Abstract:
A method of converting a frame-format in a taking optical system comprises steps of arranging a plurality of lens units constituting the taking optical system except for the lens unit disposed at the object-side end or at the image-side end and determining the configuration of the lens unit disposed at the object-side end or at the image-side end based on the desired frame-format.

Description:
This application is based on applications Nos. H11-023420 and H11-023433 filed in Japan on Feb. 1, 1999, the entire content of which is hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a taking optical system, and, particularly, to a taking optical system which can cope with different frame-formats (i.e. different numbers of pixels), for example a taking optical system that can be used with image sensing devices having different frame-formats. 
     BACKGROUND OF THE INVENTION 
     In recent years, as personal computers become prevalent, digital still cameras have been coming into wider and wider use that allow easy storage of images as electronic data. Such digital still cameras employ an image sensing device. In the modern design of image sensing devices, there are two mutually conflicting trends: one toward smaller frame-formats in keeping with the demand for more compact and more inexpensive cameras, and the other toward higher resolutions within given frame-formats in keeping with the demand for higher quality in images obtained. 
     For this reason, in the modern design of digital still cameras, it is customary to use, in combination with image sensing devices having different frame-formats according to their respective applications, taking optical systems dedicated exclusively thereto. Thus, developing a taking optical system that can be used with image sensing devices having different frame-formats is expected to lead to a considerable reduction in the costs of taking optical systems in general that are designed for similar applications. 
     As one example of a taking optical system that can be used with image sensing devices having different frame-formats, it has conventionally been known to apply simply a taking optical system designed for a relatively large frame-format to a relatively small frame-format. As another example, Japanese Laid-Open Patent Applications Nos. H8-114742 and H10-319314 propose using a relay lens system which refocuses the images formed by a taking optical system so as to vary the magnification. As another example, Japanese Laid-Open Patent Applications Nos. H10-123416, H9-329743, H9-329744, and H7-199067 propose disposing a detachable or exchangeable conversion lens unit somewhere in the optical path of a taking optical system so that the construction of the taking optical system can be changed in accordance with the frame-format by detaching or exchanging the conversion lens unit. 
     However, the first conventional method mentioned above of applying a taking optical system designed for a large frame-format to a small frame-format is impractical, not only because the taking optical system is unduly large relative to a small frame-format, but also because, due to the relationship between the angle of view and the focal length, the focal-length range is shifted toward the longest-focal-length side. The second conventional method mentioned above of using a relay lens system requires securing an extra optical path for the relay lens system, and thus makes the taking optical systems as a whole extremely large. 
     The third conventional method mentioned above of changing the construction of a taking optical system in accordance with the frame-format by detaching or exchanging a conversion lens unit provided therein requires that the structures of the individual lens barrels for holding the constituent lens units of the taking optical system be changed in accordance with the frame-format, or that the middle portion of the taking optical system be made movable so as to allow the conversion lens unit to be detached or exchanged, and thus makes the design of the taking optical system extremely complicated. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a taking optical system that can be used with image sensing devices having different frame-formats and that offers satisfactorily high image quality despite being compact. 
     To achieve the above object, according to one aspect of the present invention, a method of converting a frame-format in a taking optical system comprises steps of arranging a plurality of lens units constituting the taking optical system except for the lens unit disposed at the object-side end or at the image-side end and determining the configuration of the lens unit disposed at the object-side end or at the image-side end based on the desired frame-format. 
     According to another aspect of the present invention, a taking optical system is composed of a main optical system that can form an object image on its own and a conversion optical system that can be removably disposed at the image-side end of the main optical system, wherein, when the object image is taken as the image of the first frame-format, the main optical system alone is used, and, when the object image is taken as the image of the second frame-format that is different from the first frame-format, the main optical system is used with the conversion optical system disposed at the image-side end thereof. 
     According to another aspect of the present invention, an image taking apparatus is provided with a taking optical system. The taking optical system is composed of a main optical system that can form an object image on its own and a conversion optical system that can be removably disposed at the image-side end of the main optical system, wherein, when the object image is taken as the image of the first frame-format, the main optical system alone is used, and, when the object image is taken as the image of the second frame-format that is different from the first frame-format, the main optical system is used with the conversion optical system disposed at the image-side end thereof. The image taking apparatus can cope with both of the first and second frame-formats. 
     According to another aspect of the present invention, a method of converting a frame-format in a taking optical system comprises a step of designing the taking optical system to have a main optical system that can form an object image on its own and a conversion optical system that can be removably disposed at the image-side end of the main optical system, and a step of using the main optical system alone when the object image is taken as the image of the first frame-format and using the main optical system with the conversion optical system disposed at the image-side end thereof when the object image is taken as the image of the second frame-format that is different from the first frame-format. 
     According to another aspect of the present invention, a taking optical system is provided with, from the object side, an object-side lens unit and a plurality of lens units disposed behind the object-side lens unit and performs zooming by moving, of the object-side lens unit and the lens units disposed behind it, at least two lens units along the optical axis, wherein, when an object image is taken as the image of the first frame-format, as the object-side lens unit, a first object-side lens unit is used, and, when the object image is taken as the image of the second frame-format that is larger than the first frame-format, as the object-side lens unit, a second object-side lens unit is used that is differently configured from the first object-side lens unit, and wherein the following condition is fulfilled: 
     
