Miniature and large aperture retrofocus wide-angle photographic lens
SUMMARY OF THE INVENTION 
     This invention relates to a retrofocus wide-angle photographic lens having an aperture ratio of 1:1.4 and a large angular field of 95°. The invention successfully maintains a sufficient back focal length, provides correction of various types of aberrations despite the extreme brightness of a lens having an aperture ratio of 1:1.4, and is relatively small in size. 
     This is accomplished by providing a lens system having five lens components satisfying the following conditions (I) to (IV): 
     
         ν.sub.a, ν.sub.b &gt; 55                                (i) ##EQU2## 
    
     
         F &lt; d.sub.C.D &lt; 2F                                         (IV) 
    
     where 
     F: the resultant focal length of the entire system, 
     F a .b....i : the resultant focal length to the i group, 
     r j  : the radius of curvature of the j surface of the lenses, counting from the first lens surface nearest the objective side, 
     d j  : the thickness of air gap between the j and j+l surfaces, 
     N k  : the refractive index of the kth lens 
     ν k  : Abbe&#39;s number for the kth lens 
     ν A  : The Abbe&#39;s number of the positive lens within A group 
     ν B  : The average Abbe&#39;s number of the negative lens within B group 
     d C .D : The distance along the optical axis between the first surface of C group and the last surface of D group 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The specific nature of the invention, as well as other objects, aspects, uses and advantages thereof, will clearly appear from the following description and from the accompanying drawings, in which: 
     FIG. 1 is a longitudinal view showing the lens system in accordance with the first embodiment of the invention; 
     FIGS. 2a and 2d show aberration curves obtained by the lens system in accordance with the first embodiment of the invention; 
     FIG. 3 is a longitudinal view showing the lens system in accordance with the second embodiment of the invention; 
     FIGS. 4a to 4d show aberration curves obtained by the lens system in accordance with the second embodiment of the invention; 
     FIG. 5 is a longitudinal view showing the lens system in accordance with the third embodiment of the invention. 
     FIGS. 6a to 6d show aberration curves obtained by the lens system in accordance with the third embodiment of the invention; 
     FIG. 7 is a longitudinal view showing the lens system in accordance with the fourth embodiment of the invention; 
     FIGS. 8a to 8d show aberration curves obtained by the lens system in accordance with the fourth embodiment of the invention; 
     FIG. 9 is a longitudinal view showing the lens system in accordance with the fifth embodiment of the invention 
     FIGS. 10a to 10d show aberration curves obtained by the lens system in accordance with the fifth embodiment of the invention; 
     FIG. 11 is a longitudinal view showing the lens system in accordance with the sixth embodiment of the invention; 
     FIGS. 12a to 12d show aberration curves obtained by the lens system in accordance with the sixth embodiment of the invention; 
     FIG. 13 is a longitudinal view showing the lens system in accordance with the seventh embodiment of the invention; 
     FIGS. 14a to 14d show aberration curves obtained by the lens system in accordance with the seventh embodiment of the invention; 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     According to the present invention, as shown in each of the seven embodiments of FIGS. 1, 3, 5, 7, 9, 11 and 13, there is provided a lens system consisting of five groups identified as A thru E. The A group comprises a positive lens 10. The B group is a negative meniscus lens 20 with its convex surface directed toward the object side of the lens system. The lens 20 may consist of two negative meniscus lenses 21 and 22, as shown in FIGS. 1 and 3, or three negative meniscus lenses 21, 22 and 23 as shown in FIGS. 5, 7, 9, 11 and 13. The C group is a positive lens 30 consisting of either a single positive lens element 31 as shown in FIGS. 9, 11 and 13, or positive and negative lens elements 31 and 32 joined together as shown in FIGS. 1, 3, 5 and 7. The D group has a positive resultant focal length and is in the form of a compound lens comprising positive and negative lenses 41 and 42, respectively. The E group has a positive resultant focal length and consists of either, two single lens elements 51 and 52 as shown in FIG. 13, a single lens element 53 and a positive lens consisting of joined positive and negative lens elements 51 and 52, as shown in FIGS. 1, 3, 5, and 11, or a single lens element 51 and a positive lens consisting of joined positive and negative lens elements 52 and 53, as shown in FIGS. 7 and 9. A filter 60 is interposed between the B group, and the C group, and a diaphragm 70 is interposed between the C group and said the D group. 
     The wide-angle lens according to the invention is characterized by the following four conditions as noted below, which will be described in greater detail later: 
     
