Compact-size zoom lens system
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a compact-size zoom lens system, especially of a type suited for a built-in zoom lens system of a lens shutter camera. 
     2. Description of the Related Art 
     A lens system built in a lens shutter camera is required to be compact, light-weight and low cost. When a zoom lens system is used in a lens shutter camera, the requirements are just the same. For making a zoom lens system compact including the lens shifting space for zooming the refractive power of every lens group must be strong. In order to obtain a strong refractive power of a lens group while maintaining a high optical quality, the number of lenses in the lens group should increase. However, the increase in the number of lenses naturally increases the weight and the cost. Thus, the prior art is still seeking to provide an improved compact-size zoom lens system. 
     SUMMARY OF THE INVENTION 
     Therefore an object of the present invention is to provide a compact-size, light-weight and low-cost zoom lens system by restricting undesirable light rays. 
     One feature of the zoom lens system according to the present invention is that the zoom lens system includes a ray restrictor at the object side of any of the lenses of the zoom lens system, and the ray restrictor can move along the optical axis of the zoom lens system according to a zooming operation at a speed different from that of the most object side lens of the zoom lens system. 
     Another feature of the zoom lens system according to the present invention is that the zoom lens system includes a ray restrictor at the object side of any of the lenses of the zoom lens system, and the ray restrictor has an aperture whose diameter is variable according to a zooming operation. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a sectional view illustrating the lens configuration with the movement of every lens group during a zooming operation from the shortest focal length &lt;S&gt; to the longest focal length &lt;L&gt; of the first example of the present invention. 
     FIG. 2 is a sectional view illustrating the lens configuration with the movement of every lens group during a zooming operation from the shortest focal length &lt;S&gt; to the longest focal length &lt;L&gt; of the second example of the present invention. 
     FIG. 3 is a sectional view illustrating the lens configuration with the movement of every lens group during a zooming operation from the shortest focal length &lt;S&gt; to the longest focal length &lt;L&gt; of the third example of the present invention. 
     FIGS. 4A, 4B and 4C show aberration curves of the first example at the shortest focal length (S), at the midpoint focal length (M) and at the longest focal length (L), respectively. 
     FIGS. 5A, 5B and 5C show aberration curves of the first example at the shortest focal length (S), at the midpoint focal length (M) and at the longest focal length (L), respectively. 
     FIGS. 6A, 6B and 6C show aberration curves of the first example at the shortest focal length (S), at the midpoint focal length (M) and at the longest focal length (L), respectively. 
     FIG. 7 is a light path diagram of the first example at the shortest focal length (S). 
     FIG. 8 is a light path diagram of the first example at the longest focal length (L). 
     FIG. 9 is a light path diagram of the second example at the shortest focal length (S). 
     FIG. 10 is a light path diagram of the second example at the longest focal length (L). 
     FIG. 11A is a light path diagrams of the third example at the shortest focal length (S), and FIG. 11B is that at the longest focal length (L). 
     FIG. 12A is a light path diagrams of the fourth example at the shortest focal length (S), FIG. 12B is that at the midpoint focal length (M), and FIG. 12C is that at the longest focal length (L). 
     FIGS. 13A, 13B and 13C show aberration curves of the fourth example at the shortest focal length (S), at the midpoint focal length (M) and at the longest focal length (L), respectively. In FIGS. 4A-6C and 13A-13C, f is the focal length of the whole zoom lens system, d denotes aberrations for the d line, SC denotes the sine condition, and DM and DS denote the astigmatism for the maridional direction and for the sagittal direction, respectively. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention is especially preferred to be applied in a two-component zoom lens system. That is, the zoom lens system is composed of, from the object side to the image side, a front lens group having a positive refractive power and a rear lens group having a negative refractive power. In this case, the front lens group and the rear lens group move from the image side to the object side when a zooming operation is performed from a shorter focal length to a longer focal length, and the ray restrictor also moves from the image side to the object side. Since the ray restrictor is placed near the front lens group at the shortest focal length condition, the peripheral light is not restricted and enough amount of light is admitted in the peripheral area. Since the ray restrictor recedes from the front lens group at a position intermediate to the longest focal lengths, coma flare due to intermediate rays (rays passing through the intermediate area between the on-axial area and the peripheral area) is effectively eliminated. 
     It is preferable that the aperture diameter is less than 1.2 times that of the axial light flux (an entrance pupil) at either the shortest focal length condition or the longest focal length condition, because otherwise it is difficult to eliminate coma flare due to intermediate rays especially at the longest focal length condition. It is more preferable to make the diameter of the ray restrictor less than 1.05 times the diameter of the axial light flux to eliminate coma flare due to the off-axial light flux at the longest focal length condition. 
     It is further preferable to make the ray restrictor shift in a linked body with the rear lens group (or shift at a preset rate of the shift of the rear lens group) while the zoom lens system is zoomed from the shortest focal length to the longest focal length because the structure of the lens barrel can be made simple. 
     An aspherical surface satisfying the following condition (1) is preferred to be included in the front lens group: for a height y from the optical axis of the zoom lens system satisfying 0.7y MAX  &lt;y&lt;y MAX  where y MAX  is the maximum effective radius of the aspherical surface, 
     
