Abstract:
A telephoto lens system including a positive first lens group, a negative second lens group, and a positive third lens group, in this order from the object; and focusing is performed by moving the second lens group along the optical axis. The telephoto lens system satisfies the following conditions: 
     
       
         1.0&lt; f/f 1&lt;1.4  (1) 
       
     
     
       
         1.0&lt;| f/f 2|&lt;1.6  (2) 
       
     
     wherein 
     f designates the focal length of the entire lens system; 
     f1 designates the focal length of the first lens group; and 
     f2 designates the focal length of the second lens group.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an inner-focusing telephoto lens system. 
     2. Description of the Related Art 
     In a conventional inner-focusing telephoto lens system for a medium-format camera (6×7; 6×4.5) with a focal length of about 200 mm (equivalent to a focal length of about 135 mm for the 35 mm camera), despite the F-number being relatively larger (e.g., about F4), a large number of lens element, such as seven lens elements, is required, which is disadvantageous for miniaturization of the lens system and the production costs thereof as well. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an inner-focusing telephoto lens system which is constituted by a smaller number of lens elements, and which corrects aberrations sufficiently. 
     In order to achieve the above object, there is provided a telephoto lens system including a positive first lens group, a negative second lens group, and a positive third lens group, in this order from the object; and focusing is performed by moving the second lens group along the optical axis. The telephoto lens system satisfies the following conditions: 
     
       
         1.0&lt; f/f 1&lt;1.4  (1) 
       
     
     
       
         1.0&lt;| f/f 2|&lt;1.6  (2) 
       
     
     wherein 
     f designates the focal length of the entire lens system; 
     f1 designates the focal length of the first lens group; and 
     f2 designates the focal length of the second lens group. 
     In the above-described telephoto lens system, for the purpose of reducing the number of lens elements, the lens system preferably includes six lens elements in total, e.g., the first lens group includes two positive lens elements and a negative lens element, the second lens group includes a cemented sub-lens group having a positive lens element and a negative lens element, and the third lens group includes a positive lens element, in this order from the object. According to this arrangement, conditions (1) and (2) can easily be satisfied, and thereby the correcting of aberrations can suitably be made. 
     On the other hand, in the above-described telephoto lens system, if an attempt is made to obtain a much shorter camera-to-object distance (hereinafter, a photographing distance), the traveling distance of the second lens group has to be largely increased, since the power of the second lens group, i.e., the focusing lens group, is determined as defined in condition (2). Therefore in order to reduce fluctuations in chromatic aberration due to the movement of the second lens group, it is preferable to correct chromatic aberration within the second lens group. More concretely, for sufficiently correcting chromatic aberration, the second lens group preferably includes a cemented sub-lens group having a positive lens element and a negative lens element. The order of the positive and negative lens elements is not required. Further, the second lens group preferably satisfies the following conditions: 
     
       
         | n 1− n 2|&lt;0.1  (3) 
       
     
     
       
         0.7&lt;{(ν1−ν2)/( r 2× f 2)}×1000&lt;1.1  (4) 
       
