Imaging lens system
This is a continuation of application Ser. No. 07/915,766, filed Jul. 21, 1992, now abandoned, which is a continuation of application Ser. No. 07/634,907, filed Dec. 27, 1990, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to an imaging lens for imaging and focusing an image of an object on an image plane, and relates to a compact lens system having a small number of lens elements and a lens system having a large number of lens elements with high performance. 
     Imaging lenses which are to be used in equipment that requiring high resolution must have comparable imaging performance as compared to conventional photographic lenses such as those used with single-lens reflex cameras. However, if imaging lenses are to be used with equipment such as handy picturephones which comparatively low resolution, they should satisfy more of the requirement for compactness than imaging performance and it is necessary to design a most compact system using the smallest possible number of lens elements. Imaging lens systems that have been commonly used in these applications are composed of three glass lens elements having spherical surfaces. As long as spherical lens elements are used, it is difficult to further reduce their number without sacrificing the imaging performance of the system. 
     FIG. 51 is a simplified cross section of a prior art imaging lens system that comprises three lens elements 1, 2 and 3. FIG. 52 shows lateral aberrations caused in the lens system shown in FIG. 51. Shown by 4 in FIG. 51 is cover glass. FIG. 53 is a simplified cross section of another prior art imaging lens system comprising only one aspheric lens element 5 to achieve reduction in the number of lens elements used. However, as is clear from FIG. 54, this system experiences considerable deterioration in performance, particularly in the marginal area. Although the imaging lens shown in FIG. 51 meets the requirement of the imaging lens performance, the number of the lens elements is increased. Inversely, although the lens shown in FIG. 53 has the minimum small number of elements, the performance thereof degrades in the marginal portion. 
     SUMMARY OF THE INVENTION 
     The present invention has been made under these circumstances and has as a primary object providing an imaging lens system that uses less than three lens elements and which yet insures the necessary performance. 
     An imaging lens according to the invention is characterized in that in order to attain the above-noted and other objects, an imaging lens and a compensation lens having aspherical surfaces on both sides are used in combination. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a simplified cross section of an imaging lens system according to the first example of the present invention; 
     FIG. 2 is a set of graphs plotting the aberration curves obtained with the imaging lens system shown in FIG. 1; 
     FIG. 3 is a set of graphs plotting the lateral aberration curves obtained with the lens system shown in FIG. 1; 
     FIG. 4 is a simplified cross section of an imaging lens system according to the second example of the present invention; 
     FIG. 5 is a set of graphs plotting the aberration curves obtained with the lens system shown in FIG. 4; 
     FIG. 6 is a simplified cross section of an imaging lens system according to the third example of the present invention; 
     FIG. 7 is a set of graphs plotting the aberration curves obtained with the lens system shown in FIG. 6; 
     FIG. 8 is a simplified cross section of an imaging lens system according to the fourth example of the present invention; 
     FIG. 9 is a set of graphs plotting the aberration curves obtained with the lens system shown in FIG. 8; 
     FIG. 10 is a simplified cross section of an imaging lens system according to the fifth example of the present invention; 
     FIG. 11 is a set of graphs plotting the aberration curves obtained with the lens system shown in FIG. 10; 
     FIG. 12 is a simplified cross section of an imaging lens system according to the sixth example of the present invention; 
     FIG. 13 is a set of graphs plotting the aberration curves obtained with the lens system shown in FIG. 12; 
     FIG. 14 is a sectional view showing a lens system according to Example 7 at the focal length of 10 mm; 
     FIG. 15 is an enlarged sectional view showing the correcting lens according to Example 7; 
     FIG. 16 is graphs showing various aberrations of Example 7 at the focal length of 10 mm; 
     FIG. 17 is graphs showing various aberrations of Example 7 at the focalf length of 20 mm; 
     FIG. 18 is graphs showing various aberrations of Example 7 at the focal length of 40 mm; 
     FIG. 19 is a sectional view showing a lens system according to Example 8 at the focal length of 10 mm; 
     FIG. 20 is graphs showing aberrations of Example 8 at the focal length of 10 mm without the correcting lens; 
     FIG. 21 is graphs showing aberrations of Example 8 at the focal length of 20 mm without the correcting lens; 
     FIG. 22 is graphs showing aberrations of Example 8 at the focal length of 40 mm without the correcting lens; 
     FIG. 23 is graphs showing aberrations of the overall lens system of Example 9 at the focal length of 10 mm; 
     FIG. 24 is graphs showing aberrations of the overall lens system of Example 9 at the focal length of 20 mm; 
     FIG. 25 is graphs showing the aberrations of the overall lens system of Example 8 at the focal length of 40 mm; 
     FIG. 26 is a sectional view showing a lens system according to Example 9 at the focal length of 8 mm; 
     FIG. 27 is an enlarged view showing the correcting lens according to Example 9; 
     FIG. 28 is graphs showing aberrations of Example 9 at the focal length of 8 mm; 
     FIG. 29 is graphs showing aberrations of Example 9 at the focal length of 20 mm; 
     FIG. 30 is graphs showing aberrations of Example 9 at the focal length of 48 mm; 
     FIG. 31 is a sectional view of a lens system according to Example 10; 
     FIG. 32 is graphs showing aberrations of Example 10 at the magnification of -0.168. 
     FIG. 33 is a sectional view showing a lens system of Example 11 at the focal length of 10 mm; 
     FIG. 34 is an enlarged sectional view showing the correcting lens according to Example 11; 
     FIG. 35 is graphs showing aberrations of Example 11 at the magnification of -0.112; 
     FIG. 36 is graphs showing aberrations of the system of Example 11 without the correcting lens; 
     FIG. 37 is a sectional view showing a lens system according to Example 12; 
     FIG. 38 is graphs showing aberrations according to Example 12; 
     FIG. 39 is a sectional view showing a lens system according to Exasmple 13; 
     FIG. 40 is graphs showing aberrations of Example 13; 
     FIG. 41 is a sectional view showing a lens system according to Example 14; 
     FIG. 42 is graphs showing the aberrations of Example 14; 
     FIG. 43 is a sectional view showing a lens system according to Example 15; 
     FIG. 44 is graphs showing the aberrations of Example 15; 
     FIG. 45 is a sectional view showing a lens system according to Example 16; 
     FIG. 46 is graphs showing the aberrations of Example 16; 
     FIG. 47 is a sectional view showing the system according to Example 17; 
     FIG. 48 is graphs showing the aberrations of Example 17; 
     FIG. 49 is a sectional view showing a lens system according to Example 18; 
     FIG. 50 is graphs showing aberrations of Example 18; 
     FIG. 51 is a simplified cross section of a prior art imaging lens system composed of three lens elements; 
     FIG. 52 is a set of graphs plotting the lateral aberration curves obtained with the lens system shown in FIG. 51; 
     FIG. 53 is a simplified cross section of another prior art imaging lens system composed of a single lens element; and 
     FIG. 54 is a set of graphs plotting the lateral aberration curves obtained with the lens system shown in FIG. 53. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention will now be described with respect to the accompanying drawings. 
     According to the present invention, it provides a lens system which satisfies the following conditions: 
     