         -0.03&lt;φ.sub.1 ·(N&#39;-N)·d{x(y)-x.sub.o (y)}/dy&lt;0(1) 
    
     where 
     φ 1  : refractive power of the front lens group, 
     N: refractive index of the medium at the object side of the aspherical surface, 
     N&#39;: refractive index of the medium at the image side of the aspherical surface, 
     x(y): axial deviation of the aspherical surface from its vertex at the height y, which is give by 
     
         x(y)=(r/ε){1-(1-ε(y.sup.2 r.sup.2)).sup.1/2 }+ΣA.sub.i y.sup.i 
    
     (summation Σ made for i≧2) 
     x o  (y): axial deviation of the reference spherical surface of the aspherical surface from its vertex at the height y, which is given by 
     
         x.sub.o (y)=r{1-(1-y.sup.2 r.sup.2).sup.1/2 } 
    
     r: radius of curvature of the aspherical surface at the vertex, 
     ε: quadric surface parameter, 
     A i  : aspherical coefficient of the i-th order, and 
     r: radius of curvature at the vertex, which is given by 
     
         1/r=1/r+2A.sub.2 
    
     Condition (1) indicates that the aspherical surface of the front lens group has a weaker positive refractive power (i.e., stronger negative refractive power) at the peripheral area than at the axial area. The aspherical surface is introduced to correct spherical aberrations. If the upper limit of the condition (1) is violated, the spherical aberrations cannot be corrected enough, and if the lower limit is violated, the spherical aberrations are over-corrected in the entire zooming region. 
     The rear lens group is preferred to include at least one aspherical surface satisfying the following condition (2): 
     for a height y from the optical axis of the zoom lens system satisfying 0.8y MAX  &lt;y&lt;y MAX  where y MAX  is the maximum effective radius of the aspherical surface, 
     
         -0.10&lt;φ.sub.2 ·(N&#39;-N)·d{x(y)-x.sub.o (y)}/dy&lt;0(2) 
    
     where φ 2  : refractive power of the rear lens group. 
     The condition (2) indicates that the aspherical surface of the rear lens group has a weaker negative refractive power (i.e., stronger positive refractive power) at the peripheral area than at the axial area. The aspherical surface is introduced in the rear lens group to correct the distortion and field curvature on balance at high levels. If the upper limit of the condition (2) is violated, the distortion at the shortest focal length positively grows conspicuously, and if the lower limit is violated, the field curvature apparently grows negative in the entire zooming range. 
     Every aspherical surface in the front lens group is preferred to satisfy the following condition (3): 
     for a height y from the optical axis of the zoom lens system satisfying y≦0.7 y MAX  where y MAX  is the maximum effective radius of the aspherical surface, 
     
         -0.02&lt;φ.sub.1 ·(N&#39;-N)·d{x(y)-x.sub.o (y)}/dy&lt;0.01(3) 
    
     If the upper limit of the condition (3) is violated, the zonal aberration grows negative and the focus point deviates as the aperture becomes small. If the lower limit is violated, the spherical aberration is over-corrected for the intermediate rays causing unbalance between the spherical aberration and other aberrations and the spherical aberration becomes wavy. 
     Similarly, every aspherical surface in the rear lens group is preferred to satisfy the following condition (4): 
     for a height y from the optical axis of the zoom lens system satisfying y≦0.8 y MAX  where y MAX  is the maximum effective radius of the aspherical surface, 
     
         -0.05&lt;φ.sub.2 ·(N&#39;-N)·d{x(y)-x.sub.o (y)}/dy&lt;0.02(4) 
    
     If the upper limit of the condition (4) is violated, the positive distortion and field curvature further grows positive in the intermediate focal lengths, i.e., between the shortest focal length and the midpoint focal length. If the lower limit is violated, on the other hand, the negative distortion grows in the range between the midpoint to the longest focal lengths, and the field curvature shifts toward negative in the entire zooming range. 
     Thus, by placing a ray restrictor at the object side of the front lens group and shifting the ray restrictor toward the object at a speed different from that of the most object side lens of the zoom lens system when the zoom lens system is zoomed from the shorter to the longer focal length, various aberrations, especially coma flare due to the intermediate rays, are adequately corrected. When the ray restrictor is used in combination with an aspherical surface (or surfaces) provided in the front or rear lens group, the lens construction can be very simple. For example, it is possible to compose the front lens group with two lens elements and the rear lens group with only one lens element. 
     The axial distance between the front lens group and the rear lens group at the longest focal length condition is preferred to satisfy the following condition (5): 
     
         0.1&lt;ΔT.sub.12 /f.sub.T &lt;0.4                          (5) 
    
     where 
     ΔT 12  : axial distance between the most image side surface of the front lens group to the most object side surface of the rear lens group, and 
     f T  : the longest focal length of the zoom lens system. 
     When the upper limit of the condition (5) is violated, the overall length (i.e., the distance between the most object side surface of the front lens group and the film surface at the shortest focal length condition) of the zoom lens system becomes too large. When the lower limit is violated, the optical quality deteriorates, specifically the off-axial coma grows at the longest focal length condition. 
     The zoom lens system according to the present invention is further preferred to satisfy the following condition (6): 
     