       
         0.65 &lt;f   1   b/f   1   s&lt; 0.95 
       
     
     wherein 
     f 1 s represents the focal length of the first object-side lens unit; and 
     f 1 b represents the focal length of the second object-side lens unit. 
     According to another aspect of the present invention, a taking optical system is provided with, from the object side, an object-side lens unit and a plurality of lens units disposed behind the object-side lens unit and performs zooming by moving, of the object-side lens unit and the lens units disposed behind it, at least two lens units along the optical axis, wherein, when an object image is taken as the image of the first frame-format, as the object-side lens unit, a first object-side lens unit is used, and, when the object image is taken as the image of the second frame-format that is different from the first frame-format, in the zoom range between the middle-focal-length position and the telephoto end of the taking optical system as determined using the first object-side lens unit, as the object-side lens unit, a second object-side lens unit is used that is differently configured from the first object-side lens unit. 
     According to another aspect of the present invention, a taking optical system is provided with, from the object side, a positively-powered object-side lens unit, a negatively-powered second lens unit, and lens units disposed behind them and performs zooming by moving, of these lens units, at least two lens units along the optical axis, wherein, when an object image is taken as the image of the first frame-format, as the object-side lens unit, a first object-side lens unit is used, and, when the object image is taken as the image of the second frame-format that is larger than the first frame-format, as the object-side lens unit, a second object-side lens is used that is differently configured from the first object-side lens unit. 
     According to another aspect of the present invention, an image taking apparatus is provided with a taking optical system. The taking optical system is provided with, from the object side, an object-side lens unit and a plurality of lens units disposed behind the object-side lens unit and performs zooming by moving, of the object-side lens unit and the lens units disposed behind it, at least two lens units along the optical axis, wherein, when an object image is taken as the image of the first frame-format, as the object-side lens unit, a first object-side lens unit is used, and, when the object image is taken as the image of the second frame-format that is larger than the first frame-format, as the object-side lens unit, a second object-side lens unit is used that is differently configured from the first object-side lens unit, and wherein the condition noted above is fulfilled. The image taking apparatus can cope with both of the first and second frame-formats. 
     According to another aspect of the present invention, a method of converting a frame-format in a taking optical system comprises a step of designing the taking optical system to have, from the object side, an object-side lens unit and a plurality of lens units disposed behind it and to perform zooming by moving, of the object-side lens unit and the lens units disposed behind it, at least two lens units along the optical axis and a step of using, as the object-side lens unit, a first object-side lens unit when an object image is taken as the image of the first frame-format and using, as the object-side lens unit, a second object-side lens unit that is differently configured from the first object-side lens unit when the object image is taken as the image of the second frame-format that is larger than the first frame-format, wherein the following condition is fulfilled: 
     