     
     wherein 
     n1 designates the refractive index of the negative lens element of the cemented sub-lens group; 
     n2 designates the refractive index of the positive lens element of the cemented sub-lens group; 
     ν1 designates the Abbe number of the negative lens element of the cemented sub-lens group; 
     ν2 designates the Abbe number of the positive lens element of the cemented sub-lens group; and 
     r2 designates the radius of curvature of the cemented surface of the cemented sub-lens group. 
     The present disclosure relates to subject matter contained in Japanese Patent Application No.Hei-11-27886 (filed on Feb. 4, 1999) which is expressly incorporated herein by reference in its entirety. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be discussed below in detail with reference to the accompanying drawings, in which: 
     FIG. 1 is a lens arrangement of a first embodiment of a telephoto lens system, according to the present invention; 
     FIGS. 2A,  2 B,  2 C and  2 D are aberration diagrams of the lens arrangement shown in FIG. 1; 
     FIG. 3 is a lens arrangement of a second embodiment of the telephoto lens system, according to the present invention; 
     FIGS. 4A,  4 B,  4 C and  4 D are aberration diagrams of the lens arrangement shown in FIG. 3; 
     FIG. 5 is a lens diagram of a third embodiment of the telephoto lens system, according to the present invention; 
     FIGS. 6A,  6 B,  6 C and  6 D are aberration diagrams of the lens arrangement shown in FIG. 5; 
     FIG. 7 is a lens diagram of a fourth embodiment of the telephoto lens system, according to the present invention; 
     FIGS. 8A,  8 B,  8 C and  8 D are aberration diagrams of the lens arrangement shown in FIG. 7; 
     FIG. 9 is lens arrangement of a fifth embodiment of the telephoto lens system, according to the present invention; 
     FIGS. 10A,  10 B,  10 C and  10 D are aberration diagrams of the lens arrangement shown in FIG. 9; 
     FIG. 11 is a lens arrangement of a sixth embodiment of the telephoto lens system, according to the present invention; 
     FIGS. 12A,  12 B,  12 C and  12 D are aberration diagrams of the lens arrangement shown in FIG. 11; 
     FIG. 13 is a lens arrangement of a seventh embodiment of the telephoto lens system, according to the present invention; and 
     FIGS. 14A,  14 B,  14 C and  14 D are aberration diagrams of the lens arrangement shown in FIG.  13 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As shown in FIGS. 1,  3 ,  5 ,  7 ,  9 ,  11  and  13 , the telephoto lens system includes a positive first lens group  10 , a negative second lens group  20  and a positive third lens group  30 , in this order from the object. A diaphragm S is fixed at a position between the first lens group  10  and the second lens group  20 . The first and third lens groups remain stationary, while the second lens group  20  is made movable along the optical axis upon focusing. 
     In the above-described telephoto lens system, in order to correct aberrations, the power of the first lens group  10  is reduced, and that of the second lens group  20  is reduced accordingly. If the power of the second lens group  20  is strong, the back focal distance becomes long, which results in an increase of the entire length of the lens system; or, if the power of the second lens group  20  is strong, the power of the third lens group  30  has to be increased, which is not desirable because the telephoto ratio increases. 
     Condition (1) is for reducing the power of the first lens group  10 . 
     If the power of the first lens group is reduced to the extent that f/f1 exceeds the lower limit of condition (1), the entire length of the lens system becomes too long. 
     If the power of the first lens group is increased to the extent that f/f1 exceeds the upper limit of condition (1), the occurrences of aberrations is quite noticeable. 
     Condition (2) is for reducing the power of the second lens group in accordance with the power of the first lens group. 
     If the power of the second lens group is reduced to the extent that |f/f2| exceeds the lower limit of condition (2), the traveling distance of the second lens group upon focusing becomes too long, and further, it becomes difficult to make the shortest photographing distance sufficiently shorter. 
     If the power of the second lens group is increased to the extent that |f/f2| exceeds the upper limit of condition (2), the back focal distance becomes longer, so that the entire length of the lens system is made longer; or, the power of the third lens group  30  has to be increased, so that the occurrences of aberrations is quite noticeable. 
     A preferable six-lens-element arrangement, as a practical example, is as follows: 
     (i) the first lens group includes a positive sub-lens group and a negative sub-lens group for the purpose of reducing chromatic aberration; and the positive sub-lens group includes two lens elements in order to correct aberrations; 
     (ii) the second lens group which is arranged to move upon focusing includes a cemented sub-lens group having a positive lens element and a negative lens element in order to correct chromatic aberration; and 
     (iii) the third lens group, which has the weakest power among those of the three lens groups, includes a positive lens element. 
     Under the condition that the power of the second lens group, i.e., the focusing lens group, is reduced according to condition (2), if the shortest photographing distance is made shorter, the traveling distance of the second lens group is inevitably increased. 
     Conditions (3) and (4) are specified to sufficiently correct chromatic aberration in the second lens group constituted by the above described cemented sub-lens group, and to reduce fluctuations in aberrations in the entire lens system even when the traveling distance the second lens group becomes longer. 
     Condition (3) specifies the difference between the refractive indexes of the two lens elements of the second lens group  20  in order to reduce fluctuations in chromatic aberration. 
     If |n1−n2| exceeds the upper limit of condition (3), fluctuation in chromatic aberration cannot be reduced sufficiently. 
     Condition (4) specifies the amount of color correction on the cemented surface of the second lens group in order to reduce fluctuations in chromatic aberration. 
     If {(ν1−ν2)/(r2×f2)}×1000 exceeds the upper limit of condition (4), the color correction in the second lens group becomes excessive, so that the correcting of chromatic aberration over the entire lens system becomes insufficient (in particular, at an infinity photographing distance). 
     If {(ν1−ν2)/(r2×f2)}×1000 exceeds the lower limit of condition (4), the color correction in the second lens group becomes insufficient, so that the correcting of chromatic aberration over the entire lens system becomes excessive (in particular, at the shortest photographing distance). 
     Specific numerical examples will herein be discussed. In the diagrams of chromatic aberration (axial chromatic aberration) represented by spherical aberration, the solid lines and the two types of dotted lines respectively indicate spherical aberration with respect to the d, g and C lines. Also, in the diagrams of lateral chromatic aberration, the solid lines and the two types of dotted lines respectively indicate magnification with respect to the d, g and C lines. S designates the sagittal image, and M designates the meridional image. In the tables, F NO  designates the F-number, f designates the focal length of the entire lens system, W designates the half angle-of-view (°), f B  designates the back focal distance, r designates the radius of curvature, d designates the lens thickness or space between lens surfaces, N d  designates the refractive index with respect to the d-line, and ν designates the Abbe number. 
     [Embodiment 1] 
     FIG. 1 is a lens arrangement of the first embodiment of a telephoto lens system, and FIGS. 2A,  2 B,  2 C and  2 D are aberration diagrams of the lens arrangement shown in FIG.  1 . Table 1 shows the numerical data thereof. Surface Nos. 1 through 6 represent a positive first lens group  10 ; surface Nos. 7 through 9 represent a negative second lens group  20 ; and surface Nos. 10 and 11 represent a positive third lens group  30 . The first lens group  10  includes a positive lens element, a positive lens element, and a negative lens element, in this order from the object. The second lens group  20  includes a cemented sub-lens group having a negative lens element and a positive lens element, in this order from the object. The third lens group  30  includes a positive lens element. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 t = 195.99 
               