         0.40&lt;f.sub.2 /f.sub.w &lt;0.75                                (6) 
    
     where 
     f 2  : focal length of the image side lens element of the front lens group, and 
     f w  : the shortest focal length of the zoom lens system. 
     When the upper limit of the condition (6) is violated, coma flare due to the intermediate rays grows conspicuously in the shortest focal length condition. When the lower limit is violated, the optical quality of the zoom lens system deteriorates, specifically the coma flare due to the intermediate rays grows large in the longest focal length condition. 
     It is further preferred that at least one lens element composing a zoom lens system of the present invention has aspherical surfaces at both sides. 
     Altering the aperture diameter of the ray restrictor while shifting the ray restrictor in a linked body with the most object side lens of the zoom lens system has the same effect as above (where the ray restrictor shifts at a speed different from that of the most object side lens). 
     Four examples of the zoom lens system according to the present invention are described now. In the following list of lens data of the examples: 
     r i  (1≦i≦6) is the radius of curvature of the i-th surface as counted from the object side, 
     d i  (1≦i≦6) is the axial distance between two adjacent surfaces i and i+1 (or between a surface and the ray restrictor or stop), 
     N j  (1≦i≦3) is the refractive index for the d line of the j-th lens element as counted from the object side, 
     ν j  (1≦i≦3) is the Abbe number of the j-th lens element, 
     f is the focal length of the zoom lens system, and 
     F NO  is the open (minimum) f-number. 
     The surface with an asterisk (*) after the radius of curvature (r i ) in the list is an aspherical surface, whose surface shape is defined by the formulae as described above. 
     Example 1 shown in FIG. 1 is a zoom lens system composed of, from the object side: a ray restrictor (B); a front lens group including a first lens element having a negative refractive power, an aperture stop (A), and a second lens element having a strong positive refractive power; and a rear lens group including solely a third lens element having a negative refractive power. The first lens element is a negative meniscus lens concave at the object side, the second lens element is convex at the image side, and the third lens element is a bi-concave lens. The object side and image side surfaces of the first lens element, the image side surface of the second lens element and the object side and image side surfaces of the third lens elements are aspherical. 
     Example 2 shown in FIG. 2 is a zoom lens system composed of, from the object side: a ray restrictor (B); a front lens group including a first lens element having a negative refractive power, an aperture stop (A), and a second lens element having a strong positive refractive power; and a rear lens group including solely a third lens element having a negative refractive power. The first lens element is a negative meniscus lens concave at the object side, the second lens element is convex at the image side, and the third lens element is a bi-concave lens. The object side and image side surfaces of the first lens element, the image side surface of the second lens element and the object side and image side surfaces of the third lens elements are aspherical. 
     Example 3 shown in FIG. 3 is a zoom lens system composed of, from the object side; a ray restrictor (B); a front lens group including a first lens element having a negative refractive power, a second lens element having a strong positive refractive power, and an aperture stop (A); and a rear lens group including solely a third lens element having a negative refractive power. The first lens element is a negative meniscus lens concave at the object side, the second lens element is convex at the image side, and the third lens element is a bi-concave lens. The object side and image side surfaces of the first lens element, the image side surface of the second lens element and the object side and image side surfaces of the third lens elements are aspherical. 
     Example 4 has the same optical structure as that of the example 1 shown in FIG. 1, except that the ray restrictor (B) shifts in a linked body with the first lens group on the optical axis and the aperture diameter of the ray restrictor (B) varies during a zooming operation. 
     The aberrations of the example zoom lens systems are shown in FIGS. 4A-6C and 13A-13C respectively for the shortest &lt;S&gt;, midpoint &lt;M&gt; and longest &lt;L&gt; focal length conditions. 
     FIGS. 7 and 8 show the effect of the ray restrictor (B) of the first example. If the ray restrictor (B) moves in a linked body with the front lens group in zooming, the ray restrictor would be at the position B&#39; at the longest focal length condition (FIG. 8). In such a case, harmful off-axial ray denoted by the dashed line would come in the front lens group. In the example 1, however, the ray restrictor (B) recedes from the front lens group as the zoom lens system is zoomed toward the longest focal length, and the harmful off-axial ray is blocked. 
     Tables 1-3 respectively show values of the second term of conditions (1) through (4) of the examples 1-4. Table 4 shows the values of ΔT 12  /f T  of the condition (5), f 2  /f w  of the condition (6), and the refractive power φ G2  of the image side lens element of the front lens group (i.e., the second lens element). 
     The four examples according to the present invention have the focal length range of 38-70 mm or 38-80 mm. No conventional zoom lens system composed of three lens elements has such focal length range. Since, in the zoom lens system of one embodiment of the present invention, the ray restrictor placed at the object side shifts toward the object at a speed different from that of the most object side lens as the zoom lens system is zoomed to the longest focal length, the ray restrictor blocks coma-flare-causing rays and only the most suitable rays are allowed to pass therethrough at any position during the zooming operation. In a zoom lens system of another embodiment of the present invention, the ray restrictor placed at the object side has the aperture whose diameter decreases when the zoom lens system is zoomed to a longer focal length. Therefore, the ray restrictor also restricts undesirable rays incident on the zoom lens system. 
     When an aspherical surface or surfaces are used in the zoom lens system of the present invention as described above, various aberrations are further corrected at a high level, which has enabled composing a high quality zoom lens with a less number of lens elements. For example, the examples described below are composed of only three lens elements and have a zoom ratio exceeding 1.7. Thus the zoom lens system of the present invention is suitable for a built-in zoom lens system of a compact-size lens shutter camera. 
     EXAMPLE 1 
     
