Abstract:
An afocal zoom lens system comprising a first lens group having positive refractive power, a second lens group having negative refractive power, a third lens group having positive refractive power, and a fourth lens group having negative refractive power, the zoom lens system as a whole being arranged as an afocal lens system, the afocal zoom lens system being arranged to be zoomed by respectively varying the airspaces between respective lens groups.

Description:
BACKGROUND OF THE INVENTION 
     (a) Field of the Invention 
     The present invention relates to an afocal zoom lens system and, more particularly, to an afocal zoom lens system to be used with microscopes and the like. 
     (b) Description of the Prior Art 
     Many zoom lens systems with comparatively low magnifications to be used with stereomicroscopes, operation microscopes, etc. are known, for example, as disclosed in Japanese published examined patent applications Nos. 31259/73, 2916/69, 18356/68, 12714/68 and so forth. Though the zoom lens systems disclosed in said patent applications have individually different zoom ratios, they are all converging optical systems and, therefore, it is impossible to use them in combination with a photographing device, television device, incident light illumination device provided coaxially with the optical axis of an observation optical system, etc. 
     Besides, afocal zoom lens systems for photographic cameras are known, for example, as disclosed in Japanese published examined patent applications Nos. 41402/80, 40849/80, 9094/78 and No. 13663/76. However, none of the zoom lens systems desclosed in said patent applications have sufficiently large zoom ratio. 
     SUMMARY OF THE INVENTION 
     It is, therefore, a primary object of the present invention to provide an afocal zoom lens system with a large zoom ratio which is capable of being used in combination with a photographing device, television device and so forth. 
     The afocal zoom lens system according to the present invention comprises, in the order from the object side as shown in FIG. 3, a first lens group comprising at least one positive cemented doublet, which consists of a positive lens element and a negative lens element, and having positive refractive power, a second lens group comprising at least one negative cemented doublet, which consists of a positive lens element and a negative lens element, and having negative refractive power, a third lens group comprising at least one positive cemented doublet, which consists of a negative lens element and a positive lens element, and having positive refractive power, and a fourth lens group comprising at least one negative cemented meniscus doublet, which consists of a negative lens element and a positive lens element, and having negative refractive power, said afocal zoom lens system according to the present invention being arranged to vary the focal length of the lens system as a whole by varying the airspace between the first and second lens groups, the airspace between the second and third lens groups, and the airspace between the third and fourth lens groups respectively, said afocal zoom lens system according to the present invention being further arranged to fulfill the conditions (1) through (7) shown below: 
     
         -0.35×f.sub.I &lt;f.sub.II &lt;-0.25×f.sub.I         ( 1) 
    
     
         0.4×f.sub.I &lt;f.sub.III &lt;0.6×f.sub.I            ( 2) 
    
     
         -1×f.sub.I &lt;f.sub.IV &lt;-0.6l ×f.sub.I           ( 3) 
    
     
         25&lt;ν.sub.1T -ν.sub.1O                                ( 4) 
    
     
         20&lt;ν.sub.2O -ν.sub.2T                                ( 5) 
    
     
         35&lt;ν.sub.3T -ν.sub.3O                                ( 6) 
    
     
         0&lt;ν.sub.4O -ν.sub.4T                                 ( 7) 
    
     where, reference symbols f I , f II , f III  and f IV  respectively represent focal lengths of the first, second, third and fourth lens groups, reference symbols ν 1T , ν 2T , ν 3T  and ν 4T  respectively represent mean values of Abbe&#39;s numbers of positive lens elements in the first, second, third and fourth lens groups and reference symbols ν 1O , νv 2O , ν 3O  and ν 4O  respectively represent mean values of Abbe&#39;s numbers of negative lens elements in the first, second, third and fourth lens group. 
     Out of respective conditions shown in the above, the conditions (1) through (3) respectively define the basic composition of the afocal zoom lens system according to the present invention. By selecting the ratios between the focal lengths of respective lens groups so as to fulfill the conditions (1) through (3), it is possible to obtain a zoom lens system with a large zoom ratio by providing the distances between the principal points of respective lens groups and airspaces betewen respective lens groups so that respective lens groups will not interfere with each other in the maximum focal length position or in the minimum focal length position. 
     When the value of f II  becomes smaller than the lower limit of the condition (1), it is convenient for correction of aberrations. However, the first and second lens groups will interfere with each other in the minimum focal length position. Besides, when it is attempted to prevent interference between the first and second lens groups by maintaining a large zoom ratio, it is unavoidable to shift the zooming range toward the maximum focal length side. In that case, the second lens group will interfere with the third lens group, and this is not desirable. To prevent the second lens group from interfering with the third lens group, it is necessary to make the focal length of the third lens group long. In that case, the amount of movement of the third lens group at the time of zooming becomes large, variation of aberrations in respective states of zooming increases, and this is not preferable. Moreover, the overall length of the lens system becomes long, and the intensity of light in the marginal portion becomes insufficient. When the value of f II  becomes larger than the upper limit of the condition (1), the first, second and third lens groups do not interfere with each other, and it is possible to make the zoom ratio still larger. However, aberrations caused by the second lens group becomes large, variation of aberrations at the time of zooming becomes large, and it is impossible to correct aberrations favourably over the range from the minimum focal length position to the maximum focal length position. 
     If the value of f III  becomes smaller than the lower limit of the condition (2), the third lens group will interfere with the second lens group in the maximum focal length position and with the fourth lens group in the minimum focal length position, and it is impossible to make the zoom ratio large. To prevent the above, the absolute values of focal lengths of the second and fourth lens groups should be made small. As a result, aberrations caused by the second lens group become large, and variation of aberrations at the time of zooming become large. Besides, aberrations caused by the fourth lens group also become large, and aberrations become unfavourable in all states of zooming. When the value of f III  becomes larger than the upper limit of the condition (2), the third lens group will not tend to interfere with the second lens group or the fourth lens group, and it is possible to make the zoom ratio still larger. However, the amount of movement of the third lens group at the time of zooming becomes large and, consequently, variation of aberrations becomes large. Moreover, the overall length of the lens system becomes long, and the intensity of light in the marginal portion tends to become insufficient. 
     If the value of f IV  becomes smaller than the lower limit of the condition (3), the third lens group tends to interfere with the fourth lens group in the minimum focal length position, and it is impossible to make the zoom ratio large. To prevent the above, it is necessary to make the focal length of the third lens group long. As a result, the amount of movement of the third lens group at the time of zooming becomes large, variation of aberrations becomes large, the overall length of the lens system becomes long, and the intensity of light in the marginal portion tends to become insufficient. When the value of f IV  becomes larger that the upper limit of the condition (3), the third and fourth lens groups will not tend to interfere with each other, and it is possible to make the zoom ratio still larger. However, aberrations caused by the fourth lens group become large, and aberrations become unfavourable in all states of zooming. 
     The conditions (4) through (7) are established in order to correct chromatic aberration favourably over a wide zooming range. By selecting Abbe&#39;s numbers of respective lens elements so as to fulfill these conditions, it is possible to obtain an image with favourable contrast which is free from chromatic aberration over a wide range from the maximum focal length position to the minimum focal length position. 
     If the value of (ν 1T  -ν 1O ) becomes lower than the lower limit of the condition (4), longitudinal chromatic aberration becomes unfavourable especially in the maximum focal length position. When it is attempted to correct said longitudinal chromatic aberration by means of selection of Abbe&#39;s numbers of respective lens elements in the other lens group, lateral chromatic aberration in the minimum focal length position becomes unfavourable. When it is attempted to correct said longitudinal chromatic aberration by adjusting the bending of the cemented surface of the cemented doublet in the first lens group, spherical chromatic aberration becomes unfavourable especially in the maximum focal length position though it is possible to correct paraxial chromatic aberration favourably. 
     If the value of (ν 2O  -ν 2T ) becomes lower than the lower limit of the condition (5), longitudinal chromatic aberration becomes unfavourable in the positions of maximum focal length to medium focal length. When it is attempted to correct said longitudinal chromatic aberration by means of selection of Abbe&#39;s numbers of respective lens elements in the other lens groups, lateral chromatic aberration becomes unfavourable in the positions of medium focal length to minimum focal length. When it is attempted to correct said lateral chromatic aberration by adjusting the bendings of respective lens surfaces, the difference between chromatic aberration in the maximum focal length position and chromatic aberration in the minimum focal length position becomes large, and it is difficult to favourably correct chromatic aberration in the maximum focal length position and chromatic aberration in the minimum focal length position at the same time. 
     If the value of (ν 3T  -ν 3O ) becomes smaller than the lower limit of the condition (6), longitudinal chromatic aberration becomes unfavourable in the positions of maximum focal length to medium focal length. When it is attempted to correct said longitudinal chromatic aberration by means of selection of Abbe&#39;s numbers of respective lens elements in the other lens groups, lateral chromatic aberration becomes unfavourable in the positions of medium focal length to minimum focal length. When it is attempted to correct said lateral chromatic aberration by adjusting the bendings of respective lens surfaces, the difference between chromatic aberration in the maximum focal length position and chromatic aberration in the minimum focal length position become large, and it is difficult to favourably correct chromatic aberration in the maximum focal length position and chromatic aberration in the minimum focal length position at the same time. 
     If the value of (ν 4O  -ν 4T ) becomes lower than the lower limit of the condition (7), chromatic aberration becomes unfavourable in the whole zooming range. When it is attempted to correct said chromatic aberration by adjusting the bendings of respective lens surfaces, chromatic aberration in the maximum focal length position becomes unfavourable, and it is impossible to obtain a favourable image. 
     By adopting the lens configuration shown in FIG. 3 and arranging to fulfill the conditions (1) through (7) described so far, it is possible to obtain an afocal zoom lens system having favourable performance over a wide range from the minimum focal length position to the maximum focal length position. However, it is possible to obtain a more favourable afocal zoom lens system when it is arranged to further fulfill the conditions (8) through (13) shown below: 
     