         0.75&lt;f/f.sub.1 &lt;1.0                                        (1) 
    
     
         -0.10&lt;f/f.sub.2 &lt;0                                         (2) 
    
     
         0.3&lt;r.sub.1 /d.sub.1 &lt;1.0                                  (3) 
    
     where f is the focal length of the overall system at a predominant wavelength, f 1  is the focal length of the focusing lens element, f 2  is the focal length of the correcting lens element, r 1  is the paraxial radius of curvature of the first surface of the focusing lens element and d 1  is the on-axis thickness of the focusing lens element. 
     Conditions (1) and (2) relate to curvature of the field and astigmatism. If the lower limit of condition (1) is not reached or if the upper limit of condition (2) is exceeded, sagittal curvature of the field will become excessive. If, on the other hand, the upper limit of condition (1) is exceeded or if the lower limit of condition (2) is not reached, not only does astigmatism increase but also the refractive powers of the focusing and correcting lens elements will become excessive to produce coma. 
     Condition (3) relates to curvature of the field and coma. If the upper limit of this condition is exceeded, meridional curvature of the field will increase. If the lower limit of condition (3) is not reached, coma will develop. 
     Further, an imaging lens system satisfies the following conditions: 
     
         -1.0×10.sup.-1 &lt;ΔX.sub.1 (0.2f)/f&lt;-1.0×10.sup.-3(4) 
    
     
         -1.0×10.sup.-1 &lt;ΔX.sub.2 (0.2f)/f&lt;-1.0×10.sup.-3(5) 
    
     where f is the focal length of the overall system, assuming that ΔX N  (Y), or the dedication from a paraxial curved surface of a point of the aspheric object-side surface (N=1) or image-side surface (N=2) of the correcting lens element at height Y from the optical axis, is defined by the following equation: ##EQU1## where An signifies the 4th, 6th, 8th, . . . and nth order asphericity coefficients of lens; K is a conicity coefficient; and C is the curvature (1/r) of the apex of an aspheric surface. 
     Conditions (4) and (5) both relate to astigmatism and distortion. If the lower limit of either condition is not reached negative distortion will develop in the range of small image heights. If the upper limit of either condition is exceeded, not only meridional curvature of the field but also astigmatism will increase. 
     In order to effectively use the correcting lens, the inlet pupil of the correcting lens is located inside the imaging lens, and the following condition should be met: 
     
         -0.4&lt;d.sub.0 /f&lt;-0.2                                       (6) 
    
     where d 0  is the distance from a surface on the object side of the correcting lens to the inlet pupil of the correcting lens and f is the overall focal length. 
     Condition (6) define the position of the inlet pupil of the correcting lens. If this condition is not met, the astigmatism is increased to deteriorate the focusing performance. 
     EXAMPLES 
     The present invention is described below more specifically with reference to FIGS. 1-13 which show six examples of the imaging lens system of the present invention. 
     EXAMPLE 1 
     FIGS. 1-3 show the first example of the imaging lens system of the present invention. As shown, this example of the imaging lens system comprises a focusing lens element 10 having aspheric surfaces on both sides and a correcting lens element 20 that is positioned on the image side of the focusing lens element 10 and which has aspheric surfaces on both sides. A sensor (not shown) for reading the signal associated with the image to be formed is positioned on the image side of the correcting lens element 20. The sensor is sealed with cover glass 30 to insure that its light-receiving surface will not be directly exposed to moisture. The space between the light-receiving surface of the sensor and the cover glass is filled with nitrogen gas. 
     The correcting lens element 20 has a convex surface toward the object on both sides in the paraxial area and it has such a special geometry that the direction of a displacement along the aspheric surface is opposite the paraxial radius of curvature of said aspheric surface. An aspheric shape that satisfies these conditions can be easily realized using plastic materials. 
     The numerical values that characterize the arrangement of the first example of the imaging lens system of the present invention are listed in Table 1 below, in which: F NO  is the F number; f is the focal length at a predominant wavelength; m is the magnification; r is the radius of curvature of an individual lens surface; d is the lens thickness or the aerial distance between lenses; n d  is the refractive index of lens at the d-lien (588 nm); ν is the Abbe number; and n e  is the refractive index of lens at the e-line (546 nm). The numerals listed in the column of r(radius of curvature) for aspheric surface refer to the radius of curvature of the apex of the aspheric surface. The shape of an aspheric surface is expressed by: ##EQU2## where X is the distance between a plane tangential to the apex of the aspheric surface and a point on that surface at height Y from the optical axis, C is the curvature (1/r) of the apex of the aspheric surface, K is a conicity coefficient, and A 4  -A 10  are the fourth to tenth order asphericity coefficients. The conicity and asphericity coefficients of individual lens surfaces are listed in the lower part of Table 1. 
     
                       TABLE 1                                                     
______________________________________                                    
Predominant wavelength = 546 nm; F.sub.no = 1:2.0; f = 6.01;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.     r         d      n.sub.d  ν N.sub.e                            
______________________________________                                    
1       3.042     5.74   1.49186  57.4 1.49399                            
2       12.990    0.50                                                    
3       3.000     1.00   1.49186  57.4 1.49399                            
4       2.660     0.50                                                    
5       ∞   0.70   1.51633  64.1 1.51825                            
6       ∞                                                           
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.194624 × 10                                                  
                   K = -0.130050 × 10                               
A.sub.4 = 0.713727 × 10.sup.-2                                      
                   A.sub.4 = -0.135549 × 10.sup.-1                  
A.sub.6 = 0.778110 × 10.sup.-5                                      
                   A.sub.6 = 0.297119 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.978653      K = -0.789604 × 10                               
A.sub.4 = - 0.428196 × 10.sup.-1                                    
                   A.sub.4 = 0.227504 × 10.sup.-2                   
A.sub.6 = 0.759195 × 10.sup.-2                                      
                   A.sub.6 = -0.438489 ×`10.sup.-2                  
A.sub.8 = -0.637356 × 10.sup.-3                                     
                   A.sub.8 = 0.102247 × 10.sup.-2                   
A.sub.10 = -0.319293 × 10.sup.-5                                    
                   A.sub.10 = -0.749587 × 10.sup.-4                 
______________________________________                                    
 
    
     FIG. 2 is a set of graphs plotting the aberration curves obtained with the lens arrangement shown in Table 1, and FIG. 3 is a set of graphs plotting the lateral aberration curves obtained with the same lens arrangement. 
     EXAMPLE 2 
     FIG. 4 shows the second example of the imaging lens system of the present invention. As shown, the correcting lens element 20 provided on the image side of the focusing lens element 10 also serves as the cover of the sensor. 
     The numerical values that characterize the lens arrangement of this system are listed in Table 2 below, in which the respective symbols have the same meanings as those appearing in Table 1 FIG. 5 is a set of graphs plotting the aberration curves obtained with the lens arrangement shown in Table 2. 
     