         ______________________________________                                    
f = 39.3˜51.8˜68.2  F.sub.NO = 4.1˜5.3˜7.0        
radius of    axial     refractive Abbe                                    
curvature    distance  index      number                                  
______________________________________                                    
 restrictor(B)                                                            
           d.sub.0 4.896˜7.396˜10.896                         
r.sub.1 * -51.463                                                         
             d.sub.1 1.000                                                
                       N.sub.1 1.83350                                    
                                  ν.sub.1 21.00                        
r.sub.2 * -209.509                                                        
             d.sub.2 3.349                                                
 stop(A)                                                                  
             d.sub.3 2.000                                                
r.sub.3 -334.805                                                          
             d.sub.4 4.989                                                
                       N.sub.2 1.51680                                    
                                  ν.sub.2 64.20                        
r.sub.4 * -11.561                                                         
           d.sub.5 22.876˜18.367˜14.943                       
r.sub.5 * -24.139                                                         
             d.sub.6 1.044                                                
                       N.sub.3 1.77250                                    
                                  ν.sub.3 49.77                        
r.sub.6 * 144.891                                                         
           Σ d = 40.153˜38.145˜38.220                   
        aspherical coefficients                                           
        r.sub.1 :                                                         
            ε                                                     
                   = 0.27563 × 10                                   
            A.sub.4                                                       
                   = -0.57377 × 10.sup.-4                           
            A.sub.6                                                       
                   = -0.28791 × 10.sup.-6                           
            A.sub. 8                                                      
                   = -0.25981 × 10.sup.-7                           
            A.sub.10                                                      
                   = 0.71952 × 10.sup.-9                            
            A.sub.12                                                      
                   = -0.17910 × 10.sup.-10                          
        r.sub.2 :                                                         
            ε                                                     
                   = -0.95676                                             
            A.sub.4                                                       
                   = 0.32319 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.31975 × 10.sup.-6                            
            A.sub.8                                                       
                   = -0.29096 × 10.sup.-8                           
            A.sub.10                                                      
                   = -0.86424 × 10.sup.-10                          
            A.sub.12                                                      
                   = -0.16278 × 10.sup.-11                          
        r.sub.4 :                                                         
            ε                                                     
                   = 0.11348 × 10                                   
            A.sub.4                                                       
                   = 0.34973 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.13838 × 10.sup.-6                            
            A.sub.8                                                       
                   = 0.65555 × 10.sup.-9                            
            A.sub.10                                                      
                   = -0.92932 × 10.sup.-11                          
            A.sub.12                                                      
                   = 0.48225 × 10.sup.-12                           
        r.sub.5 :                                                         
            ε                                                     
                   = 0.25432 × 10                                   
            A.sub.4                                                       
                   = 0.55479 × 10.sup.-4                            
            A.sub.6                                                       
                   = -0.16122 × 10.sup.- 6                          
            A.sub.8                                                       
                   = 0.22221 × 10.sup.-8                            
            A.sub.10                                                      
                   = -0.53141 × 10.sup.-10                          
            A.sub.12                                                      
                   = 0.26081 × 10.sup.-12                           
        r.sub.6 :                                                         
            ε                                                     
                   = -0.22241 × 10                                  
            A.sub.4                                                       
                   = 0.26936 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.27385 × 10.sup.-8                            
            A.sub.8                                                       
                   = -0.25504 × 10.sup.-8                           
            A.sub.10                                                      
                   = 0.11840 × 10.sup.-10                           
            A.sub.12                                                      
                   = 0.11070 × 10.sup.-13                           
______________________________________                                    
 