         0.1&lt;n.sub.1O -n.sub.1T                                     ( 8) 
    
     
         n.sub.T -n.sub.2O &lt;0.25                                    (9) 
    
     
         0.2&lt;n.sub.3O -n.sub.3T                                     ( 10) 
    
     
         -1&lt;r.sub.1F /r.sub.1R &lt;-0.3                                (11) 
    
     
         r.sub.3F /r.sub.3R &lt;0                                      (12) 
    
     
         1&lt;r.sub.bR /r.sub.4F &lt;3                                    (13) 
    
     where, reference symbols n 1T , n 2T  and n 3T  respectively represent mean values of refractive indices of positive lens elements constituting the first, second and third lens groups, reference symbols n 1O , n 2O  and n 3O  respectively represent mean values of refractive indices of negative lens elements constituting the first, second and third lens groups, reference symbols r 1F  and r 1R  respectively represent radii of curvature of the surface on the object side and surface on the image side of the cemented doublet in the first lens group, reference symbols r 3F  and r 3R  respectively represent radii of curvature of the surface on the object side and surface on the image side of the cemented doublet in the third lens group, and reference symbols r 4F  and r 4R  respectively represent radii of curvature of the surface on the object side and surface on the image side of the cemented doublet in the fourth lens group. 
     Out of the conditions (8) through (13) shown in the above, the conditions (8) through (10) are established in order to maintain Petzval&#39;s sum favourably and to correct curvature of field favourably over a wide zooming range. 
     When the value of (n 1O  -n 1T ) becomes smaller than the lower limit of the condition (8), Petzval&#39;s sum becomes a negative value with a large absolute value, and curvature of field becomes unfavourable. When it is attempted to correct it by adjusting the bendings of respective lens surfaces, spherical aberration in the maximum focal length position and spherical chromatic aberration become unfavourable. 
     When the value of (n 2T  -n 2O ) becomes larger than the upper limit of the condition (9), Petzval&#39;s sum becomes a negative value with a large absolute value, and curvature of field becomes unfavourable. When it is attempted to correct it by adjusting the bendings of respective lens surfaces, spherical aberration and astigmatism become unfavourable in the positions of maximum focal length to medium focal length. 
     When the value of (n 3O  -n 3T ) becomes smaller than the lower limit of the condition (10), Petzval&#39;s sum becomes a negative value with a large absolute value, and curvature of field becomes unfavourable. When it is attempted to correct it by adjusting the bendings of respective lens surfaces, astigmatism becomes unfavourable in the whole zooming range. 
     When the value of r 1F  /r 1R  becomes smaller than the lower limit of the condition (11), the first and second lens groups will not tend to interfere with each other, and it is possible to obtain a still larger zoom ratio. However, spherical aberration in the maximum focal length position will be aggravated considerably and, when it is attempted to correct said spherical aberration by adjusting the bendings of the other lens surfaces or by some other means, astigmatism and coma become unfavourable in the minimum focal length position. When the value of r 1F  /r 1R  becomes larger than the upper limit of the condition (11), the first and second lens groups tend to interfere with each other in the maximum focal length position, and it is difficult to obtain a large zoom ratio. 
     When the value of r 3F  /r 3R  becomes larger than the upper limit of the condition (12), spherical aberration becomes unfavourable in the minimum focal length position. When it is attempted to correct said spherical aberration by adjusting the bendings of the lens elements in the first lens group or second lens group, spherical aberration becomes unfavourable in the maximum focal length position. When it is attempted to correct said spherical aberration in the minimum focal length position by adjusting the bendings of the lens elements in the fourth lens group, spherical aberration becomes unfavourable in the whole zooming range from the minimum focal length position to the maximum focal length position. 
     When the value of r 4R  /r 4F  becomes smaller than the lower limit of the condition (13), spherical aberration becomes unfavourable in the whole zooming range from the minimum focal length position to the maximum focal length position. When it is attempted to correct said spherical aberration by adjusting the bendings of the other lens surfaces, it is impossible to correct spherical aberration in the maximum focal length position favourable. When the value of r 4R  /r 4F  becomes larger than the upper limit of the condition (13), spherical aberration will be corrected favourably. However, the third and fourth lens groups tend to interfere with each other in the maximum focal length position, and it is difficult to obtain a wide zooming range. When the focal length of the third lens group is made large in order to prevent the above-mentioned interference, the amount of movement of the third lens group at the time of zooming becomes large, and variation of aberrations becomes large. Moreover, the overall length of the lens system becomes long, and the intensity of light in the marginal position becomes insufficient in the minimum focal length position. 
     To correct aberrations more favourably, it is preferable to arrange that the afocal zoom lens system according to the present invention further fulfills the conditions (14) through (16) shown below: 
     