                       TABLE 2                                                     
______________________________________                                    
Predominant wavelength = 546 nm; F.sub.no = 1:2.0; f = 5.99;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.     r         d      n.sub.d  ν N.sub.e                            
______________________________________                                    
1       3.124     6.00   1.49186  57.4 1.49399                            
2       12.581    0.50                                                    
3       2.366     1.00   1.49186  57.4 1.49399                            
4       2.031                                                             
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.187101 × 10                                                  
                   K = -0.131636 × 10                               
A.sub.4 = 0.625802 × 10.sup.-2                                      
                   A.sub.4 = -0.258346 × 10.sup.-1                  
A.sub.6 = -0.380279 × 10.sup.-4                                     
                   A.sub.6 = 0.474393 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.149829 × 10                                                  
                   K = -0.737499 × 10                               
A.sub.4 = -0.559767 × 10.sup.-1                                     
                   A.sub.4 = 0.481425 × 10.sup.-2                   
A.sub.6 = 0.106388 × 10.sup.-1                                      
                   A.sub.6 = -0.500481 × 10.sup.-2                  
A.sub.8 = -0.144178 × 10.sup.-2                                     
                   A.sub.8 = 0.940866 × 10.sup.-3                   
A.sub.10 = 0.792364 × 10.sup.-4                                     
                   A.sub.10 = -0.645239 × 10.sup.-4                 
______________________________________                                    
 
    
     EXAMPLE 3 
     FIG. 6 shows the third example of the imaging lens system of the present invention. As in Example 1, the third example of the imaging lens system comprises a focusing lens element 10 and the correcting lens element 20, with sensor cover glass 30 being provided on the image side of the correcting lens. 
     The numerical values that characterize the arrangement of the this imaging lens system are listed in Table 3, and the aberration curves obtained with that lens arrangement are plotted in graphs in FIG. 7. 
     In this third example, as well as the fourth and fifth examples that follow, both the focusing lens 10 and the correcting lens 20 are formed of APO® (the trademark for an amorphous polyolefin). PMMA (polymethyl methacrylate) which is conventionally used as the constituent material of plastic lenses experiences substantial changes in refraction with temperature or humidity and, hence, its optical performance is highly depended on the environment. In particular, changes in humidity will not only cause defocusing but also disturb the wavefronts of light flux. APO®, the low moisture absorption plastic material developed by Mitsui Petrochemical Industries, Ltd., has a water absorption of no more than 0.01% which is one tenth the value for PMMA and is less sensitive to changes in humidity. Therefore, the use of APO® as a lens material is effective in further stabilizing the performance of the lens system. 
     
                       TABLE 3                                                     
______________________________________                                    
Predominant wavelength = 588 nm; F.sub.no = 1;2.0; f = 6.01;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.        r       d          n.sub.d                                     
                                    ν                                  
______________________________________                                    
1          3.412   5.94       1.55000                                     
                                    55.0                                  
2          14.137  0.50                                                   
3          2.903   1.00       1.55000                                     
                                    55.0                                  
4          2.527   0.50                                                   
5          ∞ 0.70       1.51633                                     
                                    64.1                                  
6          ∞                                                        
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.784881      K = -0.126037 × 10                               
A.sub.4 = 0.164109 × 10.sup.-2                                      
                   A.sub.4 = -0.149559 × 10.sup.-1                  
A.sub.6 = 0.342210 × 10.sup.-4                                      
                   A.sub.6 = 0.246460 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.966747      K = -0.783520 × 10                               
A.sub.4 = -0.656687 × 10.sup.-1                                     
                   A.sub.4  = 0.466273 × 10.sup.-3                  
A.sub.6 = 0.135790 × 10.sup.-1                                      
                   A.sub.6 = -0.800952 × 10.sup.-2                  
A.sub.8 = -0.486677 × 10.sup.-3                                     
                   A.sub.8 = 0.218457 × 10.sup.-2                   
A.sub.10 = -0.301009 × 10.sup.-3                                    
                   A.sub.10 = -0.192248 × 10.sup.-3                 
______________________________________                                    
 
    
     EXAMPLE 4 
     FIG. 8 shows the fourth example of the imaging lens system of the present invention. As in Example 1, the fourth example of the imaging lens system comprises a focusing lens element 10 and the correcting lens 20, with sensor cover glass 30 being provided on the image side of the correcting lens. 
     The numerical values that characterize the arrangement of the this imaging lens system are listed in Table 4, and the aberration curves obtained with that lens arrangement are plotted in graphs in FIG. 9. 
     
                       TABLE 4                                                     
______________________________________                                    
Predominant wavelength = 588 nm; F.sub.no = 1:2.0; f = 6.01;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.        r       d          n.sub.d                                     
                                    ν                                  
______________________________________                                    
1          3.338   5.77       1.55000                                     
                                    55.0                                  
2          12.011  0.50                                                   
3          3.027   1.00       1.55000                                     
                                    55.0                                  
4          2.648   0.50                                                   
5          ∞ 0.70       1.51633                                     
                                    64.1                                  
6          ∞                                                        
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.731898      K = -0.125657 × 10                               
A.sub.4 = 0.157031 × 10.sup.-2                                      
                   A.sub.4 = -0.146472 × 10.sup.-1                  
A.sub.6 = 0.383063 × 10.sup.-4                                      
                   A.sub.6 = 0.274962 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.970902      K = -0.855780 × 10                               
A.sub.4 = -0.682295 × 10.sup.-1                                     
                   A.sub.4  = -0.154062 × 10.sup.-2                 
A.sub.6 = 0.148957 × 10.sup.-1                                      
                   A.sub.6 = -0.829566 × 10.sup.-2                  
A.sub.8 = -0.358825 × 10.sup.-3                                     
                   A.sub.8 = 0.244783 × 10.sup.-2                   
A.sub.10 = -0.409921 × 10.sup.-3                                    
                   A.sub.10 = -0.228862 × 10.sup.-3                 
______________________________________                                    
 