    
     EXAMPLE 2 
     
         ______________________________________                                    
f = 39.3˜55.2˜77.5  F.sub.NO = 4.0˜5.7˜8.0        
radius of    axial     refractive Abbe                                    
curvature    distance  index      number                                  
______________________________________                                    
 restrictor(B)                                                            
           d.sub.0 5.215˜8.715˜15.215                         
r.sub.1 * -36.716                                                         
             d.sub.1 1.222                                                
                       N.sub.1 1.83350                                    
                                  ν.sub.1 21.00                        
r.sub.2 * -64.476                                                         
             d.sub.2 5.066                                                
 stop(A)                                                                  
             d.sub.3 2.000                                                
r.sub.3 -188.456                                                          
             d.sub.4 4.548                                                
                       N.sub.2 1.51680                                    
                                  ν.sub.2 64.20                        
r.sub.4 * -12.087                                                         
           d.sub.5 22.768˜16.425˜11.908                       
r.sub.5 * -50.454                                                         
             d.sub.6 1.000                                                
                       N.sub.3 1.77250                                    
                                  ν.sub.3 49.77                        
r.sub.6 * 45.050                                                          
           Σ d = 41.818˜38.975˜40.958                   
        aspherical coefficients                                           
        r.sub.1 :                                                         
            ε                                                     
                   = 0.15018 × 10                                   
            A.sub.4                                                       
                   = -0.32667 × 10.sup.-4                           
            A.sub.6                                                       
                   = -0.19314 × 10.sup.-8                           
            A.sub. 8                                                      
                   = -0.26162 × 10.sup.-7                           
            A.sub.10                                                      
                   = 0.75722 × 10.sup.-9                            
            A.sub.12                                                      
                   = -0.13941 × 10.sup.-10                          
        r.sub.2 :                                                         
            ε                                                     
                   = -0.94829                                             
            A.sub.4                                                       
                   = 0.28608 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.18842 × 10.sup.-6                            
            A.sub.8                                                       
                   = -0.24996 × 10.sup.-8                           
            A.sub.10                                                      
                   = 0.49380 × 10.sup.-10                           
            A.sub.12                                                      
                   = -0.67270 × 10.sup.-11                          
        r.sub.4 :                                                         
            ε                                                     
                   = 0.10020 × 10                                   
            A.sub.4                                                       
                   = 0.41090 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.37818 × 10.sup.-7                            
            A.sub.8                                                       
                   = 0.58283 × 10.sup.-9                            
            A.sub.10                                                      
                   = 0.36793 × 10.sup.-10                           
            A.sub.12                                                      
                   = -0.34580 × 10.sup.-12                          
        r.sub.5 :                                                         
            ε                                                     
                   = 0.27377 × 10                                   
            A.sub.4                                                       
                   = 0.48509 × 10.sup.-4                            
            A.sub.6                                                       
                   = -0.23791 × 10.sup.-6                           
            A.sub.8                                                       
                   = 0.21497 × 10.sup.-8                            
            A.sub.10                                                      
                   = -0.42474 × 10.sup.-10                          
            A.sub.12                                                      
                   = 0.17971 × 10.sup.-12                           
        r.sub.6 :                                                         
            ε                                                     
                   = -0.21359 × 10                                  
            A.sub.4                                                       
                   = 0.29356 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.29483 × 10.sup.-7                            
            A.sub.8                                                       
                   = -0.25430 × 10.sup.-8                           
            A.sub.10                                                      
                   = 0.79055 × 10.sup.-11                           
            A.sub.12                                                      
                   = 0.40582 × 10.sup.-14                           
______________________________________                                    
 
    
     EXAMPLE 3 
     
         ______________________________________                                    
f = 39.3˜51.8˜68.2  F.sub.NO = 3.6˜4.7˜6.0        
radius of    axial     refractive Abbe                                    
curvature    distance  index      number                                  
______________________________________                                    
 restrictor(B)                                                            
           d.sub.0 2.000˜5.500˜9.000                          
r.sub.1 * -45.265                                                         
             d.sub.1 2.737                                                
                       N.sub.1 1.84666                                    
                                  ν.sub.1 23.82                        
r.sub.2 * -134.812                                                        
             d.sub.2 6.647                                                
r.sub.3 443.093                                                           
             d.sub.3 4.479                                                
                       N.sub.2 1.51680                                    
                                  ν.sub.2 64.20                        
r.sub.4 * -13.153                                                         
             d.sub.4 3.700                                                
 stop(A)                                                                  
           d.sub.5 21.181˜14.940˜10.200                       
r.sub.5 * -32.438                                                         
             d.sub.6 1.044                                                
                       N.sub.3 1.72900                                    
                                  ν.sub.3 53.48                        
r.sub.6 * 115.276                                                         
           Σ d = 41.789˜53.664˜71.663                   
        aspherical coefficients                                           
        r.sub.1 :                                                         
            ε                                                     
                   = -0.17535                                             
            A.sub.4                                                       
                   = -0.29592 × 10.sup.-4                           
            A.sub.6                                                       
                   = 0.12066 × 10.sup.-6                            
            A.sub.8                                                       
                   = - 0.20055 × 10.sup.-7                          
            A.sub.10                                                      
                   = 0.82177 × 10.sup.-9                            
            A.sub.12                                                      
                   = -0.11741 × 10.sup.-10                          
        r.sub.2 :                                                         
            ε                                                     
                   = 0.23617 × 10                                   
            A.sub.4                                                       
                   = 0.27941 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.54904 × 10.sup.-6                            
            A.sub.8                                                       
                   = 0.98187 × 10.sup.-9                            
            A.sub.10                                                      
                   = 0.84612 × 10.sup.-11                           
            A.sub.12                                                      
                   = -0.11309 × 10.sup.-11                          
        r.sub.4 :                                                         
            ε                                                     
                   = 0.13359 × 10                                   
            A.sub.4                                                       
                   = 0.43666 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.42178 × 10.sup.-7                            
            A.sub.8                                                       
                   = 0.71801 × 10.sup.-9                            
            A.sub.10                                                      
                   = 0.18344 × 10.sup.-10                           
            A.sub.12                                                      
                   = 0.13664 × 10.sup.-12                           
        r.sub.5 :                                                         
            ε                                                     
                   = 0.26567 × 10                                   
            A.sub.4                                                       
                   = 0.24062 × 10.sup.-4                            
            A.sub.6                                                       
                   = -0.21968 × 10.sup.-6                           
            A.sub.8                                                       
                   =  0.13828 × 10.sup.-8                           
            A.sub.10                                                      
                   = -0.88598 × 10.sup.-11                          
            A.sub.12                                                      
                   = 0.13382 × 10.sup.-13                           
        r.sub.6 :                                                         
            ε                                                     
                   = 0.13573 × 10                                   
            A.sub.4                                                       
                   = 0.17944 × 10.sup.-5                            
            A.sub.6                                                       
                   = 0.55391 × 10.sup.-7                            
            A.sub.8                                                       
                   = -0.18417 × 10.sup.-8                           
            A.sub.10                                                      
                   = 0.11461 × 10.sup.-10                           
            A.sub.12                                                      
                   = -0.27114 × 10.sup.-13                          
______________________________________                                    
 