         ν.sub.A, ν.sub.B &gt; 55                                (I) ##EQU3## 
    
     
         f &lt; d.sub.C.D &lt; 2F                                         (IV) 
    
     wherein the terms in the equations are as defined previously. 
     The various conditions as described above will be explained in detail in the following. 
     Condition (I) 
     
         ν.sub.A, ν.sub.B &gt; 55 
    
     this condition is provided to reduce the difference between chromatic aberrations of the multiplying factor in the peripheral and midportions of the image plane. When the angular field is more than 95°, the chromatic aberration of the multiplying factor in the peripheral portion of the image plane is greater, in comparison with that in the midportion of the image plane. In particular, the chromatic aberrations tend to occur in A and B groups, which have large incident angles. If ν A  and ν B  are smaller than 55, there will be excessive chromatic aberration which would have to be compensated for by an excessive converging system following the C group. Thus, condition (I) is desirable. 
     Condition (II) ##EQU4## 
     This condition is provided to obtain the back focal length required for attaching the lens to a camera. If |F A .B | is greater than the upper limit (F/0.7), it would be necessary, in order to obtain the necessary back focal length, to increase the spacing or thickness of converging systems after the B group. Furthermore, in order to obtain the same quantity of peripheral light, it would be necessary to design the lens system so that the A, B and E groups have a greater diameter resulting in a larger lens system, which is contrary to the object of minituarization. On the other hand, if |F A .B | is smaller than the lower limit (F/1.2), the required back focal length could be readily obtained with a minituarized lens system. However, this would result in a shortening of the focal length of the covering system after the B group and a decrease in the sum of Petzval thereby leading to an undesirable increase of the spherical aberration and the coma aberration. 
     Condition (III) ##EQU5## 
     This condition is important to correct satisfactorily the coma aberration and simultaneously to obtain the required back focal length. If |F A .B.C.D | is greater than the upper limit (F/0.2), it would be necessary to increase the lens thickness of the C group or the air spacing along the optical axis between the C and D groups in order to obtain the necessary back focal length. However, that would result in a larger lens system but a smaller quantity of light passing therethrough. If an attempt is made to obtain the same quantity of light, the diameter of lenses of A, B and E groups would have to be larger. This would result in a larger lens system, which will not satisfy the object of miniturization. On the other hand, if |F A .B.C.D | is smaller than the lower limit (F/0.8), the required back focal length would be readily obtainable. However, this would result in a shortening of the focal length of the positive lens of the E group and a decrease in the radius of curvature below that required, thereby undesirably increasing the coma aberration. 
     Condition (IV) 
     
         F &lt; d.sub.C.D &lt; 2F 
    
     this condition is important in maintaining the balance of aberrations, particularly, the balance of the coma aberration. If d C .D is less than the lower limit F, and assuming that the resultant focal length of the C and D group is constant, the height of light incident upon and emitted from the C and D groups regarding to the light above the diaphragm and the light below the diaphragm become lower. As a result the radius of curvature of the C and D groups would have to be further reduced and the action to the coma aberration would have to be further enhanced in order to correct the coma aberration, thus leading an increase in the spherical aberration. On the other hand, if d C .D is greater than the upper limit, 2F, the height of light incident upon and emitted from the C and D groups becomes higher. This results in that action of light passing above the diaphragm and of light passing below the diaphragm must be enhanced to readily maintain the balance of the coma aberration, while the overall length of lens system becomes longer and simultaneously when an attempt is made to obtain the same quantity of light, the lenses of A, B and E groups must be designed to have a greater diameter thereof. 
     According to the specific feature of the invention, there is provided a wide angle photographic lens having an aperture ratio of 1:1.4 and a large angular field of 95°,  which can maintain sufficient back focal length and properly correct various aberrations despite the extreme brightness of the lens, while maintaining the lens system in a miniaturized type. 
     Seven specific examples of the invention are illustrated in FIGS. 1, 3, 5, 7, 9, 11 and 13. The parameters for these examples are given in Examples 1, 2, 3, 4, 5, 6 and 7 below. The aberration curves for the seven specific examples are given in FIGS. 2, 4, 6, 8, 10, 12 and 14, respectively. 
     The lens data in Examples 1, 2, 3, 4, 5, 6 and 7, according to the present invention are given below for a lens system having a resultant focal length F = 100 
     