         0.5&lt;r.sub.3F /f.sub.III                                    ( 14) 
    
     
         1.54&lt;n.sub.2O                                              ( 15) 
    
     
         1.57&lt;n.sub.4O                                              ( 16) 
    
     where, reference symbol n 4O  represents the mean value of refractive indices of negative lens elements in the fourth lens group. 
     The condition (14) is established in order to correct spherical aberration in the minimum focal length position favourably. When the condition (14) is not fulfilled, spherical aberration becomes unfavourable in the minimum focal length position, and it is difficult to correct spherical aberration in a well balanced state over the whole zooming range. 
     The conditions (15) and (16) are established in order to correct curvature of field favourably in well balanced state over a wide range from the minimum focal length position to the maximum focal length position. 
     When the value of n 2O  becomes smaller than the lower limit of the condition (15), Petzval&#39;s sum becomes a negative value with a large absolute value, and curvature of field becomes unfavourable. When it is attempted to correct it by adjusting the bendings of respective lens surfaces, spherical aberration and astigmatism become unfavourable in the positions of maximum focal length to medium focal length. 
     When the value of n 4O  becomes smaller than the lower limit of the condition (16), Petzval&#39;s sum becomes a negative value with a large absolute value, and curvature of field becomes unfavourable. When it is attempted to correct it by adjusting the bendings of respective lens surfaces, spherical aberration becomes unfavourable in the positions of minimum focal length to maximum focal length. 
     The afocal zoom lens system according to the present invention explained so far is to be used generally by arranging an objective on the object side and an imaging lens system on the image side as described before. Therefore, when used in combination with various kinds of objectives and imaging lens systems having individually different focal lengths, it is possible to use the afocal zoom lens system according to the present invention at various magnifications suitable for the purposes of application. Besides, by coaxially arranging an incident light illumination device between the objective and afocal zoom lens system or between the afocal zoom lens system and imaging lens system or by arranging a photographing device, television device, discussion microscope or the like in combination with the afocal zoom lens system according to the present invention, it is possible to perform various kinds of observation systematically. 
     FIG. 1 shows the basic composition of an optical system which employs the afocal zoom lens system according to the present invention. In FIG. 1, numeral 1 designates an object, numeral 2 designates an objective, numeral 3 designates the afocal zoom lens system according to the present invention, numeral 4 designates an imaging lens system, and numeral 5 designates the image position. 
     As shown in FIG. 1, the rays from the object 1, which is placed at the front focal point of the objective 2, become parallel rays passing through the objective 2 and enter the afocal zoom lens system 3. The parallel rays coming out of the afocal zoom lens system 3 form the image 5 at the rear focal point of the imaging lens system 4 by means of the imaging lens system 4. The imaging magnification β T  at that time is expressed by the following formula where the magnification of the afocal zoom lens system is represented by reference symbol β A , the focal length of the imaging lens system is represented by reference symbol f F , and the focal length of the objective is represented by reference symbol f 0 . 
     
         β.sub.T =β.sub.A ×f.sub.F /f.sub.O 
    
     As it is evident from the formula shown in the above, it is possible to obtain various imaging magnifications by the same afocal zoom lens system by varying the focal length of the objective and/or the focal length of the imaging lens system. When a long working distance is required, the purpose will be attaihed by using an objective of such type that makes the distance from the objective to its front focal point long, for example, a telephoto type objective, or by using an objective which has a long focal length. In that case, the imaging magnification becomes small, but this problem can be solved by using an imaging lens system which has a long focal length. In that case, the distance from the lens system to the rear focal point becomes long, but this problem can be easily solved by selecting an adequate type of imaging lens system, for example, by using an imaging lens system of telephoto type. 
     As described in the above, it is possible to use the afocal zoom lens system according to the present invention in various magnification ranges. Besides the above-mentioned various kinds of combinations, the afocal zoom lens system according to the present invention enables to perform various kinds of observation by combining it with various kinds of units as described below. 
     FIGS. 2A, 2B, 2C and 2D respectively show examples of use of the afocal zoom lens system according to the present invention in combination with several units. In these figures, numeral 1 designates an object, numeral 2 designates an objective, numeral 3 designates the afocal zoom lens system according to the present invention, numeral 4 designates an imaging lens system, numeral 5 designates the image position, and these are substantially the same as those shown in FIG. 1. Numeral 6 designates an eyepiece, numeral 7 designates an eye of an observer, numeral 8 designates a photographing device, numeral 9 a photographic camera, numeral 10 designates an incident light illumination device provided coaxially, numeral 11 designates a lamp, numeral 12 designates a television device, and numeral 13 designates a television camera. 
     FIG. 2A shows the basic composition of an observation optical system, FIG. 2B shows an optical system when combined with a photographing device, FIG. 2C shows an optical system when combined with an incident light illumination device provided coaxially and a photographic device, and FIG. 2D shows an optical system when combined with an incident light illumination device provided coaxially, a photographing device and a television device. 
     In any of combinations shown in these figures, the quality of image does not decrease compared with the basic composition shown in FIG. 2A because the rays coming out of the afocal zoom lens system 3 are parallel rays. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows the basic composition of an optical system in which the afocal zoom lens system according to the present invention is used; 
     FIGS. 2A, 2B, 2C and 2D respectively show various examples of use of the afocal zoom lens system according to the present invention; 
     FIG. 3 shows a sectional view of Embodiments 1 through 11 of the afocal zoom lens system according to the present invention; 
     FIG. 4 shows an example of an imaging lens system to be used in combination with the afocal zoom lens system according to the present invention; and 
     FIGS. 5 through 15 respectively show graphs illustrating aberration curves of Embodiments 1 through 11 of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Now, preferred embodiments of the afocal zoom lens system according to the present invention are shown below. 
     