    
     EXAMPLE 4 
     
         ______________________________________                                    
f = 39.3˜51.8˜68.2  F.sub.NO = 4.1˜5.3˜7.0        
radius of    axial     refractive Abbe                                    
curvature    distance  index      number                                  
______________________________________                                    
 restrictor(B)                                                            
             d.sub.0 10.896                                               
r.sub.1 * -51.463                                                         
             d.sub.1 1.000                                                
                       N.sub.1 1.83350                                    
                                  ν.sub.1 21.00                        
r.sub.2 * -209.509                                                        
             d.sub.2 3.349                                                
 stop(A)                                                                  
             d.sub.3 2.000                                                
r.sub.3 -334.805                                                          
             d.sub.4 4.989                                                
                       N.sub.2 1.51680                                    
                                  ν.sub.2 64.20                        
r.sub.4 * -11.561                                                         
           d.sub.5 22.876˜18.367˜14.943                       
r.sub.5 * -24.139                                                         
             d.sub.6 1.044                                                
                       N.sub.3 1.77250                                    
                                  ν.sub.3 49.77                        
r.sub.6 * 144.891                                                         
           Σ d = 40.153˜38.145˜38.220                   
        aspherical coefficients                                           
        r.sub.1 :                                                         
            ε                                                     
                   = 0.27563 × 10                                   
            A.sub.4                                                       
                   = -0.57377 × 10.sup.-4                           
            A.sub.6                                                       
                   = -0.28791 × 10.sup.-6                           
            A.sub.8                                                       
                   = -0.25981 × 10.sup.- 7                          
            A.sub.10                                                      
                   = 0.71952 × 10.sup.-9                            
            A.sub.12                                                      
                   = -0.17910 × 10.sup.-10                          
        r.sub.2 :                                                         
            ε                                                     
                   = -0.95676                                             
            A.sub.4                                                       
                   = 0.32319 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.31975 × 10.sup.-6                            
            A.sub.8                                                       
                   = -0.29096 × 10.sup.-8                           
            A.sub.10                                                      
                   = -0.86424 × 10.sup.-10                          
            A.sub.12                                                      
                   = -0.16278 × 10.sup.-11                          
        r.sub.4 :                                                         
            ε                                                     
                   = 0.11348 × 10                                   
            A.sub.4                                                       
                   = 0.34973 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.13838 × 10.sup.-6                            
            A.sub.8                                                       
                   = 0.65555 × 10.sup.-9                            
            A.sub.10                                                      
                   = -0.92932 × 10.sup.-11                          
            A.sub.12                                                      
                   = 0.48225 × 10.sup.-12                           
        r.sub.5 :                                                         
            ε                                                     
                   = 0.25432 × 10                                   
            A.sub.4                                                       
                   = 0.55479 × 10.sup.-4                            
            A.sub.6                                                       
                   = -0.16122 × 10.sup.-6                           
            A.sub.8                                                       
                   = 0.22221 ×  10.sup.-8                           
            A.sub.10                                                      
                   = -0.53141 × 10.sup.-10                          
            A.sub.12                                                      
                   = 0.26081 × 10.sup.-12                           
        r.sub.6 :                                                         
            ε                                                     
                   = -0.22241 × 10                                  
            A.sub.4                                                       
                   = 0.26936 × 10.sup.-4                            
            A.sub.6                                                       
                   = 0.27385 × 10.sup.-8                            
            A.sub.8                                                       
                   = -0.25504 × 10.sup.-8                           
            A.sub.10                                                      
                   = 0.11840 × 10.sup.-10                           
            A.sub.12                                                      
                   = 0.11070 × 10.sup.-13                           
______________________________________                                    
 