                       Example 1                                                   
______________________________________                                    
Aperture ratio 1 : 1.4 Angular field 94.5°                         
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
lens #                                                                    
      Curvature r or Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 = 282.073                                                   
                  d.sub.1 = 38.390                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 857.893                                                   
                  d.sub.2 =  0.488                                        
2     r.sub.3 = 141.907                                                   
                  d.sub.3 =  5.878                                        
                             N.sub.2 /ν.sub.2 = 1.64000/60.2           
2     r.sub.4 =  68.712                                                   
                  d.sub.4 = 41.707                                        
3     r.sub.5 = 166.702                                                   
                  d.sub.5 =  5.854                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  67.168                                                   
                  d.sub.6 = 24.878                                        
filter                                                                    
      ∞     7.317      1.51633/64.1                                 
filter                                                                    
      ∞     2.537                                                   
4     r.sub.7 = 484.917                                                   
                  d.sub.7 = 76.927                                        
                             N.sub.4 /ν.sub.4 = 1.80518/25.4           
4 &amp; 5 r.sub.8 =-250.893                                                   
                  d.sub.8 =  6.244                                        
                             N.sub.5 /ν.sub.5 = 1.71700/47.9           
5     r.sub.9 = -574.546                                                  
                  d.sub.9 = 13.658                                        
6     r.sub.10 = 551.585                                                  
                  d.sub.10 = 47.659                                       
                             N.sub.6 /ν.sub.6 = 1.73400/51.5           
6     r.sub.11 = -150.249                                                 
                  d.sub.11 =  0.390                                       
7     r.sub.12 = -384.688                                                 
                  d.sub.12 = 5.854                                        
                             N.sub.7 /ν.sub.7 = 1.84666/23.9           
7     r.sub.13 = 198.849                                                  
                  d.sub.13 = 17.268                                       
8     r.sub.14 =-1536.502                                                 
                  d.sub.14 = N.sub.8 /ν.sub.8 = 1.84666/23.9           
8 &amp; 9 r.sub.15 = 400.410                                                  
                  d.sub.15 = 32.780                                       
                             N.sub.9 /ν.sub.9 = 1.69680/55.5           
9     r.sub.16 = -157.551                                                 
                  d.sub.16 =  0.488                                       
10    r.sub.17 = 322.741                                                  
                  d.sub.17 = 26.366                                       
                             N.sub.10 /ν.sub.10 = 1.77250/49.7         
10    r.sub.18 = -470.980                                                 
back focal length = 179.000                                               
F.sub.A.B = -116.836                                                      
F.sub. A.B.C.D = -237.079                                                 
d.sub.C.D = 150.732                                                       
Sum of Petzval = 0.090                                                    
All linear dimensions are given in millimeters                            
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                       Example 2                                                   
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Aperture ratio 1 : 1.4  Angular field 95°                          
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
lens #                                                                    
      Curvature r or Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 = 290.595                                                   
                  d.sub.1 = 41.024                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 867.896                                                   
                  d.sub.2 =  0.488                                        
2     r.sub.3 = 146.068                                                   
                  d.sub.3 =  5.854                                        
                             N.sub.2 /ν.sub.2 = 1.64000/60.2           
2     r.sub.4 =  70.405                                                   
                  d.sub.4 = 43.805                                        
3     r.sub.5 = 164.917                                                   
                  d.sub.5 =  5.854                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  66.983                                                   
                  d.sub.6 = 24.732                                        
filter                                                                    
      ∞     7.317      1.51633/64.1                                 
filter                                                                    
      ∞     2.439                                                   
4     r.sub.7 = 497.780                                                   
                  d.sub.7 =  9.756                                        
                             N.sub.4 /ν.sub.4 = 1.72000/50.2           
4 &amp; 5 r.sub.8 = 243.902                                                   
                  d.sub.8  = 70.732                                       
                             N.sub.5 /ν.sub.5 = 1.80518/25.4           
5     r.sub.9 =-557.507                                                   
                  d.sub.9 = 13.659                                        
6     r.sub.10 = 558.663                                                  
                  d.sub.10 = 49.854                                       