         ______________________________________Embodiment 1______________________________________f = 1˜8.5r.sub.1 = 0.6433d.sub.1 = 0.040 n.sub.1 = 1.48749                        ν.sub.1 = 70.2r.sub.2 = -0.5318d.sub.2 = 0.025 n.sub.2 = 1.71852                        ν.sub.2 = 33.5r.sub.3 = -1.1600d.sub.3 = 0.030˜0.493r.sub.4 = -1.2264d.sub.4 = 0.025 n.sub.3 = 1.78472                        ν.sub.3 = 25.7r.sub.5 = -0.3422d.sub.5 = 0.019 n.sub.4 = 1.48749                        ν.sub.4 = 70.2r.sub.6 = 0.5427d.sub.6 = 0.031r.sub.7 = -0.3931d.sub.7 = 0.019 n.sub.5 = 1.6228                        ν.sub.5 = 57.1r.sub.8 = 0.6539d.sub.8 = 1.014˜0.099r.sub.9 = 0.4629d.sub.9 = 0.020 n.sub.6 =  1.74                        ν.sub.6 = 28.3r.sub.10 = 0.2683d.sub.10 = 0.041           n.sub.7 = 1.4645                        ν.sub.7 = 65.9r.sub.11 = -0.5143d.sub.11 = 0.002r.sub.12 = 0.6598d.sub.12 = 0.020           n.sub.8 = 1.48749                        ν.sub.8 = 70.2r.sub.13 = 1.5338d.sub.13 = 0.093˜0.544r.sub.14 = 3.2732d.sub.14 = 0.020           n.sub.9 = 1.78472                        ν.sub.9 = 25.7r.sub.15 = 0.5110d.sub.15 = 0.045r.sub.16 = -0.2105d.sub.16 = 0.020           n.sub.10 = 1.58904                        ν.sub.10 = 53.2r.sub.17 = 0.2374d.sub.17 = 0.053           n.sub.11 = 1.60342                        ν.sub.11 = 38.0r.sub.18 = -0.2624f.sub.II = -0.284 × f.sub.I, f.sub.III = 0.499 ×  f.sub.If.sub.IV = -0.714 × f.sub.I, ν.sub.1T - ν.sub.1O = 36.7ν.sub.2O - ν.sub.2T = 37.9, ν.sub.3T - ν.sub.3O = 39.8ν.sub.4O - ν.sub.4T = 13.8, n.sub.1O - n.sub.1T = 0.23103n.sub.2T - n.sub.2O = 0.22957, n.sub.3O - n.sub.3T = 0.264r.sub.1F /r.sub.1R = -0.555, r.sub.3F /r.sub.3R = -0.900r.sub.4R /r.sub.4F = 1.247, r.sub.3F /f.sub.III = 0.869n.sub.2O = 1.55515, n.sub.4O = 1.68688______________________________________ 
    
     
         ______________________________________Embodiment 2______________________________________f = 1˜8.5r.sub.1 = 0.7084d.sub.1 = 0.041 n.sub.1 = 1.48749                        ν.sub.1 = 70.2r.sub.2 = -0.4971d.sub.2 = 0.027 n.sub.2 = 1.68893                        ν.sub.2 = 31.1r.sub.3 = -1.0800d.sub.3 = 0.027˜0.503r.sub.4 = -1.2765d.sub.4 = 0.027 n.sub.3 = 1.78472                        ν.sub.3 = 25.7r.sub.5 = -0.3023d.sub.5 = 0.019 n.sub.4 = 1.48749                        ν.sub.4 = 70.2r.sub.6 = 0.6301d.sub.6 = 0.029r.sub.7 = -0.3473d.sub.7 = 0.019 n.sub.5 = 1.62280                        ν.sub.5 = 57.1r.sub.8 = 0.6646d.sub.8 = 1.046˜0.104r.sub.9 = 0.5261d.sub.9 = 0.020 n.sub.6 =  1.69895                        ν.sub.6 = 30.1r.sub.10 = 0.2696d.sub.10 = 0.042           n.sub.7 = 1.48749                        ν.sub.7 = 70.2r.sub.11 = -0.5369d.sub.11 = 0.002r.sub.12 = 0.4993d.sub.12 = 0.020           n.sub.8 = 1.48749                        ν.sub.8 = 70.2r.sub.13 = 0.8153d.sub.13 = 0.086˜0.553r.sub.14 = 1.0709d.sub.14 = 0.020           n.sub.9 = 1.76182                        ν.sub.9 = 26.5r.sub.15 = 0.3729d.sub.15 = 0.046r.sub.16 = -0.2144d.sub.16 = 0.020           n.sub.10 = 1.57135                        ν.sub.10 = 52.9r.sub.17 = 0.2915d.sub.17 = 0.048           n.sub.11 = 1.61659                        ν.sub.11 = 36.6r.sub.18 = -0.2814f.sub.II = -0.286 × f.sub.I, f.sub.III = 0.502 ×  f.sub.If.sub.IV = -0.718 × f.sub.I, ν.sub.1T - ν.sub.1O = 39.1ν.sub.2O - ν.sub.2T = 37.9, ν.sub.3T - ν.sub.3O = 40.0ν.sub.4O - ν.sub.4T = 3.09, n.sub.1O - n.sub.1T = 0.20144n.sub.2T - n.sub.2O = 0.22957, n.sub.3O - n.sub.3T = 0.21146r.sub.1F /r.sub.1R = -0.656, r.sub.3F /r.sub.3R = -0.980r.sub.4R /r.sub.4F = 1.312, r.sub.3F /f.sub.III = 0.958n.sub.2O = 1.55515, n.sub.4O = 1.66659______________________________________ 
    