               
                 W = 10.0 
               
               
                 f B  = 100.28 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 55.863 
                 10.868 
                 1.61800 
                 63.4 
               
               
                 2 
                 −1336.509 
                 0.200 
                 — 
                 — 
               
               
                 3 
                 44.905 
                 6.879 
                 1.61800 
                 63.4 
               
               
                 4 
                 121.091 
                 1.991 
                 — 
                 — 
               
               
                 5 
                 746.782 
                 2.994 
                 1.63017 
                 36.2 
               
               
                 6 
                 32.625 
                 15.327 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 2.000 
                 — 
                 — 
               
               
                 7 
                 383.088 
                 2.000 
                 1.71300 
                 53.9 
               
               
                 8 
                 22.897 
                 5.358 
                 1.71687 
                 46.6 
               
               
                 9 
                 77.745 
                 38.408 
                 — 
                 — 
               
               
                 10  
                 156.708 
                 3.690 
                 1.63643 
                 59.0 
               
               
                 11  
                 −355.651 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 2] 
     FIG. 3 is a lens arrangement of the second embodiment of the telephoto lens system, according to the present invention, and FIGS. 4A,  4 B,  4 C and  4 D are aberration diagrams of the lens arrangement shown in FIG.  3 . Table 2 shows the numerical data thereof. The lens basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 f = 196.00 
               
               
                 W = 10.0 
               
               
                 f B  = 98.71 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 54.228 
                 8.834 
                 1.61800 
                 63.4 
               
               
                 2 
                 −1674.369 
                 0.200 
                 — 
                 — 
               
               
                 3 
                 45.693 
                 6.629 
                 1.61800 
                 63.4 
               
               
                 4 
                 114.813 
                 2.169 
                 — 
                 — 
               
               
                 5 
                 754.108 
                 5.491 
                 1.62004 
                 36.3 
               
               
                 6 
                 31.055 
                 6.459 
                 — 
                 — 
               
               
                 7 
                 318.607 
                 4.844 
                 1.72000 
                 43.7 
               
               
                 8 
                 −46.723 
                 2.000 
                 1.72000 
                 50.2 
               
               
                 9 
                 95.737 
                 30.000 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 18.981 
                 — 
                 — 
               
               
                 10  
                 177.960 
                 5.000 
                 1.57099 
                 50.8 
               