                             N.sub.6 /ν.sub.6 = 1.72916/54.7           
6     r.sub.11 =-146.740                                                  
                  d.sub.11 =  0.390                                       
7     r.sub.12 =-369.015                                                  
                  d.sub.12 = N.sub.7 /ν.sub.7 = 1.84666/23.9           
7     r.sub.13 = 194.379                                                  
                  d.sub.13 = 17.024                                       
8     r.sub.14 =-1876.346                                                 
                  d.sub.14 = N.sub.8 /ν.sub.8 = 1.84666/23.9           
8 &amp; 9 r.sub.15 = 539.834                                                  
                  d.sub.15 = 29.512                                       
                             N.sub.9 /ν.sub.9 = 1.69680/55.5           
9     r.sub.16 =-166.635                                                  
                  d.sub.16 =  0.488                                       
10    r.sub.17 = 340.673                                                  
                  d.sub.17 = 26.439                                       
                             N.sub.10 /ν.sub.10 = 1.77250/49.7         
10    r.sub.18 = 375.661                                                  
back focal length = 178.161                                               
F.sub.A.B = -117.288                                                      
F.sub.A.B.C.D =  -223.214                                                 
d.sub.C.D = 151.220                                                       
Sum of Petzval = 0.097                                                    
All linear dimensions are given in millimeters                            
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                       Example 3                                                   
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Aperture ratio 1 : 1.4 Angular field 95°                           
                             Refractive                                   
                  Lens       Index/                                       
      Radius of   Thickness  Abbe                                         
lens #                                                                    
      Curvature r or Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 =  349.515                                                  
                  d.sub.1 = 33.883                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 1026.524                                                  
                  d.sub.2 =  0.485                                        
2     r.sub.3 =  134.820                                                  
                  d.sub.3 =  5.825                                        
                             N.sub.2 /ν.sub.2 = 1.61800/63.4           
2     r.sub.4 =  76.010                                                   
                  d.sub.4 = 36.650                                        
3     r.sub.5 =  122.500                                                  
                  d.sub.5 =  5.825                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  77.874                                                   
                  d.sub.6 = 15.631                                        
4     r.sub.7 =  160.796                                                  
                  d.sub.7 =  5.874                                        
                             N.sub.4 /ν.sub.4 = 1.61800/63.4           
4     r.sub.8 =  79.277                                                   
                  d.sub.8 = 19.417                                        
filter                                                                    
      ∞     7.282      1.51633/64.1                                 
filter                                                                    
      ∞     2.427                                                   
5     r.sub.9 =  358.447                                                  
                  d.sub.9 = 10.874                                        
                             N.sub.5 /ν.sub.5 = 1.69680/55.5           
5 &amp; 6 r.sub.10 =  277.141                                                 
                  d.sub.10 = 78.350                                       
                             N.sub.6 /ν.sub.6 = 1.80518/25.4           
6     r.sub.11 = -611.117                                                 
                  d.sub.11 = 13.592                                       
7     r.sub.12 =  614.078                                                 
                  d.sub.12 = 56.699                                       
                             N.sub.7 /ν.sub.7 = 1.72000/50.2           
7     r.sub.13 = -152.981                                                 
                  d.sub.13 =  0.388                                       
8     r.sub.14 = -465.534                                                 
                  d.sub.14 = N.sub.8 /ν.sub.8 = 1.84666/23.9           
8     r.sub.15 =  198.544                                                 
                  d.sub.15 = 15.243                                       
9     r.sub.16  ∞                                                   
                  d.sub.16 = N.sub.9 /ν.sub.9 = 1.84666/23.9           
9 &amp; 10                                                                    
      r.sub.17 =  386.976                                                 
                  d.sub.17 = 31.893                                       
                             N.sub.10 /ν.sub.10 = 1.61800/63.4         
10    r.sub.18 = -162.636                                                 
                  d.sub.18 =  0.485                                       
11    r.sub.19 =  291.641                                                 
                  d.sub.19 = 29.612                                       
                             N.sub.11 /ν.sub.11 = 1.75700/47.9         
11    r.sub.20 = -449.447                                                 
Back focal length = 181.155                                               
F.sub.A.B = - 108.554                                                     
F.sub.A.B.C.D. = -232.072                                                 
d.sub.C.D = 165.728                                                       
Sum of Petzval = 0.102                                                    
All linear dimensions are given in millimeters                            
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                       Example 4                                                   