    
     EXAMPLE 5 
     FIG. 10 shows the fifth example of the imaging lens system of the present invention. As in Example 2, the fifth example of the imaging lens system comprises a focusing lens element 10 and the correcting lens element 20 that is provided on the image side of the focusing lens and which also serves as the sensor cover. Both lenses are formed of APO®. If the correcting lens 20 serving as the cover glass is formed of PMMA or some other highly hygroscopic resins, it absorbs and rejects moisture, potentially causing devitrification that is deleterious to the sensor performance. However, if the correcting lens is made of APO® as in Example 5, the light-receiving surface of the sensor is protected against moisture, thereby preventing the deterioration of the sensor performance. 
     The numerical values that characterize the arrangement of the fifth example of the imaging lens system are listed in Table 5 and the aberration curves obtained with that lens arrangement are plotted in graphs in FIG. 11. 
     
                       TABLE 5                                                     
______________________________________                                    
Predominant wavelength = 588 nm; F.sub.no = 1:2.0; f = 6.03;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.        r       d          n.sub.d                                     
                                    ν                                  
______________________________________                                    
1          3.326   5.88       1.55000                                     
                                    55.0                                  
2          12.215  0.50                                                   
3          3.349   1.00       1.55000                                     
                                    55.0                                  
4          2.968                                                          
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.754667      K = -0.125619 × 10                               
A.sub.4 = 0.156275 × 10.sup.-2                                      
                   A.sub.4 = -0.174198 × 10.sup.-1                  
A.sub.6 = 0.378961 × 10.sup.-4                                      
                   A.sub.6 = 0.298733 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.974257      K = -0.878669 × 10                               
A.sub.4 = -0.755966 × 10.sup.-1                                     
                   A.sub.4 = -0.986136 × 10.sup.-2                  
A.sub. 6 = 0.142915 × 10.sup.-1                                     
                   A.sub.6 = -0.765810 × 10.sup.-2                  
A.sub.8 = -0.167593 × 10.sup.-3                                     
                   A.sub.8 = 0.233115 × 10.sup.-2                   
A.sub.10 = -0.669631 × 10.sup.-3                                    
                   A.sub.10 = -0.256260 × 10.sup.-3                 
______________________________________                                    
 
    
     EXAMPLE 6 
     FIG. 12 shows the sixth example of the imaging lens system of the present invention. As in Example 2, the sixth example of the imaging lens system comprises a focusing lens element 10 and the correcting lens 20 that is provided on the image side of the focusing lens and which also serves as the sensor cover. 
     The numerical values that characterize the arrangement of the sixth example of the imaging lens system are listed in Table 6 below and the aberration curves obtained with that lens arrangement are plotted in graphs in FIG. 13. 
     
                       TABLE 6                                                     
______________________________________                                    
Predominant wavelength = 588 nm; F.sub.no = 1:2.0; f = 6.03;              
m = -0.020                                                                
______________________________________                                    
Surface                                                                   
No.        r       d          n.sub.d                                     
                                    ν                                  
______________________________________                                    
1          3.074   6.00       1.49186                                     
                                    57.4                                  
2          8.748   0.50                                                   
3          2.450   1.00       1.62041                                     
                                    60.3                                  
4          2.062                                                          
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.130940 × 10                                                  
                   K = -0.130433 × 10                               
A.sub.4 = 0.447807 × 10.sup.-2                                      
                   A.sub.4 = -0.242819 × 10.sup.-1                  
A.sub.6 = 0.117284 × 10.sup.-4                                      
                   A.sub.6 = 0.451440 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.112895 × 10                                                  
                   K = -0.765573 × 10                               
A.sub.4 = -0.519064 × 10.sup.-1                                     
                   A.sub.4 = 0.293394 ×  10.sup.-2                  
A.sub.6 = 0.969186 × 10.sup.-2                                      
                   A.sub.6 = -0.403625 × 10.sup.-2                  
A.sub.8 = -0.117606 × 10.sup.-2                                     
                   A.sub.8 = 0.799504 × 10.sup.-3                   
A.sub.10 = 0.528630 × 10.sup.-4                                     
                   A.sub.10 = -0.555438 × 10.sup.-4                 
______________________________________                                    
 
    
     The numerical values that satisfy conditions (1)-(6) are shown below for the foregoing Examples. 
     
         __________________________________________________________________________
Condition                                                                 
Example                                                                   
      1   2    3   4        5        6                                    
__________________________________________________________________________
1     0.890                                                               
          -0.003                                                          
               0.530                                                      
                    -133 × 10.sup.-2                                
                            -1.31 × 10.sup.-2                       
                                     -0.179                               
2     0.861                                                               
          -0.003                                                          
               0.520                                                      
                   -2.02 × 10.sup.-2                                
                            -2.32 × 10.sup.-2                       
                                     -0.296                               
3     0.879                                                               
          -0.010                                                          
               0.575                                                      
                   -1.86 × 10.sup.-2                                
                            -1.65 × 10.sup.-2                       
                                     -0.281                               
4     0.885                                                               
          -0.010                                                          
               0.578                                                      
                   -1.86 × 10.sup.-2                                
                            -1.60 × 10.sup.-2                       
                                     -0.264                               
5     0.896                                                               
          -0.009                                                          
               0.565                                                      
                   -2.13 × 10.sup.-2                                
                            -1.60 × 10.sup.-2                       
                                     -0.274                               
6     0.844                                                               
          -0.004                                                          
               0.513                                                      
                   -1.79 × 10.sup.-2                                
                            -2.35 × 10.sup.-2                       
                                     -0.273                               
__________________________________________________________________________
 
    
     The foregoing first through sixth examples relates to an imaging lens for use with a compact camera such as a picturephone or a doorphone camera. In order to meet this field, the lens system according to the first through sixth examples is made compact only with a single imaging element and a single correcting element. 
     In the following examples, a plurality of lens elements are used as an imaging lens to thereby enhance the imaging efficiency in comparison with the foregoing examples. It should be further noted that the seventh through ninth examples relate to zoom lenses. 
     EXAMPLE 7 
     FIG. 14 shows an imaging lens according to Example 7 of the invention. The lens system is composed of an imaging lens having three groups and a correcting lens element having a negative focal length in the paraxial area and aspherical surfaces. The imaging lens system is composed, in order from the object side, of a positive first lens group, a negative second lens group and a positive third lens group. This system is of the zoom lens type which varies its focal length by moving the first and second lens groups in the axial direction and effects focusing by moving the first lens group in the axial direction. 
     FIG. 15 is an enlarged view showing the shape of the correcting lens. 
     Numerical data of the seventh example are shown in Table 7, FIG. 16 shows various aberrations at the focal length of 10 mm, FIG. 17 shows aberrations at the focalf length of 20 mm and FIG. 18 shows the aberrations at the focal length of 40 mm. 
     
