.60311                                      60.7f.sub.2 =    13     3.9906  0.30651.4844       14     1.2515  0.1716  1.60311                                      60.7        15     20.2809 0.0804        16     -1.7496 0.0625  1.80518                                      25.4        17     1.1255  0.1022        18     6.5772  0.2752  1.80610                                      40.9        19     -1.2218______________________________________ 
    
     Lens Separation during Zooming 
     
         ______________________________________f                D.sub.9______________________________________1.0              0.88511.2              0.47261.5              0.0601______________________________________ 
    
     Figuring constants for the non-spherical surfaces at R 1  and R 19 . ##EQU9## 
     The diaphragm aperture is located at a distance of 0.2440 rearwardly from the surface R 13 . 
     
         ______________________________________No.   α    h         -α -h______________________________________ 1     0.000000  1.000000  -1.000000                               -1.164659 2     0.231249  0.987141  -1.269327                               -1.094076 3    -0.418416  1.168507  -0.549284                               -0.855984 4    -0.337277  1.211644  -0.608722                               -0.778129 5    -0.100251  1.213191  -0.755805                               -0.767328 6    -0.319308  1.228203  -0.622314                               -0.758070 7    -0.390772  1.269237  -0.579369                               -0.677233 8    -0.149363  1.556530  -0.174604                               -0.633589 9    -0.462243  1.610417  -0.454298                               -0.58062810    -0.600000  2.141485  -0.404630                               -0.22248511    -0.722943  2.186374  -0.391857                               -0.19815312    -0.208760  2.187244  -0.438458                               -0.19632613     1.066807  2.059476  -0.552952                               -0.130101AP     0.755555  1.875152  -0.533290                                0.00000014     0.755555  1.827930  -0.533290                                0.03333115     1.636423  1.652738  -0.517228                                0.08870416     1.587274  1.525095  -0.519866                                0.13051017     0.885407  1.494440  -0.579928                                0.15058818    -0.183672  1.513220  -0.687655                                0.22090119     0.001787  1.512948  -0.660581                                0.321559   1.000000           -0.448424______________________________________ 
    
     Aberration Coefficient in Example 6 
     
         ______________________________________Wide angle      Medium      TelephotoSetting         Setting     Setting______________________________________L       0.006295    0.005465    0.003888T       0.001097    0.001153    0.001224LS      -0.015582   -0.010138   -0.005937I       1.79689     2.05961     2.06139II      -0.00047    0.02017     0.01178III     -0.01397    -0.00907    -0.00492P       0.10765     0.10765     0.10765V       0.21985     0.11106     0.04355I.sup.s -0.03328    -0.04583    -0.03194I*      -110.13489  -155.29774  -183.31447II*     -14.40455   -16.54563   -10.69619I.sub.F -3.85138    -3.85619    -2.71460II.sub.P   0.41627     0.30896     0.28786I       -8.44452    -9.70400    -10.91943II      -0.15906    -0.50519    -0.72425III     0.12861     0.08409     0.02002IV      -0.47587    -0.39867    -0.36368V       -1.03655    -0.45993    -0.18156IIz*    0.24366     0.25989     0.24249Iz      3.94177     4.36512     5.04278IIz     0.00673     0.03236     0.01949______________________________________