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Aperture ratio 1 : 1.4 Angular field 94.5°                         
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
Lens #                                                                    
      Curvature r of Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 =  427.020                                                  
                  d.sub.1 = 34.858                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 1503.451                                                  
                  d.sub.2 =  0.485                                        
2     r.sub.3 =  139.474                                                  
                  d.sub.3 =  7.069                                        
                             N.sub.2 /ν.sub.2 = 1.62041/60.3           
2     r.sub.4 =  77.004                                                   
                  d.sub.4 = 29.367                                        
3     r.sub.5 =  129.595                                                  
                  d.sub.5 =  5.908                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  81.507                                                   
                  d.sub.6 = 15.705                                        
4     r.sub.7 =  148.761                                                  
                  d.sub.7 =  5.370                                        
                             N.sub.4 /ν.sub.4 = 1.62041/60.3           
4     r.sub.8 =  75.801                                                   
                  d.sub.8 = 23.062                                        
filter                                                                    
      ∞     7.282      1.51633/64.1                                 
filter                                                                    
      ∞     1.876                                                   
5     r.sub.9 =  357.740                                                  
                  d.sub.9 = 10.712                                        
                             N.sub.5 /ν.sub.5 = 1.69350/53.3           
5 &amp; 6 r.sub.10 =  382.976                                                 
                  d.sub.10 = 79.048                                       
                             N.sub.6 /ν.sub.6 = 1.80518/25.4           
6     r.sub.11 = -713.896                                                 
                  d.sub.11 = 13.592                                       
7     r.sub.12 =  628.800                                                 
                  d.sub.12 = 56.899                                       
                             N.sub.7 /ν.sub.7 = 1.72000/50.2           
7     r.sub.13 = -160.170                                                 
                  d.sub.13 =  0.388                                       
8     r.sub.14 = -723.035                                                 
                  d.sub.14 = N.sub.8 /ν.sub.8 = 1.84666/23.9           
8     r.sub.15 =  189.463                                                 
                  d.sub.15 = 16.275                                       
9     r.sub.16 = 1358.156                                                 
                  d.sub.16 = 47.573                                       
                             N.sub.9 /ν.sub.9 = 1.75700/47.9           
9     r.sub.17 = -197.235                                                 
                  d.sub.17 =  0.485                                       
10    r.sub.18 =  285.591                                                 
                  d.sub.18 = N.sub. 10 /ν.sub.10 = 1.84666/23.9        
10 &amp; 11                                                                   
      r.sub.19 =  180.289                                                 
                  d.sub.19 = 33.113                                       
                             N.sub.11 /ν.sub.11 = 1.61800/60.3         
11    r.sub.20 = -450.043                                                 
Back focal length = 178.650                                               
F.sub.A.B = - 106.564                                                     
F.sub.A.B.C.D = - 223.914                                                 
d.sub.C.D = 166.458                                                       
Sum of petzval = 0.082                                                    
All linear dimensions are given in millimeters                            
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                       Example 5                                                   
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Aperture ratio 1 : 1.4 Angular field 94.5°                         
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
Lens #                                                                    
      Curvature r or Distance D                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 =  427.020                                                  
                  d.sub.1 = 34.858                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 1503.451                                                  
                  d.sub.2 =  0.485                                        
2     r.sub.3 =  139.474                                                  
                  d.sub.3 =  7.069                                        
                             N.sub.2 /ν.sub.2 = 1.62041/60.3           
2     r.sub.4 =  77.004                                                   
                  d.sub.4 = 29.367                                        
3     r.sub.5 =  129.595                                                  
                  d.sub.5 =  5.908                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  81.507                                                   
                  D.sub.6 = 15.705                                        
4     r.sub.7 =  148.761                                                  
                  d.sub.7 =  5.370                                        
                             N.sub.4 /ν.sub.4 = 1.62041/60.3           
4     r.sub.8 =  75.801                                                   
                  d.sub.8 = 23.062                                        
filter                                                                    
      ∞     7.282      1.51633/64.1                                 
filter                                                                    
      ∞     1.876                                                   
5     r.sub.9 =  357.740                                                  