                       TABLE 7                                                     
______________________________________                                    
Stop position: 0.0 mm after thirteenth surface;                           
F.sub.no = 1:2.4                                                          
______________________________________                                    
Surface                                                                   
No.      r          d           n     ν                                
______________________________________                                    
 1       84.694     1.00        1.80518                                   
                                      25.4                                
 2       37.958     8.00        1.62041                                   
                                      60.3                                
 3       -500.000   0.10                                                  
 4       36.815     4.96        1.66600                                   
                                      56.9                                
 5       173.484    variable                                              
 6       -554.810   1.00        1.77250                                   
                                      49.6                                
 7       11.416     3.52                                                  
 8       -55.561    1.00        1.77250                                   
                                      49.6                                
 9       24.419     0.00                                                  
10       17.395     2.80        1.80518                                   
                                      25.4                                
11       1326.514   variable                                              
12       13.456     2.00        1.77250                                   
                                      49.6                                
13       -1190.200  6.46                                                  
14       -10.467    1.00        1.80518                                   
                                      25.4                                
15       21.233     0.38                                                  
16       48.326     3.00        1.74800                                   
                                      52.9                                
17       -14.443    3.29                                                  
18       23.127     3.60        1.69680                                   
                                      55.5                                
19       -34.620    9.22                                                  
20       8.348      2.00        1.49176                                   
                                      57.4                                
21       7.774                                                            
______________________________________                                    
Asphericity coefficient:                                                  
20th surface     21st surface                                             
K = -0.14803000 × 10                                                
                 K = -0.56210000                                          
A.sub.4 = -0.96124875 × 10.sup.-5                                   
                 A.sub.4 = -0.23738250 × 10.sup.-3                  
A.sub.6 = -0.10790938 × 10.sup.-4                                   
                 A.sub.6 = -0.55681875 × 10.sup.-5                  
A.sub.8 = 0.29441875 × 10.sup.-6                                    
                 A.sub.8 = -0.30791016 × 10.sup.-6                  
A.sub.10 = -0.12693965 × 10.sup.-7                                  
                 A.sub.10 = -0.79271484 × 10.sup.-8                 
ω 22.3°   11.0°                                       
                              5.6°                                 
f       10.00          20.00  40.00                                       
d.sub.5 1.00           15.52  22.78                                       
d.sub.11                                                                  
        22.85          15.48  0.72                                        
______________________________________                                    
 
    
     EXAMPLE 8 
     FIG. 19 shows an eighth example of the invention. The lens system is composed of a four group imaging lens and a correcting lens having a negative focal length in the paraxial area and aspherical surfaces on both sides. The imaging lens is composed, in order from the object side, of a positive first lens group, a negative second lens group, a negative third lens group and a positive fourth lens group. The second and third lens groups are moved in the axial direction to thereby change the focal length , whereas the first lens group is moved in the axial direction to effect focusing. 
     Numerial data of the eighth exafmple are shown in Table 8. FIGS. 20, 21 and 22 show various aberrations at the focal lengths of 10 mm, 20 mm and 40 mm, respectively. 
     The avberrations of the imaging lens system without the correcting lens are shown in FIGS. 23, 24 and 25 at the focal lengths at 10 mm, 20 mm and 40 mm, respectively, for comparison. 
     
                       TABLE 8                                                     
______________________________________                                    
F.sub.no = 1:2.4                                                          
Stop position: 0.0 mm after fifteenth surface                             
______________________________________                                    
Surface                                                                   
No.       r         d           n     ν                                
______________________________________                                    
 1        84.599    1.00        1.80518                                   
                                      25.4                                
 2        39.340    7.00        1.62041                                   
                                      60.3                                
 3        -685.764  0.10                                                  
 4        37.832    4.70        1.65830                                   
                                      57.3                                
 5        144.178   variable                                              
 6        901.443   1.00        1.77250                                   
                                      49.6                                
 7        11.335    3.77                                                  
 8        -68.435   1.00        1.77250                                   
                                      49.6                                
 9        29.457    0.00                                                  
10        18.251    2.80        1.80518                                   
                                      25.4                                
11        243.228   variable                                              
12        -18.903   1.00        1.80518                                   
                                      25.4                                
13        -23.741   variable                                              
14        14.625    2.00        1.77250                                   
                                      49.6                                
15        -78.864   6.60                                                  
16        -9.569    1.00        1.80518                                   
                                      25.4                                
17        49.906    0.35                                                  
18        -663.895  3.00        1.77250                                   
                                      49.6                                
19        -13.600   0.00                                                  
20        20.299    3.00        1.69680                                   
                                      55.5                                
21        -86.820   10.66                                                 
22        12.131    2.00        1.49176                                   
                                      57.4                                
23        11.433                                                          
______________________________________                                    
Asphericity coefficient:                                                  
22nd surface     23rd surface                                             
K = -0.23580000 × 10                                                
                 K = -0.86670000                                          
A.sub.4 = -0.46588125 × 10.sup.-3                                   
                 A.sub.4 = -0.53498250 × 10.sup.-3                  
A.sub.6  = -0.19610156 × 10.sup.-4                                  
                 A.sub.6 = -0.14864906 × 10.sup.-4                  
A.sub.8 = 0.22914219 × 10.sup.-6                                    
                 A.sub.8 = -0.76494844 × 10.sup.-6                  
A.sub.10 = -0.20033789 × 10.sup.-7                                  
                 A.sub.10 = 0.98121094 × 10.sup.-8                  
ω 22.2°   11.1°                                       
                              5.6°                                 
f       10.00          20.00  40.00                                       
d.sub.5 1.00           15.21  24.89                                       
d.sub.11                                                                  
        24.85          1.00   1.00                                        
d.sub.13                                                                  
        1.00           10.67  0.98                                        
______________________________________                                    
 
    
     EXAMPLE 9 
     FIG. 26 shows an imaging system according to Example 9. The system is composed of a four lens group imaging lens and a correcting lens having aspherical surfaces on both sides and a negative focal length in the paraxial area. The imaging lens is composed of a positive first lens group, a negative second lens group, a negative third lens group and a positive fourth lens group. The second and third lens groups are moved in the axial direction to thereby change the focal length, whereas the first lens group is moved in the axial direction to effect focusing. 
     FIG. 27 is an enlarged view showing the correcting lens. 
     Numerical data of Example 9 are shown in Table 9. The various aberrations are shown at the focal lengths of 8 mm, 20 mm and 48 mm, respectively, in FIGS. 28, 29 and 30. 
     