    
     
                                           TABLE 1                                 
__________________________________________________________________________
[ Example 1, Example 4]                                                   
A.sub.FR *1                  A.sub.RE *2                                  
y    r.sub.1 r.sub.2 r.sub.4 r.sub.5 r.sub.6                              
__________________________________________________________________________
0.1 y.sub.max                                                             
     -1.12 × 10.sup.-6                                              
             -6.64 × 10.sup.-6                                      
                     -5.24 × 10.sup.-7                              
                             -6.04 × 10.sup.-6                      
                                     6.80 × 10.sup.-6               
0.2 y.sub.max                                                             
     -9.08 × 10.sup.-6                                              
             -5.40 × 10.sup.-6                                      
                     -4.19 × 10.sup.-6                              
                             -4.71 × 10.sup.-5                      
                                     5.41 × 10.sup.-5               
0.3 y.sub.max                                                             
     -3.10 × 10.sup.-5                                              
             -1.86 × 10.sup.-5                                      
                     -1.42 × 10.sup.-5                              
                             -1.53 × 10.sup.-4                      
                                     1.77 × 10.sup.-4               
0.4 y.sub.max                                                             
     -7.54 × 10.sup.-5                                              
             -4.53 × 10.sup.-5                                      
                     -3.41 × 10.sup.-5                              
                             -3.43 × 10.sup.-4                      
                                     3.86 × 10.sup.-4               
0.5 y.sub.max                                                             
     -1.53 ×  10.sup.-4                                             
             -9.12 × 10.sup.-5                                      
                     -6.73 × 10.sup.-5                              
                             -6.14 × 10.sup.-4                      
                                     6.35 × 10.sup.-4               
0.6 y.sub.max                                                             
     -2.79 × 10.sup.-4                                              
             -1.62 × 10.sup.-4                                      
                     -1.23 × 10.sup.-4                              
                             -9.09 × 10.sup.-4                      
                                     7.90 × 10.sup.-4               
0.7 y.sub.max                                                             
     -4.75 × 10.sup.-4                                              
             -2.62 × 10.sup.-4                                      
                     -1.90 × 10.sup.-4                              
                             -1.07 × 10.sup.-3                      
                                     6.63 × 10.sup.-4               
0.8 y.sub.max                                                             
     -7.80 × 10.sup.-4                                              
             -3.90 × 10.sup.-4                                      
                     -2.91 × 10.sup.-4                              
                             -8.09 × 10.sup.-4                      
                                     9.45 × 10.sup.-5               
0.9 y.sub.max                                                             
     -1.26 × 10.sup.-3                                              
             -5.31 × 10.sup.-4                                      
                     -4.30 × 10.sup.-4                              
                              6.74 × 10.sup.-5                      
                                     -6.94 × 10.sup.-4              
1.0 y.sub.max                                                             
     -2.18 × 10.sup.-3                                              
             -6.37 × 10.sup.-4                                      
                     - 6.30 × 10.sup.-4                             
                              8.31 × 10.sup.-4                      
                                     -6.07 × 10.sup.-4              
__________________________________________________________________________
 *1 A.sub.FR = φ.sub.1 · (N&#39; - N) · d{x(y) - x.sub.0
 (y)}/dy                                                                  
 *2 A.sub.RE = φ.sub.2 · (N&#39; - N) · d{x(y) - x.sub.0
 (y)}/dy                                                                  
 
    
     