     
         ______________________________________Embodiment 3______________________________________f = 1˜8.5r.sub.1 = 0.6961d.sub.1 = 0.036 n.sub.1 = 1.48749                        ν.sub.1 = 70.2r.sub.2 = -0.6168d.sub.2 = 0.020 n.sub.2 = 1.68893                        ν.sub.2 = 31.1r.sub.3 = -1.4581d.sub.3 = 0.032˜0.553r.sub.4 = -0.6233d.sub.4 = 0.027 n.sub.3 = 1.68893                        ν.sub.3 = 31.1r.sub.5 = -0.1986d.sub.5 = 0.015 n.sub.4 = 1.617                        ν.sub.4 = 62.8r.sub.6 = 1.3167d.sub.6 = 0.020r.sub.7 = -1.0605d.sub.7 = 0.013 n.sub.5 = 1.618                        ν.sub.5 = 63.4r.sub.8 = 0.7140d.sub.8 = 1.099˜0.026r.sub.9 = 0.9852d.sub.9 = 0.022 n.sub.6 =  1.72151                        ν.sub.6 = 29.2r.sub.10 = 0.4857d.sub.10 = 0.042           n.sub.7 = 1.497                        ν.sub.7 = 81.6r.sub.11 = -0.6691d.sub.11 = 0.003r.sub.12 = 0.9359d.sub.12 = 0.038           n.sub.8 = 1.497                        ν.sub.8 = 81.6r.sub.13 = -6.6689d.sub.13 = 0.110˜0.663r.sub.14 = -1.7152d.sub.14 = 0.015           n.sub.9 = 1.6968                        ν.sub.9 = 55.5r.sub.15 = 0.9348d.sub.15 = 0.023r.sub.16 = -0.3374d.sub.16 = 0.017           n.sub.10 = 1.48749                        ν.sub.10 = 70.2r.sub.17 = 0.4072d.sub.17 = 0.050           n.sub.11 = 1.5927                        ν.sub.11 = 35.3r.sub.18 = -0.5438f.sub.II = -0.306 × f.sub.I, f.sub.III =  -0.528 × f.sub.If.sub.IV = -0.743 × f.sub.I, ν.sub.1T - ν.sub.1O = 39.1ν.sub.2O - ν.sub.2T = 32.0, ν.sub.3T - ν.sub.3O = 52.4ν.sub.4O - ν.sub.4T = 27.55, n.sub.1O - n.sub.1T = 0.20144n.sub.2T - n.sub.2O = 0.07143, n.sub.3O - n.sub.3T = 0.22451r.sub.1F /r.sub.1R = -0.477, r.sub.3F /r.sub.3R = -1.472r.sub.4R /r.sub.4F = 1.612, r.sub.3F /f.sub.III = 1.572n.sub.2O = 1.6175, n.sub.4O = 1.59215______________________________________ 
    
     
         ______________________________________Embodiment 4______________________________________f = 1˜8.5r.sub.1 = 0.4890d.sub.1 = 0.044 n.sub.1 = 1.48749                        ν.sub.1 = 70.2r.sub.2 = -0.5133d.sub.2 = 0.025 n.sub.2 = 1.74                        ν.sub.2 = 31.7r.sub.3 = -1.2298d.sub.3 = 0.028˜0.415r.sub.4 = -1.7147d.sub.4 = 0.026 n.sub.3 = 1.78472                        ν.sub.3 = 25.7r.sub.5 = -0.2409d.sub.5 = 0.019 n.sub.4 = 1.72916                        ν.sub.4 = 54.7r.sub.6 = 0.6446d.sub.6 = 0.02r.sub.7 = -0.6745d.sub.7 = 0.019 n.sub.5 = 1.6968                        ν.sub.5 = 56.5r.sub.8 = 0.5799d.sub.8 = 0.899˜0.067r.sub.9 = 30.6851d.sub.9 = 0.02  n.sub.6 =  1.78472                        ν.sub.6 = 25.7r.sub.10 = 0.8484d.sub.10 = 0.029           n.sub.7 = 1.497                        ν.sub.7 = 81.6r.sub.11 = -0.4200d.sub.11 = 0.001r.sub.12 = 0.6021d.sub.12 = 0.026           n.sub.8 = 1.497                        ν.sub.8 = 81.6r.sub.13 = -1.9742d.sub.13 = 0.058˜0.503r.sub.14 = 1.0666d.sub.14 = 0.02 n.sub.9 = 1.8044                        ν.sub.9 = 39.6r.sub.15 = 0.4589d.sub.15 = 0.042r.sub.16 = -0.2689d.sub.16 = 0.02 n.sub.10 = 1.51118                        ν.sub.10 = 51.0r.sub.17 = 0.3069d.sub.17 = 0.042           n.sub.11 = 1.5927                        ν.sub.11 = 35.3r.sub.18 = -0.5009f.sub.II = -0.296 × f.sub.I, f.sub.III = 0.563 × f.sub.If.sub.IV = -0.838 × f.sub.I, ν.sub.1T - ν.sub.1O = 38.5ν.sub.2O - ν.sub.2T = 29.9, ν.sub.3T - ν.sub.3O = 55.9ν.sub.4O - ν.sub.4T = 10.01, n.sub.1O - n.sub.1T = 0.25251n.sub.2T - n.sub.2O = 0.07174, n.sub.3O - n.sub.3T = 0.28772r.sub.1F /r.sub.1R = -0.398, r.sub.3F /r.sub.3R = -73.068r.sub.4R /r.sub.4F = 1.863, r.sub.3F /f.sub.III = 59.867n.sub.2O = 1.71298, n.sub.4O = 1.65779______________________________________ 
    
     
         ______________________________________Embodiment 5______________________________________f = 1˜8.5r.sub.1 = 0.9250d.sub.1 = 0.037 n.sub.1 = 1.48749                        ν.sub.1 = 70.2r.sub.2 = -0.4910d.sub.2 = 0.025 n.sub.2 = 1.66446                        ν.sub.2 = 35.7r.sub.3 = -1.0438d.sub.3 = 0.039˜0.594r.sub.4 = -1.1582d.sub.4 = 0.028 n.sub.3 = 1.69895                        ν.sub.3 = 30.1r.sub.5 = -0.2321d.sub.5 = 0.016 n.sub.4 = 1.6425                        ν.sub.4 = 58.4r.sub.6 = 0.9213d.sub.6 = 0.019r.sub.7 = -0.6726d.sub.7 = 0.016 n.sub.5 = 1.6425                        ν.sub.5 = 58.4r.sub.8 = 1.1459d.sub.8 = 1.197˜0.070r.sub.9 = 0.8980d.sub.9 = 0.022 n.sub.6 =  1.72825                        ν.sub.6 = 28.5r.sub.10 = 0.4415d.sub.10 = 0.037           n.sub.7 = 1.497                        ν.sub.7 = 81.6r.sub.11 = -0.6773d.sub.11 = 0.003r.sub.12 = 0.8232d.sub.12 = 0.033           n.sub.8 = 1.497                        ν.sub.8 = 81.6r.sub.13 = 4.7356d.sub.13 = 0.049˜0.622r.sub.14 = 2.2417d.sub.14 = 0.021           n.sub.9 = 1.74                        ν.sub.9 = 31.7r.sub.15 = 0.6773d.sub.15 = 0.029r.sub.16 = -0.3326d.sub.16 = 0.021           n.sub.10 = 1.50847                        ν.sub.10 = 60.8r.sub.17 = 0.3326d.sub.17 = 0.040           n.sub.11 = 1.5927                        ν.sub.11 = 35.3r.sub.18 = -0.6358f.sub.II = -0.302 × f.sub.I, f.sub.III = 0.530 ×  f.sub.If.sub.IV = -0.781 × f.sub.I, ν.sub.1T - ν.sub.1O = 34.4ν.sub.2O - ν.sub.2T = 28.3, ν.sub.3T - ν.sub.3O = 53.2ν.sub.4O - ν.sub.4T = 11.0, n.sub.1O - n.sub.1T = 0.17697n.sub.2T - n.sub.2O = 0.05645, n.sub.3O - n.sub.3T = 0.23125r.sub.1F /r.sub.1R = -0.886, r.sub.3F /r.sub.3R = -1.326r.sub.4R /r.sub.4F = 1.912, r.sub.3F /f.sub.III = 1.352n.sub.2O = 1.6425, n.sub.4O = 1.62424______________________________________ 
    