                       TABLE 9                                                     
______________________________________                                    
F.sub.no = 1:1.6                                                          
Stop position: 0.0 mm after fifteenth surface                             
______________________________________                                    
Surface                                                                   
No.       r         d           n     ν                                
______________________________________                                    
 1        76.224    1.00        1.80518                                   
                                      25.4                                
 2        36.696    7.00        1.62041                                   
                                      60.3                                
 3        -824.046  0.10                                                  
 4        29.356    4.70        1.65830                                   
                                      57.3                                
 5        63.288    variable                                              
 6        62.941    1.00        1.77250                                   
                                      49.6                                
 7        8.965     4.06                                                  
 8        -37.332   1.00        1.77250                                   
                                      49.6                                
 9        26.689    0.00                                                  
10        16.973    2.80        1.80518                                   
                                      25.4                                
11        4316.651  variable                                              
12        -15.738   2.00        1.80518                                   
                                      25.4                                
13        -21.661   variable                                              
14        23.378    3.00        1.80400                                   
                                      46.6                                
15        -36.426   9.59                                                  
16        -9.856    1.00        1.80518                                   
                                      25.4                                
17        63.901    0.00                                                  
18        39.059    3.00        1.77250                                   
                                      49.6                                
19        -18.435   0.92                                                  
20        17.066    3.00        1.69680                                   
                                      55.5                                
21        -876.505  10.70                                                 
22        10.515    2.00        1.49176                                   
                                      57.4                                
23        14.299                                                          
Asphericity coefficient:                                                  
22nd surface      23rd surface                                            
K = -0.11902000 × 10                                                
                  K = 0.20351000 × 10                               
A.sub.4 = -0.34344375 × 10.sup.-3                                   
                  A.sub.4 = -0.39248625 × 10.sup.-3                 
A.sub.6  = -0.21543063 × 10.sup.-4                                  
                  A.sub.6 = 0.16765094 × 10.sup.-4                  
A.sub.8 = 0.87141406 × 10.sup.-7                                    
                  A.sub.8 = -0.36826641 × 10.sup.-5                 
A.sub.10 = -0.47653125 × 10.sup.-7                                  
                  A.sub.10 = 0.47951758 × 10.sup.-7                 
ω 26.9°   11.2°                                       
                              4.7°                                 
f       8.00           20.00  48.00                                       
d.sub.5 1.00           18.15  28.09                                       
d.sub.11                                                                  
        29.08          2.42   1.99                                        
d.sub.13                                                                  
        1.00           10.51  1.00                                        
______________________________________                                    
 
    
     EXAMPLE 10 
     FIG. 31 shows a lens system according to Example 10. The system is composed of a four lens group imaging lens and a correcting lens having aspherical surfaces on both sides and a negative focal length in the paraxial area. The imaging lens is composed, in order from the object side, of a negative first lens, a positive second lens, a negative third lens and a positive fourth lens. 
     Numerical data of the system are shown in Table 10. Various aberrations at magnification of -0.168 are shown in FIG. 32. 
     
                       TABLE 10                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 20.04 ω = 24.2°                         
Stop position: 0.22 mm after fourth surface                               
______________________________________                                    
Surface                                                                   
No.       r         d          n     ν                                 
______________________________________                                    
1         7.500     3.26       1.48749                                    
                                     70.2                                 
2         4.746     2.58                                                  
3         11.113    1.96       1.80400                                    
                                     46.6                                 
4         -35.721   0.85                                                  
5         -162.033  2.55       1.84666                                    
                                     23.9                                 
6         12.416    1.39                                                  
7         -13.297   2.28       1.77250                                    
                                     49.6                                 
8         -7.268    15.20                                                 
9         18.690    2.00       1.49176                                    
                                     57.4                                 
10        13.737                                                          
______________________________________                                    
Asphericity coefficient:                                                  
9th surface      10th surface                                             
K = 0.12140000   K = -0.87000000 × 10.sup.-1                        
A.sub.4 = -0.24887700 × 10.sup.-3                                   
                 A.sub.4 = -0.26318100 × 10.sup.-3                  
A.sub.6 = 0.12765700 × 10.sup.-5                                    
                 A.sub.6 = 0.43894000 × 10.sup.-6                   
A.sub.8 = -0.10093400 × 10.sup.-8                                   
                 A.sub.8 = -0.63861200 × 10.sup.-9                  
A.sub.10 = 0.00000000                                                     
                 A.sub.10 = 0.00000000                                    
______________________________________                                    
 
    
     EXAMPLE 11 
     FIG. 33 shows an eleventh example of the invention. The lens system is composed of a four lens imaging lens and a correcting lens having a negative focal length in the paraxial area and aspherical surfaces on both sides. The imaging lens system is composed, in order from the object side, of a positive first lens, a negative second lens, a positive third lens and a negative fourth lens. The third and fourth lens elements are bonded or cemented together. 
     FIG. 34 is an enlarged view showing a shape of the correcting lens. The numerical data of the lens are shown in Table 11. FIG. 35 shows a various aberrations at magnification of -0.112. FIG. 36 shows the aberrations of the imaging lens system without correcting lens. 
     