                  d.sub.9 = 89.760                                        
                             N.sub.5 /ν.sub.5 = 1.78472/25.7           
5     r.sub.10 = -674.300                                                 
                  d.sub.10 = 13.592                                       
6     r.sub.11 =  628.800                                                 
                  d.sub.11 = 56.899                                       
                             N.sub.6 /ν.sub.6 = 1.72000/50.2           
6     r.sub.12 = -160.350                                                 
                  d.sub.12 =  0.388                                       
7     r.sub.13 = -723.035                                                 
                  d.sub.13 = N.sub.7 /ν.sub.7 = 1.84666/23.9           
7     r.sub.14 =  189.677                                                 
                  d.sub.14 = 16.275                                       
8     r.sub.15 = 1358.156                                                 
                  d.sub.15 = 47.573                                       
                             N.sub.8 /ν.sub.8 = 1.75700/47.9           
8     r.sub.16 = -197.417                                                 
                  d.sub.16 =  0.485                                       
9     r.sub.17 =  285.591                                                 
                  d.sub.17 = N.sub.9 /ν.sub.9 = 1.84666/23.9           
9 &amp; 10                                                                    
      r.sub.18 =  180.289                                                 
                  d.sub.18 = 33.113                                       
                             N.sub. 10 /ν.sub.10 = 1.61800/60.3        
10    r.sub.19 = -450.927                                                 
Back focal length = 178.806                                               
F.sub.A.B = - 106.564                                                     
F.sub.A.B.C.D = - 223.914                                                 
d.sub.C.D = 166.458                                                       
Sum of Petzval = 0.084                                                    
All linear dimensions are given in millimeters                            
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                       Example 6                                                   
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Aperture ratio 1 : 1.4 Angular field 95°                           
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
Lens #                                                                    
      Curvature r or Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 =  349.515                                                  
                  d.sub.1 = 33.883                                        
                             N.sub.1 /ν.sub.1 = 1.62041/60.3           
1     r.sub.2 = 1019.316                                                  
                  d.sub.2 =  0.485                                        
2     r.sub.3 =  134.820                                                  
                  d.sub.3 =  5.825                                        
                             N.sub.2 /ν.sub.2 = 1.61800/63.4           
2     r.sub.4 =  76.000                                                   
                  d.sub.4 = 36.650                                        
3     r.sub.5 =  122.578                                                  
                  d.sub.5 =  5.825                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  77.949                                                   
                  d.sub.6 = 15.631                                        
4     r.sub.7 =  160.757                                                  
                  d.sub.7 =  5.874                                        
                             N.sub.4 /ν.sub.4 = 1.61800/63.4           
4     r.sub.8 =  79.284                                                   
                  d.sub.8 = 19.417                                        
filter                                                                    
      ∞     7.282      1.51633/64.1                                 
filter                                                                    
      ∞     2.427                                                   
5     r.sub.9 =  351.942                                                  
                  d.sub.9 = 89.223                                        
                             N.sub.5/ν.sub.5 = 1.80518/25.4            
5     r.sub.10 = -589.338                                                 
                  d.sub.10 = 13.592                                       
6     r.sub.11 =  613.859                                                 
                  d.sub.11 = 56.699                                       
                             N.sub.6 /ν.sub.6 = 1.71700/47.9           
6     r.sub.12 = -152.055                                                 
                  d.sub.12 =  0.388                                       
7     r.sub.13 = -465.534                                                 
                  d.sub.13 = N.sub.7 /ν.sub.7 = 1.84666/23.9           
7     r.sub.14 =  198.267                                                 
                  d.sub.14 = 15.243                                       
8     r.sub.15 =  ∞                                                 
                  d.sub.15 = N.sub.8 /ν.sub.8 = 1.84666/23.9           
8 &amp; 9 r.sub.16 =  387.102                                                 
                  d.sub.16 = 31.893                                       
                             N.sub.9 /ν.sub.9 = 1.61800/63.4           
9     r.sub.17 = -162.626                                                 
                  d.sub.17 =  0.485                                       
10    r.sub.18 =  291.748                                                 
                  d.sub.18 = N.sub.10 /ν.sub.10 = 1.75700/47.9         
10    r.sub.19 = -447.530                                                 
Back focal length = 180.966                                               
F.sub.A.B. = - 108.554                                                    
F.sub.A.B.C.D = -232.072                                                  
d.sub.C.D = 165.727                                                       
Sum of Petzval = 0.105                                                    
All linear dimensions are given in millimeters                            
______________________________________                                    
 