     
         ______________________________________Embodiment 6______________________________________f = 1˜8.5r.sub.1 = 0.6785d.sub.1 = 0.041 n.sub.1 = 1.497                        ν.sub.1 = 81.6r.sub.2 = -0.4757d.sub.2 = 0.025 n.sub.2 = 1.6445                        ν.sub.2 = 40.8r.sub.3 = -1.2253d.sub.3 = 0.042˜0.503r.sub.4 = -0.8372d.sub.4 = 0.025 n.sub.3 = 1.78472                        ν.sub.3 = 25.7r.sub.5 = -0.2964d.sub.5 = 0.019 n.sub.4 = 1.48749                        ν.sub.4 = 70.2r.sub.6 = 0.6364d.sub.6 = 0.015r.sub.7 = -0.4158d.sub.7 = 0.019 n.sub.5 = 1.6228                        ν.sub.5 = 57.1r.sub.8 = 0.6018d.sub.8 = 1.010˜0.100r.sub.9 = 0.4625d.sub.9 = 0.020 n.sub.6 =  1.74                        ν.sub.6 = 28.3r.sub.10 = 0.2689d.sub.10 = 0.041           n.sub.7 = 1.4645                        ν.sub.7 = 65.9r.sub.11 = -0.5255d.sub.11 = 0.002r.sub.12 = 0.6642d.sub.12 = 0.020           n.sub.8 = 1.48749                        ν.sub.8 = 70.2r.sub.13 = 1.7010d.sub.13 = 0.103˜0.553r.sub.14 = 3.0806d.sub.14 = 0.02 n.sub.9 = 1.78472                        ν.sub.9 = 25.7r.sub.15 = 0.4844d.sub.15 = 0.031r.sub.16 = -0.1911d.sub.16 = 0.02 n.sub.10 = 1.58904                        ν.sub.10 = 53.2r.sub.17 = 0.2760d.sub.17 = 0.053           n.sub.11 = 1.60342                        ν.sub.11 = 38.0r.sub.18 = -0.2357f.sub.II = -0.284 × f.sub.I, f.sub.III = 0.499 ×  f.sub.If.sub.IV = -0.714 × f.sub.I, ν.sub.1T - ν.sub.1O = 40.81ν.sub.2O - ν.sub.2T = 37.9, ν.sub.3T - ν.sub.3O = 39.8ν.sub.4O - ν.sub.4T = 1.4, n.sub.1O - n.sub.1T = 0.1475n.sub.2T - n.sub.2O = 0.22957, n.sub.3O - n.sub.3T = 0.264r.sub.1F /r.sub.1R = -0.554, r.sub.3F /r.sub.3R = -0.880r.sub.4R /r.sub.4F = 1.233, r.sub.3F /f.sub.III = 0.872n.sub.2O = 1.55515, n.sub.4O = 1.68688______________________________________ 
    
     
         ______________________________________Embodiment 7______________________________________f = 1˜8.5r.sub.1 = 0.7291d.sub.1 = 0.041 n.sub.1 = 1.497                        ν.sub.1 = 81.61r.sub.2 = -0.4838d.sub.2 = 0.025 n.sub.2 = 1.6445                        ν.sub.2 = 40.8r.sub.3 = -1.2162d.sub.3 = 0.047˜0.519r.sub.4 = -1.9285d.sub.4 = 0.028 n.sub.3 = 1.7552                        ν.sub.3 = 27.51r.sub.5 = -0.2816d.sub.5 = 0.019 n.sub.4 = 1.641                        ν.sub.4 = 56.93r.sub.6 = 0.7541d.sub.6 = 0.012r.sub.7 = -0.5231d.sub.7 = 0.019 n.sub.5 = 1.63854                        ν.sub.5 = 55.38r.sub.8 = 0.7167d.sub.8 = 1.085˜0.076r.sub.9 = 0.7201d.sub.9 = 0.019 n.sub.6 =  1.80518                        ν.sub.6 = 25.43r.sub.10 = 0.3647d.sub.10 = 0.036           n.sub.7 = 1.50137                        ν.sub.7 = 56.4r.sub.11 = -0.5370d.sub.11 = 0.002r.sub.12 = 0.4519d.sub.12 = 0.027           n.sub.8 = 1.497                        ν.sub.8 = 81.61r.sub.13 = 0.7508d.sub.13 = 0.042˜0.579r.sub.14 = 1.2694d.sub.14 = 0.019           n.sub.9 = 1.7552                        ν.sub.9 = 27.51r.sub.15 = 0.4692d.sub.15 = 0.023r.sub.16 = -0.2983d.sub.16 = 0.019           n.sub.10 = 1.57957                        ν.sub.10 = 53.71r.sub.17 = 0.2983d.sub.17 = 0.044           n.sub.11 = 1.61659                        ν.sub.11 = 36.63r.sub.18 = -0.3977f.sub.II = -0.299 × f.sub.I, f.sub.III = 0.540 × f.sub. If.sub.IV = -0.821 × f.sub.I, ν.sub.1T - ν.sub.1O = 40.81ν.sub.2O - ν.sub.2T = 28.65, ν.sub.3T - ν.sub.3O = 43.58ν.sub.4O - ν.sub.4T = 3.98, n.sub.1O - n.sub.1T = 0.1475n.sub.2T - n.sub.2O = 0.11543, n.sub.3O - n.sub.3T = 0.30599r.sub.1F /r.sub.1R = -0.05553, r.sub.3F /r.sub.3R = -2.557r.sub.4R /r.sub.4F = 1.333, r.sub.3F /f.sub.III = 1.2n.sub.2O = 1.63977, n.sub.4O = 1.67212______________________________________ 
    