                       TABLE 11                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 30.05 ω = 22.9°                         
Stop position: 0.83 mm after fourth surface                               
______________________________________                                    
Surface                                                                   
No.       r         d          n.sub.d                                    
                                     ν                                 
______________________________________                                    
1         12.541    3.14       1.83481                                    
                                     42.7                                 
2         27.329    1.65                                                  
3         -54.425   2.00       1.76182                                    
                                     26.6                                 
4         11.764    0.86                                                  
5         20.318    2.91       1.83481                                    
                                     42.7                                 
6         -15.882   2.30       1.54814                                    
                                     45.8                                 
7         -48.458   22.00                                                 
8         51.315    2.00       1.49176                                    
                                     57.4                                 
9         25.915                                                          
______________________________________                                    
Asphericity coefficient:                                                  
8th surface      9th surface                                              
K = -1.00000000 × 10.sup.-3                                         
                 K = 0.33000000 × 10.sup.-2                         
A.sub.4 = -0.10634600 × 10.sup.-3                                   
                 A.sub.4 = -0.91343800 × 10.sup.-4                  
A.sub.6 = 0.11880200 × 10.sup.-6                                    
                 A.sub.6 = 0.31772000 × 10.sup.-7                   
A.sub.8 = 0.00000000                                                      
                 A.sub.8 = 0.00000000                                     
A.sub.10 = 0.00000000                                                     
                 A.sub.10 = 0.00000000                                    
______________________________________                                    
 
    
     EXAMPLE 12 
     FIG. 37 shows a twelfth example of the invention. The imaging lenses according to the twelfth to eighteenth examples are each composed, in order from the object side, of a correcting lens having a biconcave character is the paraxial area and having a negative focal length and a single positive imaging element. A cover glass is provided on the image side. The correcting lens has aspherical surfaces on both sides. The direction of shift from the spherical surface on the object side is opposite to the radius of curvature of the paraxial area. 
     With such an arrangement, it is possible to obtain a preferable image relative to the inlet pupil of the imaging lens with the aspherical surface on the object side of the correcting lens. The Petzval image surface is a curved surface toward the object assuming that the image surface of the imaging lens be an object. The Petzval image is formed on the object side beyond the correcting lens. The Petzval image surface of the negative correcting lens is a curved surface convex toward the object and is formed as a virtual image. In the case where these Petzval image positions and curvature are identical with each other, the image of the object is formed on the light-receiving surfaces without curvature of field or astigmatism. 
     With such an arrangement, it is possible to provide a compact and low cost lens with a wide-angle property with a simple structure. Also, by disposing the negative lens on the object side of the positive imaging lens, it is possible to insure a long backfocus. As a result, even if the focal length of the lens system is shortened, the lens is not brought into contact with the cover glass. 
     In Examples 12, 13, 14 and 16, the stop diaphragm is located in the imaging lens. In Examples 15, 17 and 18, the stop diaphragm is located on a plain on the image side of the imaging lens. 
     The numerical data of Example 12 is shown in Table 12 and the aberrations are shown in FIG. 38. 
     
                       TABLE 12                                                    
______________________________________                                    
F.sub.no = 1:2.4 f = 3.61 ω = 39.6°                          
Stop position: 0.236 mm after fourth surface                              
______________________________________                                    
Surface                                                                   
No.       r        d          n     ν                                  
______________________________________                                    
1         -4.587   1.000      1.54510                                     
                                    54.3                                  
2         3.949    3.183                                                  
3         2.207    5.884      1.54510                                     
                                    54.3                                  
4         -9.032   1.800                                                  
5         ∞  0.700      1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.402000      K = 0.578900                                           
A.sub.4 = 0.864316 × 10.sup.-2                                      
                   A.sub.4 = -0.986545 × 10.sup.-2                  
A.sub.6 = -0.266607 × 10.sup.-3                                     
                   A.sub.6 = 0.168617 × 10.sup.-2                   
A.sub.8 = 0.492237 × 10.sup.-5                                      
                   A.sub.8 = -0.983242 × 10.sup.-4                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.824091 × 10.sup.-7                  
3rd surface        4th surface                                            
K = -0.110790 × 10                                                  
                   K = - 0.130980 × 10                              
A.sub.4 = -0.780549 × 10.sup.-3                                     
                   A.sub.4 = 0.209934 × 10.sup.-1                   
A.sub.6 = 0.374558 × 10.sup.-3                                      
                   A.sub.6 = -0.165218 × 10.sup.-1                  
A.sub.8 = 0.000000 A.sub.8 = 0.118060 × 10.sup.-1                   
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
______________________________________                                    
 
    
     EXAMPLE 13 
     FIG. 39 shows the thirteenth example. The numerical data thereof is shown in Table 13. The aberrations are shown in FIG. 40. 
     
                       TABLE 13                                                    
______________________________________                                    
F.sub.no = 1:2.8 f = 3.60 ω = 39.7°                          
Stop position: 0.173 mm after fourth surface                              
______________________________________                                    
Surface                                                                   
No.       r         d         n     ν                                  
______________________________________                                    
1         -4.632    1.020     1.54510                                     
                                    54.3                                  
2         3.959     3.235                                                 
3         2.119     5.496     1.54510                                     
                                    54.3                                  
4         -13.455   1.800                                                 
5         ∞   0.700     1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.356100      K = 0.535400                                           
A.sub.4 = 0.868733 × 10.sup.-2                                      
                   A.sub.4 = -0.942661 × 10.sup.-2                  
A.sub.6 = -0.269543 × 10.sup.-3                                     
                   A.sub.6 = 0.173404 × 10.sup.-2                   
A.sub.8 = 0.501075 × 10.sup.-5                                      
                   A.sub.8 = -0.961295 × 10.sup.-4                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.116240 × 10                                                  
                   K = -0.130980 × 10                               
A.sub.4 = 0.805949 × 10.sup.-3                                      
                   A.sub.4 = 0.157393 × 10.sup.-1                   
A.sub.6 = 0.447873 × 10.sup.-3                                      
                   A.sub.6 = 0.115998 × 10.sup.-2                   
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
______________________________________                                    
 
    
     EXAMPLE 14 
     FIG. 41 shows the fourteenth example. The numerical data thereof is shown in Table 14. The aberrations are shown in FIG. 42. 
     
                       TABLE 14                                                    
______________________________________                                    
F.sub.no = 1:3.2 f = 3.60 ω= 39.7°                           
Stop position: 0.235 mm after fourth surface                              
______________________________________                                    
Surface                                                                   
No.       r         d         n     ν                                  
______________________________________                                    
1         -4.678    1.000     1.54510                                     
                                    54.3                                  
2         4.207     3.531                                                 
3         2.127     5.315     1.54510                                     
                                    54.3                                  
4         -23.109   1.800                                                 
5         ∞   0.700     1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.290700      K = 0.753500                                           
A.sub.4 = 0.869606 × 10.sup.-2                                      
                   A.sub.4 = -0.753936 × 10.sup.-2                  
A.sub.6 = -0.281279 × 10.sup.-3                                     
                   A.sub.6 = 0.146128 × 10.sup.-2                   
A.sub.8 = 0.570323 × 10.sup.-5                                      
                   A.sub.8 = -0.861100 × 10.sup.-4                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface        4th surface                                            
K = -0.122430 × 10                                                  
                   K = -0.130980 × 10                               
A.sub. 4 = 0.249318 × 10.sup.-2                                     
                   A.sub.4 = 0.167431 × 10.sup.-1                   
A.sub.6 = 0.453902 × 10.sup.-3                                      
                   A.sub.6 = 0.000000                                     
A.sub.8 = 0.000000 A.sub.8 = 0.000000                                     
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
______________________________________                                    
 
    
     EXAMPLE 15 
     FIG. 43 shows the fifteenth example. The numerical data thereof is shown in Table 15. The aberrations are shown in FIG. 44. 
     