               
                 11  
                 −419.264 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 3] 
     FIG. 5 is a lens diagram of the third embodiment of the telephoto lens system, according to the present invention, and FIGS. 6A,  6 B,  6 C and  6 D are aberration diagrams of the lens arrangement shown in FIG.  5 . Table 3 shows the numerical data thereof. The basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 f = 196.00 
               
               
                 W = 10.0 
               
               
                 f B  = 98.87 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 62.294 
                 8.973 
                 1.61800 
                 63.4 
               
               
                 2 
                 −1273.226 
                 0.200 
                 — 
                 — 
               
               
                 3 
                 47.359 
                 6.882 
                 1.61800 
                 63.4 
               
               
                 4 
                 152.181 
                 1.586 
                 — 
                 — 
               
               
                 5 
                 643.050 
                 6.337 
                 1.62588 
                 35.7 
               
               
                 6 
                 34.001 
                 14.270 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 2.508 
                 — 
                 — 
               
               
                 7 
                 958.298 
                 4.686 
                 1.80518 
                 25.4 
               
               
                 8 
                 −177.154 
                 2.000 
                 1.66672 
                 48.3 
               
               
                 9 
                 76.143 
                 39.759 
                 — 
                 — 
               
               
                 10  
                 134.386 
                 3.930 
                 1.48749 
                 70.2 
               
               
                 11  
                 −236.192 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 4] 
     FIG. 7 is a lens diagram of the fourth embodiment of the telephoto lens system, according to the present invention, and FIGS. 8A,  8 B,  8 C and  8 D are aberration diagrams of the lens arrangement shown in FIG.  7 . Table 4 shows the numerical data thereof. The basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 f = 196.00 
               
               
                 W = 10.1 
               
               
                 f B  = 95.00 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 70.145 
                 8.862 
                 1.61800 
                 63.4 
               
               
                 2 
                 −2034.433 
                 0.200 
                 — 
                 — 
               
               
                 3 
                 46.683 
                 10.227 
                 1.61800 
                 63.4 
               
               
                 4 
                 173.132 
                 1.049 
                 — 
                 — 
               
               
                 5 
                 431.908 
                 8.000 
                 1.64769 
                 33.8 
               
               
                 6 
                 33.128 
                 9.949 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 2.000 
                 — 
                 — 
               
               
                 7 
                 342.632 
                 5.000 
                 1.80518 
                 25.4 
               
               
                 8 
                 −127.145 
                 2.000 
                 1.79952 
                 42.2 
               
               
                 9 
                 82.230 
                 39.839 
                 — 
                 — 
               
               
                 10  
                 120.700 
                 7.874 
                 1.48749 
                 70.2 
               
               
                 11  
                 −246.139 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 5] 
     FIG. 9 is lens arrangement of the fifth embodiment of the telephoto lens system, according to the present invention, and FIGS. 10A,  10 B,  10 C and  10 D are aberration diagrams of the lens arrangement shown in FIG.  9 . Table 5 shows the numerical data thereof. The basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 f = 196.00 
               
               
                 W = 10.1 
               
               
                 f B  = 94.26 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 67.769 
                 8.442 
                 1.61800 
                 63.4 
               
               
                 2 
                 −2741.576 
                 0.200 
                 — 
                 — 
               
               
                 3 
                 45.591 
                 8.765 
                 1.61800 
                 63.4 
               
               
                 4 
                 154.715 
                 1.058 
                 — 
                 — 
               
               
                 5 
                 385.375 
                 8.000 
                 1.63980 
                 34.5 
               
               
                 6 
                 32.234 
                 9.976 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 1.800 
                 — 
                 — 
               
               
                 7 
                 289.341 
                 5.000 
                 1.80518 
                 25.4 
               
               
                 8 
                 −153.729 
                 2.000 
                 1.79952 
                 42.2 
               
               
                 9 
                 80.924 
                 44.955 
                 — 
                 — 
               
               
                 10  
                 115.594 
                 4.200 
                 1.48749 
                 70.2 
               
               
                 11  
                 −344.851 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 6] 
     FIG. 11 is a lens arrangement of the sixth embodiment of the telephoto lens system, according to the present invention, and FIGS. 12A,  12 B,  12 C and  12 D are aberration diagrams of the lens arrangement shown in FIG.  11 . Table 6 shows the numerical data thereof. The basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 F NO  1:4.1 
               