     
         ______________________________________Embodiment 8______________________________________f = 1˜8.5r.sub.1 = 0.9057d.sub.1 = 0.036 n.sub.1 = 1.497                        ν.sub.1 = 81.61r.sub.2 = -0.4744d.sub.2 = 0.024 n.sub.2 = 1.66755                        ν.sub.2 = 41.93r.sub.3 = -1.0323d.sub.3 = 0.038˜0.571r.sub.4 = -1.1039d.sub.4 = 0.027 n.sub.3 = 1.69895                        ν.sub.3 = 30.12r.sub.5 = -0.2230d.sub.5 = 0.015 n.sub.4 = 1.6425                        β.sub.4 = 58.37r.sub.6 = 0.9072d.sub.6 = 0.018r.sub.7 = -0.6354d.sub.7 = 0.015 n.sub.5 = 1.6425                        ν.sub.5 = 58.37r.sub.8 = 1.1111d.sub.8 = 1.1473˜0.067r.sub.9 = 0.8719d.sub.9 = 0.022 n.sub.6 =  1.72825                        ν.sub.6 = 28.46r.sub.10 = 0.4221d.sub.10 = 0.036           n.sub.7 = 1.497                        ν.sub.7 = 81.61r.sub.11 = -0.6249d.sub.11 = 0.003r.sub.12 = 0.7691d.sub.12 = 0.032           n.sub.8 = 1.497                        ν.sub.8 = 81.61r.sub.13 = 3.3266d.sub.13 = 0.035˜0.582r.sub.14 = 2.2185d.sub.14 = 0.020           n.sub.9 = 1.74                        ν.sub.9 = 31.7r.sub.15 = 0.7277d.sub.15 = 0.028r.sub.16 = -0.3759d.sub.16 = 0.020           n.sub.10 = 1.50847                        ν.sub.10 = 60.83r.sub.17 = 0.3198d.sub.17 = 0.038           n.sub.11 = 1.5927                        ν.sub.11 = 35.29r.sub.18 = -0.8989f.sub.II = -0.302 × f.sub.I, f.sub.III = 0.53 ×  f.sub.If.sub.IV = -0.782 × f.sub.I, ν.sub.1T - ν.sub.1O = 39.68ν.sub.2O - ν.sub.2T = 28.25, ν.sub.3T - ν.sub.3O = 53.15ν.sub.4O - ν.sub.4T = 11.01, n.sub.1O - n.sub.1T = 0.17155n.sub.2T - n.sub.2O = 0.05645, n.sub.3O - n.sub.3T = 0.23125r.sub.1F /r.sub.1R = -0.877, r.sub.3F /r.sub.3R = -1.395r.sub.4R /r.sub.4F = 2.392, r.sub.3F /f.sub.III = 1.366n.sub.2O = 1.6425, n.sub.4O = 1.62424______________________________________ 
    
     
         ______________________________________Embodiment 8______________________________________f = 1˜8.5r.sub.1 = 0.6822d.sub.1 = 0.038 n.sub.1 = 1.497                        ν.sub.1 = 81.61r.sub.2 = -0.5269d.sub.2 = 0.024 n.sub.2 = 1.6445                        ν.sub.2 = 40.8r.sub.3 = -1.4201d.sub.3 = 0.027˜0.517r.sub.4 = -1.4065d.sub.4 = 0.025 n.sub.3 = 1.7552                        ν.sub.3 = 27.51r.sub.5 = -0.2768d.sub.5 = 0.019 n.sub.4 = 1.641                        ν.sub.4 = 56.93r.sub.6 = 0.9065d.sub.6 = 0.017r.sub.7 = -0.5489d.sub.7 = 0.019 n.sub.5 = 1.63854                        ν.sub.5 = 55.38r.sub.8 = 0.7053d.sub.8 = 1.088˜0.078r.sub.9 = 0.5977d.sub.9 = 0.019 n.sub.6 =  1.78472                        ν.sub.6 = 25.68r.sub.10 = 0.3187d.sub.10 = 0.036           n.sub.7 = 1.50137                        ν.sub.7 = 56.4r.sub.11 = -0.5445d.sub.11 = 0.002r.sub.12 = 0.5060d.sub.12 = 0.026           n.sub.8 = 1.497                        ν.sub.8 = 81.61r.sub.13 = 0.7310d.sub.13 = 0.050˜0.570r.sub.14 = 1.0314d.sub.14 = 0.019           n.sub.9 = 1.7552                        ν.sub.9 = 27.51r.sub.15 = 0.4415d.sub.15 = 0.032r.sub.16 = -0.2832d.sub.16 = 0.019           n.sub.10 = 1.57135                        ν.sub.10 = 52.92r.sub.17 = 0.2819d.sub.17 = 0.041           n.sub.11 = 1.61659                        ν.sub.11 = 36.63r.sub.18 = -0.3990f.sub.II = -0.301 × f.sub.I, f.sub.III = 0.541 ×  f.sub.If.sub.IV = -0.809 × f.sub.I, ν.sub.1T - ν.sub.1O = 40.81ν.sub.2O - ν.sub.2T = 28.65, ν.sub.3T - ν.sub.3O = 43.33ν.sub.4O - ν.sub.4T = 3.57, n.sub.1O - n.sub.1T = 0.1475n.sub.2T - n.sub.2O = 0.11543, n.sub.3O - n.sub.3T = 0.28553r.sub.1F /r.sub.1R = -0.480, r.sub.3F /r.sub.3R = -1.098r.sub.4R /r.sub.4F = 1.409, r.sub.3F /f.sub.III = 0.99n.sub.2O = 1.63977, n.sub.4O = 1.66328______________________________________ 
    