                       TABLE 15                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 3.61 ω = 39.6°                          
______________________________________                                    
Surface                                                                   
No.       r          d         n     ν                                 
______________________________________                                    
1         -4.444     1.007     1.54510                                    
                                     54.3                                 
2         4.415      3.168                                                
3         1.941      4.612     1.54510                                    
                                     54.3                                 
4         -265.553   1.800                                                
5         ∞    0.700     1.51633                                    
                                     64.1                                 
6         ∞                                                         
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.103200      K = 0.648700                                           
A.sub.4 = 0.102554 × 10.sup.-1                                      
                   A.sub.4 = -0.842680 × 10.sup.-2                  
A.sub.6 = -0.370471 × 10.sup.-3                                     
                   A.sub.6 = 0.184347 × 10.sup.-2                   
A.sub.8 = 0.967851 × 10.sup.-5                                      
                   A.sub.8 = -0.110813 × 10.sup.-3                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface                                                               
K = -0.113200 × 10                                                  
A.sub.4 = 0.130254 × 10.sup.-2                                      
A.sub.6 = 0.863731 ×  10.sup.-3                                     
A.sub.8 = 0.000000                                                        
A.sub.10 = 0.000000                                                       
______________________________________                                    
 
    
     EXAMPLE 16 
     FIG. 45 shows the sixteenth example. The numerical data thereof is shown in Table 16. The aberrations are shown in FIG. 46. 
     
                       TABLE 16                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 1.80 ω = 39.7°                          
Stop position: 0.656 mm after fourth surface                              
______________________________________                                    
Surface                                                                   
No.       r        d          n     ν                                  
______________________________________                                    
1         -5.168   1.000      1.54510                                     
                                    54.3                                  
2         2.028    4.087                                                  
3         1.987    4.488      1.54510                                     
                                    54.3                                  
4         -4.271   0.500                                                  
5         ∞  0.700      1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = 0.324000 × 10.sup.-1                                            
                   K = 0.153200                                           
A.sub.4 = 0.134250 × 10.sup.-1                                      
                   A.sub.4 = -0.265704 × 10.sup.-1                  
A.sub.6 = -0.570018 × 10.sup.-3                                     
                   A.sub.6 = 0.700370 × 10.sup.-2                   
A.sub.8 = 0.195283 × 10.sup.-4                                      
                   A.sub.8 = -0.918400 × 10.sup.-3                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
4th surface                                                               
K = -0.882300                                                             
A.sub.4 = -0.121141 × 10.sup.- 2                                    
A.sub.6 = 0.196613 × 10.sup.-2                                      
A.sub.8 = 0.000000                                                        
A.sub.10 = 0.000000                                                       
______________________________________                                    
 
    
     EXAMPLE 17 
     FIG. 47 shows the seventheenth example. The numerical data thereof is shown in Table 17. The aberrations are shown in FIG. 48. 
     
                       TABLE 17                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 2.43 ω = 31.6°                          
Stop position: 0.236 mm after fourth surface                              
______________________________________                                    
Surface                                                                   
No.       r        d          n     ν                                  
______________________________________                                    
1         -6.091   1.000      1.54510                                     
                                    54.3                                  
2         2.350    3.708                                                  
3         2.219    4.964      1.54510                                     
                                    54.3                                  
4         -4.684   0.500                                                  
5         ∞  0.700      1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = 0.154000 × 10.sup.-1                                            
                   K = -0.152200                                          
A.sub.4 = 0.123166 × 10.sup.-1                                      
                   A.sub.4 = -0.990593 × 10.sup.-2                  
A.sub.6 = -0.790303 × 10.sup.-3                                     
                   A.sub.6 = 0.415368 × 10.sup.-2                   
A.sub.8 = 0.265373 × 10.sup.-4                                      
                   A.sub.8 = -0.562239 × 10.sup.-3                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface                                                               
K = -0.938200                                                             
A.sub.4 = -0.917848 × 10.sup. -3                                    
A.sub.6 = 0.000000                                                        
A.sub.8 = 0.000000                                                        
A.sub.10 = 0.000000                                                       
______________________________________                                    
 
    
     EXAMPLE 18 
     FIG. 49 shows the eighteenth example. The numerical data thereof is shown in Table 18. The aberrations are shown in FIG. 50. 
     
                       TABLE 18                                                    
______________________________________                                    
F.sub.no = 1:4.0 f = 2.43 ω = 31.6°                          
______________________________________                                    
Surface                                                                   
No.       r        d          n     ν                                  
______________________________________                                    
1         -6.653   1.000      1.54510                                     
                                    54.3                                  
2         2.503    3.402                                                  
3         2.031    3.888      1.54510                                     
                                    54.3                                  
4         -5.129   0.500                                                  
5         ∞  0.700      1.51633                                     
                                    64.1                                  
6         ∞                                                         
______________________________________                                    
Asphericity coefficient:                                                  
1st surface        2nd surface                                            
K = -0.105000 × 10.sup.-1                                           
                   K = -0.132000 × 10.sup.-1                        
A.sub.4 = 0.149108 × 10.sup.-1                                      
                   A.sub.4 = 0.151142 × 10.sup.-2                   
A.sub.6 = -0.797289 × 10.sup.-3                                     
                   A.sub.6 = 0.540760 × 10.sup.-2                   
A.sub.8 = 0.193630 × 10.sup.-4                                      
                   A.sub.8 = -0.165097 × 10.sup.-3                  
A.sub.10 = 0.000000                                                       
                   A.sub.10 = 0.000000                                    
3rd surface                                                               
K = -0.928400                                                             
A.sub.4 = 0.217473 × 10.sup.-2                                      
A.sub. 6 = 0.000000                                                       
A.sub.8 = 0.000000                                                        
A.sub.10 = 0.000000                                                       
______________________________________                                    
 
    
     As described above, according to the invention, it is possible to simplify the imaging lens only with the correcting lens being aspherical surfaces on both sides and imaging lens.