               
                 t = 196.00 
               
               
                 W = 10.1 
               
               
                 f B  = 94.90 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 61.985 
                 8.814 
                 1.59240 
                 68.3 
               
               
                 2 
                 −2222.678 
                 1.988 
                 — 
                 — 
               
               
                 3 
                 47.253 
                 8.294 
                 1.61800 
                 63.4 
               
               
                 4 
                 145.635 
                 1.280 
                 — 
                 — 
               
               
                 5 
                 582.939 
                 8.000 
                 1.62588 
                 35.7 
               
               
                 6 
                 32.604 
                 11.507 
                 — 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 1.800 
                 — 
                 — 
               
               
                 7 
                 358.797 
                 5.000 
                 1.80518 
                 25.4 
               
               
                 8 
                 −118.166 
                 2.000 
                 1.76200 
                 40.1 
               
               
                 9 
                 83.475 
                 41.514 
                 — 
                 — 
               
               
                 10  
                 108.373 
                 4.200 
                 1.48749 
                 70.2 
               
               
                 11  
                 −353.289 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     [Embodiment 7] 
     FIG. 13 is a lens arrangement of a seventh embodiment of the telephoto lens system, according to the present invention, and FIGS. 14A,  14 B,  14 C and  14 D are aberration diagrams of the lens arrangement shown in FIG.  13 . Table 7 shows the numerical data thereof. The basic lens arrangement is the same as in the first embodiment. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 F NO  = 1:4.1 
               
               
                 f = 196.00 
               
               
                 W = i0.i 
               
               
                 f B  = 95.68 
               
             
          
           
               
                 Surface No. 
                 r 
                 d 
                 Nd 
                 v 
               
               
                   
               
             
          
           
               
                 1 
                 56.489 
                 9.357 
                 1.56907 
                 71.3 
               
               
                 2 
                 −483.174 
                 0.412 
                 — 
                 — 
               
               
                 3 
                 49.992 
                 6.754 
                 1.69680 
                 55.5 
               
               
                 4 
                 126.977 
                 1.826 
                 — 
                 — 
               
               
                 5 
                 3565.726 
                 8.000 
                 1.62588 
                 35.7 
               
               
                 6 
                 32.642 
                 9.605 
                 — 
               
               
                 Diaphragm 
                 ∞ 
                 1.800 
                 — 
                 — 
               
               
                 7 
                 279.717 
                 4.190 
                 1.80518 
                 25.4 
               
               
                 8 
                 −58.566 
                 2.000 
                 1.80610 
                 33.3 
               
               
                 9 
                 85.700 
                 46.338 
                 — 
                 — 
               
               
                 10  
                 127.579 
                 4.038 
                 1.48749 
                 70.2 
               
               
                 11  
                 −274.211 
                 — 
                 — 
                 — 
               
               
                   
               
             
          
         
       
     
     Each condition of each embodiment is shown in Table 8. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 Cond. (1) 
                 Cond. (2) 
                 Cond. (3) 
                 Cond. (4) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Embodiment 1 
                 1.24 
                 1.39 
                 0.004 
                 — 
               
               
                 Embodiment 2 
                 1.20 
                 1.02 
                 0.000 
                 0.73 
               
               
                 Embodiment 3 
                 1.27 
                 1.39 
                 — 
                 0.92 
               
               
                 Embodiment 4 
                 1.24 
                 1.42 
                 0.006 
                 0.96 
               
               
                 Embodiment 5 
                 1.27 
                 1.36 
                 0.006 
                 0.76 
               
               
                 Embodiment 6 
                 1.17 
                 1.26 
                 0.043 
                 0.80 
               
               
                 Embodiment 7 
                 1.22 
                 1.26 
                 0.001 
                 0.86 
               
               
                   
               
             
          
         
       
     
     Each embodiment satisfies conditions (1) and (2). Each embodiment, except for the third embodiment, satisfies condition (3). Moreover, each embodiment, except for the first embodiment, satisfies condition (4). Furthermore, in each embodiment, aberrations are adequately corrected; and in each embodiment, except for the first embodiment, the shortest photographing distance can further be reduced. 
     According to the above description, an inner-focusing telephoto lens system, which has an F-number of about 4, and is constituted by a smaller number of lens elements, and further, by which aberrations are adequately corrected, can be obtained.