     
         ______________________________________Embodiment 10______________________________________f = 1˜8.5r.sub.1 = 0.7258d.sub.1 = 0.041 n.sub.1 = 1.51728                        ν.sub.1 = 69.56r.sub.2 = -0.5836d.sub.2 = 0.024 n.sub.2 = 1.85026                        ν.sub.2 = 32.28r.sub.3 = -1.1102d.sub.3 = 0.051˜0.582r.sub.4 = -1.9238d.sub.4 = 0.028 n.sub.3 = 1.7552                        ν.sub.3 = 27.51r.sub.5 = -0.2808d.sub.5 = 0.019 n.sub.4 = 1.641                        ν.sub.4 = 56.93r.sub.6 = 0.7522d.sub.6 = 0.012r.sub.7 = -0.5216d.sub.7 = 0.019 n.sub.5 = 1.63854                        ν.sub.5 = 55.38r.sub.8 = 0.7149d.sub.8 = 1.112˜0.107r.sub.9 = 0.7167d.sub.9 = 0.019 n.sub.6 =  1.80518                        ν.sub.6 = 25.43r.sub.10 = 0.3638d.sub.10 = 0.036           n.sub.7 = 1.59137                        ν.sub.7 = 56.4r.sub.11 = -0.5358d.sub.11 = 0.002r.sub.12 = 0.4508d.sub.12 = 0.026           n.sub.8 = 1.497                        ν.sub.8 = 81.61r.sub.13 = 0.7465d.sub.13 = 0.043˜0.578r.sub.14 = 1.2661d.sub.14 = 0.019           n.sub.9 = 1.7552                        ν.sub.9 = 27.51r.sub.15 = 0.4683d.sub.15 = 0.023r.sub.16 = -0.2974d.sub.16 = 0.019           n.sub.10 = 1.57957                        ν.sub.10 = 53.71r.sub.17 = 0.2974d.sub.17 = 0.044           n.sub.11 = 1.61659                        ν.sub.11 = 36.63r.sub.18 = -0.3968f.sub.II = -0.299 × f.sub.I, f.sub.III = 0.54 ×  f.sub.If.sub.IV = -0.821 × f.sub.I, ν.sub.1T - ν.sub.1O = 37.28ν.sub.2O - ν.sub.2T = 28.65, ν.sub.3T - ν.sub.3O = 43.58ν.sub.4O - ν.sub.4T = 3.97, n.sub.1O - n.sub.1T = 0.33298n.sub.2T - n.sub.2O = 0.11543, n.sub.3O - n.sub.3T = 0.30599r.sub.1F /r.sub.1R = -0.654, r.sub.3F /r.sub.3R = -1.338r.sub.4R /r.sub.4F = 1.334, r.sub.3F /f.sub.III = 1.197n.sub.2O = 1.63977, n.sub.4O = 1.66739______________________________________ 
    
     
         ______________________________________Embodiment 11______________________________________f = 1˜8.5r.sub.1 = 0.6603d.sub.1 = 0.041 n.sub.1 = 1.50137                        ν.sub.1 = 56.4r.sub.2 = -0.5920d.sub.2 = 0.024 n.sub.2 = 1.76182                        ν.sub.2 = 26.52r.sub.3 = -1.2931d.sub.3 = 0.035˜0.505r.sub.4 = 9.7907d.sub.4 = 0.033 n.sub.3 = 1.78472                        ν.sub.3 = 25.71r.sub.5 = -0.2700d.sub.5 = 0.019 n.sub.4 = 1.6425                        ν.sub.4 = 58.37r.sub.6 = 0.6562d.sub.6 = 0.012r.sub.7 = -0.4096d.sub.7 = 0.019 n.sub.5 = 1.63636                        ν.sub.5 = 35.37r.sub.8 = 0.5871d.sub.8 = 1.080˜0.076r.sub.9 = 0.9454d.sub.9 = 0.019 n.sub.6 =  1.80518                        ν.sub.6 = 25.43r.sub.10 = 0.3961d.sub.10 = 0.040           n.sub.7 = 1.50137                        ν.sub.7 = 56.4r.sub.11 = -0.4613d.sub.11 = 0.002r.sub.12 = 0.4050d.sub.12 = 0.022           n.sub.8 = 1.497                        ν.sub.8 = 81.61r.sub.13 = 0.6706d.sub.13 = 0.029˜0.563r.sub.14 = 0.8435d.sub.14 = 0.019           n.sub.9 = 1.74                        ν.sub.9 = 28.29r.sub.15 = 0.4287d.sub.15 = 0.019r.sub.16 = -0.3421d.sub.16 = 0.019           n.sub.10 = 1.55671                        ν.sub.10 = 58.68r.sub.17 = 0.3206d.sub.17 = 0.044           n.sub.11 = 1.62004                        ν.sub.11 = 36.25r.sub.18 = -0.5842f.sub.II = -0.299 × f.sub.I, f.sub.III = 0.540 ×  f.sub.If.sub.IV = -0.821 × f.sub.I, ν.sub.1T - ν.sub.1O = 29.88ν.sub.2O - ν.sub.2T = 21.16, ν.sub.3T - ν.sub.3O = 43.58ν.sub.4O - ν.sub.4T = 7.24, n.sub.1O - n.sub.1T = 0.26045n.sub.2T - n.sub.2O = 0.14529, n.sub.3O - n.sub.3T = 0.30600r.sub.1F /r.sub.1R = -0.511, r.sub.3F /r.sub.3R = -2.049r.sub.4R /r.sub.4F = 1.708, r.sub.3F /f.sub.III = -1.580n.sub.2O = 1.63943, n.sub.4O = 1.64836______________________________________ 
    
     In embodiments shown in the above, reference symbols r 1  through r 18  respectively represent radii of curvature of respective lens surfaces, reference symbols d 1  through d 17  respectively represent thicknesses of respective lenses and airspaces between respective lenses, reference symbols n 1  through n 11  respective represent refractive indices of respective lenses, and reference symbols ν 1  through ν 11  respectively represent Abbe&#39;s numbers of respective lenses. 
     These embodiments respectively have the lens configuration as shown in FIG. 3 and, as the zoom lens system according to the present invention is an afocal lens system, the numerical data of respective embodiments are arranged that, when combined with an imaging lens system having the lens configuration as shown in FIG. 4 and having the following numerical data, the total focal length f of the lens system as a whole in the wide position becomes 1. 
     
         ______________________________________r.sub.1 = 0.5002d.sub.1 = 0.027          n.sub.1 = 1.8061                        ν.sub.1 = 40.95r.sub.2 = 0.3652d.sub.2 = 0.038          n.sub.2 = 1.48749                        ν.sub.2 = 70.15r.sub.3 = 2.8677d.sub.3 = 0.959r.sub.4 = -0.4091d.sub.4 = 0.027          n.sub.3 = 1.48749                        ν.sub.3 = 70.15r.sub.5 = -0.8493f.sub.F = 2.786,          S.sub.F = 1.061______________________________________ 
    
     In the numerical data of the imaging lens system shown in the above, reference symbols f F  and S F  respectively represent the focal length and image position of the imaging lens system. 
     Aberration curves of Embodiments 1 through 11 shown in the above are respectively shown in FIGS. 5 through 15. Graphs of aberration curves in these figures show the aberration curves respectively in the wide position, standard position and teleposition when Embodiments 1 through 11 of the present invention are respectively combined with the imaging lens system shown in the above. 
     As described in detail so far and as it will be evident from respective embodiments, the afocal zoom lens system according to the present invention has a large zoom ratio, and aberrations thereof are corrected favourably. 
     Besides, as the zoom lens system according to the present invention is an afocal lens system, it is possible to use it in various magnification ranges according to selection of the objective and imaging lens system to be used in combination and, therefore, it is possible to use it in the manners suitable for respective purposes of application. Moreover, by using the afocal zoom lens system according to the present invention in combination with an incident light illumination system provided coaxially, a photographing device, a discussion microscope, etc., it is possible to systematically perform various kinds of observation according to the wide variety of purposes of application.