       
         0.65&lt; f   1   b/f   1   s&lt; 0.95 
       
     
     wherein 
     f 1 s represents the focal length of the first object-side lens unit; and 
     f 1 b represents the focal length of the second object-side lens unit. 
     According to another aspect of the present invention, a method of converting a frame-format in a taking optical system comprises a step of designing the taking optical system to have, from the object side, an object-side lens unit and a plurality of lens units disposed behind it and to perform zooming by moving, of the object-side lens unit and the lens units disposed behind it, at least two lens units along the optical axis and a step of using, as the object-side lens unit, a first object-side lens unit when an object image is taken as the image of the first frame-format and using, as the object-side lens unit, a second object-side lens unit that is differently configured from the first object-side lens unit when the object image is taken as the image of the second frame-format that is different from the first frame-format in the zoom range between the middle-focal-length position and the telephoto end of the taking optical system as determined using the first object-side lens unit. 
     According to still another aspect of the present invention, a method of converting a frame-format in a taking optical system comprises a step of designing the taking optical system to have, from the object side, a positively-powered object-side lens unit, a negatively-powered second lens unit, and lens units disposed behind them and to perform zooming by moving, of these lens units, at least two lens units along the optical axis and a step of using, as the object-side lens unit, a first object-side lens unit when an object image is taken as the image of the first frame-format and using, as the object-side lens unit, a second object-side lens unit that is differently configured from the first object-side lens unit when the object image is taken as the image of the second frame-format that is larger than the first frame-format. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     This and other objects and features of this invention will become clear from the following description, taken in conjunction with the preferred embodiments with reference to the accompanied drawings in which: 
     FIG. 1 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a first embodiment (Example 1) of the present invention; 
     FIG. 2 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the first embodiment; 
     FIG. 3 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a second embodiment (Example 2) of the present invention; 
     FIG. 4 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the second embodiment; 
     FIG. 5 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a third embodiment (Example 3) of the present invention; 
     FIG. 6 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the third embodiment; 
     FIG. 7 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a fourth embodiment (Example 4) of the present invention; 
     FIG. 8 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the fourth embodiment; 
     FIG. 9 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a fifth embodiment (Example 5) of the present invention; 
     FIG. 10 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the fifth embodiment; 
     FIGS. 11A to  11 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 1 (when set for the first frame-format); 
     FIGS. 12A to  12 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 1 (when set for the second frame-format); 
     FIGS. 13A to  13 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 2 (when set for the first frame-format); 
     FIGS. 14A to  14 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 2 (when set for the second frame-format); 
     FIGS. 15A to  15 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 3 (when set for the first frame-format); 
     FIGS. 16A to  16 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 3 (when set for the second frame-format); 
     FIGS. 17A to  17 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 4 (when set for the first frame-format); 
     FIGS. 18A to  18 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 4 (when set for the second frame-format); 
     FIGS. 19A to  19 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 5 (when set for the first frame-format); 
     FIGS. 20A to  20 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 5 (when set for the second frame-format); 
     FIG. 21 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a sixth embodiment (Example 6) of the present invention; 
     FIG. 22 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the sixth embodiment; 
     FIG. 23 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of a seventh embodiment (Example 7) of the present invention; 
     FIG. 24 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the seventh embodiment; 
     FIG. 25 is a lens arrangement diagram of the taking optical system (when set for the first frame-format) of an eighth embodiment (Example 8) of the present invention; 
     FIG. 26 is a lens arrangement diagram of the taking optical system (when set for the second frame-format) of the eighth embodiment; 
     FIGS. 27A to  27 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 6 (when set for the first frame-format); 
     FIGS. 28A to  28 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 6 (when set for the second frame-format); 