                                           TABLE 2                                 
__________________________________________________________________________
[Example 2]                                                               
A.sub.FR                     A.sub.RE                                     
y    r.sub.1 r.sub.2 r.sub.4 r.sub.5 r.sub.6                              
__________________________________________________________________________
0.1 y.sub.max                                                             
     -6.48 × 10.sup.-7                                              
             -6.19 × 10.sup.-7                                      
                     -5.48 × 10.sup.-7                              
                             -4.59 × 10.sup.-5                      
                                     5.57 × 10.sup.-6               
0.2 y.sub.max                                                             
     -5.22 × 10.sup.-6                                              
             -4.77 × 10.sup.-6                                      
                     -4.35 × 10.sup.-6                              
                             -1.59 × 10.sup.-4                      
                                     4.45 × 10.sup.-5               
0.3 y.sub.max                                                             
     -1.80 × 10.sup.-5                                              
             -1.64 × 10.sup.-5                                      
                     -1.47 × 10.sup.-5                              
                             -3.68 × 10.sup.-4                      
                                     1.47 × 10.sup.-4               
0.4 y.sub.max                                                             
     -4.41 × 10.sup.-5                                              
             -3.94 × 10.sup.-5                                      
                     -3.50 × 10.sup.-5                              
                             -6.67 × 10.sup.-4                      
                                     3.26 × 10.sup.-4               
0.5 y.sub.max                                                             
     -9.09 × 10.sup.-5                                              
             - 7.85 × 10.sup.-5                                     
                     -6.88 × 10.sup.-5                              
                             -9.94 × 10.sup.-4                      
                                     5.38 × 10.sup.-4               
0.6 y.sub.max                                                             
     -1.69 × 10.sup.-4                                              
             -1.38 × 10.sup.-4                                      
                     -1.20 × 10.sup.-4                              
                             -1.17 × 10.sup.-3                      
                                     6.53 × 10.sup.-4               
0.7 y.sub.max                                                             
     -2.95 × 10.sup.-4                                              
             -2.20 × 10.sup.-4                                      
                     -1.93 × 10.sup.-4                              
                             -8.72 × 10.sup.-4                      
                                     4.39 × 10.sup.-4               
0.8 y.sub.max                                                             
     -4.93 × 10.sup.-4                                              
             -3.19 × 10.sup.-4                                      
                     -2.93 × 10.sup.-4                              
                              1.29 × 10.sup.-4                      
                                     -3.18 × 10.sup.-4              
0.9 y.sub.max                                                             
     -8.13 × 10.sup.-4                                              
             -4.04 × 10.sup.-4                                      
                     -4.28 × 10.sup.-4                              
                              9.64 × 10.sup.-4                      
                                     -1.45 × 10.sup.-3              
1.0 y.sub.max                                                             
     -1.36 × 10.sup.-3                                              
             -3.84 × 10.sup.-4                                      
                     -6.08 ×  10.sup.-4                             
                              8.82 × 10.sup.-4                      
                                     -1.58 × 10.sup.-3              
__________________________________________________________________________
 
    
     
                                           TABLE 3                                 
__________________________________________________________________________
[Example 3]                                                               
A.sub.FR                     A.sub.RE                                     
y    r.sub.1 r.sub.2 r.sub.4 r.sub.5 r.sub.6                              
__________________________________________________________________________
0.1 y.sub.max                                                             
     -0.516 × 10.sup.-6                                             
             -0.602 × 10.sup.-6                                     
                     -0.525 × 10.sup.-6                             
                             -0.208 × 10.sup.-5                     
                                     0.315 × 10.sup.-6              
0.2 y.sub.max                                                             
     -0.413 × 10.sup.-5                                             
             -0.499 × 10.sup.-5                                     
                     -0.666 × 10.sup.-5                             
                             -0.155 × 10.sup.-4                     
                                     0.291 × 10.sup.-5              
0.3 y.sub.max                                                             
     -0.139 × 10.sup.-4                                             
             -0.176 × 10.sup.-4                                     
                     -0.139 × 10.sup.-4                             
                             -0.460 × 10.sup.-4                     
                                     0.104 × 10.sup.-4              
0.4 y.sub.max                                                             
     -0.329 × 10.sup.-4                                             
             -0.445 × 10.sup.-4                                     
                     -0.325 × 10.sup.-4                             
                             -0.908 × 10.sup.-4                     
                                     0.212 × 10.sup.-4              
0.5 y.sub.max                                                             
     -0.650 × 10.sup.-4                                             
             - 0.937 × 10.sup.-4                                    
                     -0.623 × 10.sup.-4                             
                             -0.136 × 10.sup.-3                     
                                     0.198 × 10.sup.-4              
0.6 y.sub.max                                                             
     -0.114 × 10.sup.-3                                             
             -0.176 × 10.sup.-3                                     
                     -0.105 × 10.sup.-3                             
                             -0.155 × 10.sup.-3                     
                                     -0.310 × 10.sup.-4             
0.7 y.sub.max                                                             
     -0.185 × 10.sup.-3                                             
             -0.307 × 10.sup.-3                                     
                     -0.164 × 10.sup.-3                             
                             -0.100 × 10.sup.-3                     
                                     -0.189 × 10.sup.-3             
0.8 y.sub.max                                                             
     -0.280 × 10.sup.-3                                             
             -0.503 × 10.sup.-3                                     
                     -0.241 × 10.sup.-3                             
                              0.120 × 10.sup.-3                     
                                     -0.521 × 10.sup.-3             
0.9 y.sub.max                                                             
     -0.405 × 10.sup.-3                                             
             -0.783 × 10.sup.-3                                     
                     -0.344 × 10.sup.-3                             
                              0.689 × 10.sup.-3                     
                                     -0.113 × 10.sup.-2             
1.0 y.sub.max                                                             
     -0.583 × 10.sup.-3                                             
             -0.116 ×  10.sup.-2                                    
                     -0.485 × 10.sup.-3                             
                              0.194 × 10.sup.-2                     
                                     -0.235 × 10.sup.-2             
__________________________________________________________________________
 
    
     
                       TABLE 4                                                     
______________________________________                                    
         ΔT.sub.12 /f.sub.T                                         
                      f.sub.2 /f.sub.W                                    
                             φ.sub.G2                                 
______________________________________                                    
Example 1  0.219          0.586  0.043                                    
Example 2  0.154          0.630  0.040                                    
Example 3  0.200          0.631  0.040                                    
Example 4  0.219          0.586  0.043                                    
______________________________________