    
     
                       Example 7                                                   
______________________________________                                    
Aperture ratio 1 : 1.4 Angular field 94°                           
                             Refractive                                   
                  Lens       Index N/                                     
      Radius of   Thickness  Abbe                                         
Lens #                                                                    
      Curvature r or Distance d                                           
                             No. ν                                     
______________________________________                                    
1     r.sub.1 =  408.859                                                  
                  d.sub.1 = 35.151                                        
                             N.sub.1 /ν.sub.1 = 1.61800/63.4           
1     r.sub.2 = 1326.694                                                  
                  d.sub.2 =  0.485                                        
2     r.sub.3 =  142.718                                                  
                  d.sub.3 =  5.828                                        
                             N.sub.2 /ν.sub.2 = 1.61800/63.4           
2     r.sub.4 =  78.421                                                   
                  d.sub.4 = 32.426                                        
3     r.sub.5 =  128.290                                                  
                  d.sub.5 =  5.865                                        
                             N.sub.3 /ν.sub.3 = 1.61800/63.4           
3     r.sub.6 =  81.441                                                   
                  d.sub.6 = 18.980                                        
4     r.sub.7 =  161.794                                                  
                  d.sub.7 =  5.842                                        
                             N.sub.4 /ν.sub.4 = 1.61800/63.4           
4     r.sub.8 =  78.193                                                   
                  d.sub.8 = 22.788                                        
filter                                                                    
      ∞     7.282      1.51633/64.1                                 
filter                                                                    
      ∞     0.485                                                   
5     r.sub.9 =  325.243                                                  
                  d.sub.9 = 88.180                                        
                             N.sub.5 /ν.sub.5 = 1.80518/25.4           
5     r.sub.10 = -381.074                                                 
                  d.sub.10 = 13.592                                       
6     r.sub.11 =  807.840                                                 
                  d.sub.11 = 60.410                                       
                             N.sub.6 /ν.sub.6 = 1.72916/54.7           
6     r.sub.12 = -156.014                                                 
                  d.sub.12 =  0.388                                       
7     r.sub.13 = -497.315                                                 
                  d.sub.13 = N.sub.7 /ν.sub.7 = 1.92286/20.9           
7     r.sub.14 =  194.265                                                 
                  d.sub.14 = 15.638                                       
8     r.sub.15 =-4152.361                                                 
                  d.sub.15 = 34.213                                       
                             N.sub.8 /ν.sub.8 = 1.72916/54.7           
8     r.sub.16 = -187.957                                                 
                  d.sub.16 =  0.485                                       
9     r.sub.17 =  336.916                                                 
                  d.sub.17 = 22.550                                       
                             N.sub.9 /ν.sub.9 = 1.72916/54.7           
9     r.sub.18 = -403.796                                                 
Back focal length = 179.427                                               
F.sub.A.B.  = 170.231                                                     
Sum of Petzval = 0.099                                                    
All linear dimensions are given in millimeters. -F.sub.A.B.C.D            
______________________________________                                    
= -223.914