     FIGS. 29A to  29 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 7 (when set for the first frame-format); 
     FIGS. 30A to  30 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 7 (when set for the second frame-format); 
     FIGS. 31A to  31 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 8 (when set for the first frame-format); and 
     FIGS. 32A to  32 I are graphic representations of the aberrations observed in the infinite-distance shooting condition in Example 8 (when set for the second frame-format). 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, taking optical systems embodying the present invention will be described with reference to the corresponding drawings. 
     Embodiments 1 to 5 
     FIGS. 1 and 2, FIGS. 3 and 4, FIGS. 5 and 6, FIGS. 7 and 8, and FIGS. 9 and 10 show the lens arrangement of the taking optical systems of a first to a fifth embodiment, respectively, of the invention. 
     The taking optical system of the first embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), is composed solely of a main optical system L 1 , as shown in FIG.  1 . In this figure, the left-hand side is the object side and the right-hand side is the image side. The main optical system L 1  is built as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the first embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm) has a conversion optical system A 1  additionally disposed between the main optical system L 1  and the low-pass filter LPF, as shown in FIG.  2 . The conversion optical system A 1  is composed of two lens elements G 12  and G 13 . 
     The taking optical system of the second embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), is composed solely of a main optical system L 2 , as shown in FIG.  3 . In this figure, the left-hand side is the object side and the right-hand side is the image side. The main optical system L 2  is built, like that of the first embodiment, as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the second embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm) has a conversion optical system A 2  additionally disposed between the main optical system L 2  and the low-pass filter LPF, as shown in FIG.  4 . The conversion optical system A 2  is composed of two lens elements G 12  and G 13 . 
     The taking optical system of the third embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), is composed solely of a main optical system L 3 , as shown in FIG.  5 . In this figure, the left-hand side is the object side and the right-hand side is the image side. The main optical system L 3  is built, like that of the first embodiment, as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the third embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm) has a conversion optical system A 3  additionally disposed between the main optical system L 3  and the low-pass filter LPF, as shown in FIG.  6 . The conversion optical system A 3  is composed of two lens elements G 12  and G 13 . 
     The taking optical system of the fourth embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), is composed solely of a main optical system L 4 , as shown in FIG.  7 . In this figure, the left-hand side is the object side and the right-hand side is the image side. The main optical system L 4  is built, like that of the first embodiment, as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the fourth embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm) has a conversion optical system A 4  additionally disposed between the main optical system L 4  and the low-pass filter LPF, as shown in FIG.  8 . The conversion optical system A 4  is composed of two lens elements G 12  and G 13 . 
     The taking optical system of the fifth embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=2.3 mm), is composed solely of a main optical system L 5 , as shown in FIG.  9 . In this figure, the left-hand side is the object side and the right-hand side is the image side. The main optical system L 5  is built, like that of the first embodiment, as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the fifth embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm) has a conversion optical system A 5  additionally disposed between the main optical system L 5  and the low-pass filter LPF, as shown in FIG.  10 . The conversion optical system A 5  is composed of two lens elements G 12  and G 13 . 
     In any of these embodiments, other things being equal, the taking optical system is larger when configured for the second frame-format than when configured for the first frame-format. Therefore, in converting the frame-format, rearranging the configuration for the second frame-format into the configuration for the first frame-format by adding the conversion optical system to the former results in making the thus converted taking optical system unduly large for the first frame-format. Accordingly, it is more advantageous in terms of miniaturization to rearrange the configuration for the first frame-format into the configuration for the second frame-format by adding the conversion optical system to the former, as is practiced in the embodiments described above. 
     The conditions which are preferably fulfilled by these taking optical systems will be described below. In the embodiments 1 to 5 described above, it is preferable that the taking optical system, when configured for the second frame-format, fulfill Condition (1) below. 
     
       
         2.5&lt;| fc/Yb|&lt; 11.0  (1) 
       
     
     wherein 
     fc represents the focal length of the conversion optical system; and 
     Yb represents the maximum image height of the second frame-format. 
     Condition (1) defines the focal length of the conversion optical system. If the value of Condition (1) is equal to or less than its lower limit, the focal length of the conversion optical system is so short, i.e. the optical power thereof is so strong, that it is difficult to correct aberrations, in particular barrel-shaped distortion and curvature of field. In contrast, if the value of Condition (1) is equal to or greater than its upper limit, the focal length of the conversion optical system is so long, i.e. the optical power thereof is so weak, that it is difficult to obtain sufficiently high magnification. As a result, it is not possible to obtain a significant difference between the focal lengths observed without and with the conversion optical system, and thus the taking optical system, when configured for the second frame-format, is so wide-angle oriented that it is difficult to correct peripheral imaging performance, in particular curvature of field. 
     In the embodiments 1 to 5, it is preferable that the taking optical system, when configured for the second frame-format, fulfill Condition (2) below. 
     
       
         1.1&lt;β c&lt; 1.9  (2) 
       
     
     wherein 
     βc represents the lateral magnification of the conversion optical system. 
     Condition (2) defines the magnification of the conversion optical system. If the value of Condition (2) is equal to or less than its lower limit, the conversion magnification is so low that the focal length of the taking optical system is not enlarged sufficiently even when the conversion optical system is added thereto, and thus the taking optical system is so wide-angle oriented that it is difficult to correct curvature of field. In contrast, if the value of Condition (2) is equal to or greater than its upper limit, the conversion magnification is so high that it is difficult to correct aberrations, in particular barrel-shaped distortion and curvature of field. 
     In the embodiments 1 to 5, it is preferable that the taking optical system fulfill Condition (3) below. 
     
       
         0.7&lt;( Yb/Ys )/β c&lt; 1.3  (3) 
       
     
     wherein 
     Ys represents the maximum image height of the first frame-format. 
     Condition (3) defines the relationship between the ratio of the second frame-format to the first frame-format and the conversion magnification, and thus defines the condition to be fulfilled to obtain roughly equal angles of view without and with the conversion optical system. If the value of Condition (3) is out of the range defined above, the difference between the angles of view without and with the conversion optical system is unduly great, increasing the burden on the main optical system, which is used in both the configurations for the first and second frame-formats, in terms of handling of different angles of view. This inconveniently leads to an increase in the total length of the entire taking optical system, to an increase in the diameter of the front-end lens unit, and to an increase in the number of lens elements needed to compensate for aggravated aberrations. Specifically, if the value of Condition (3) is equal to or less than its lower limit, the focal length range with the conversion optical system is shifted excessively toward the telephoto side, and thus the entire lens system needs to have an unduly long total length; in addition, unduly large spherical aberration appears. In contrast, if the value of Condition (3) is equal to or greater than its upper limit, the focal length range with the conversion optical system is shifted excessively toward the wide-angle side, and thus the front-end lens unit needs to have an unduly large diameter; in addition, unduly large curvature of field and distortion appear. 
     In the embodiments 1 to 5, it is preferable that the taking optical system, when configured for the first frame-format, fulfill Condition (4) below. 
     
       
         1.0&lt;| f   2 |/ fws&lt; 1.8  (4) 
       
     
     wherein 
     f 2  represents the focal length of the second lens unit; and 
     fws represents the focal length of the entire taking optical system, when configured for the first frame-format, as observed at the wide-angle end. 
     If the value of Condition (4) is equal to or less than its lower limit, the focal length of the second lens unit is too short, i.e. the optical power thereof is too strong, and thus, irrespective of whether the taking optical system is configured for the first frame-format or for the second frame-format with the conversion optical system added thereto, it is difficult to correct the negative distortion occurring at the wide-angle end, and in addition curvature of field exhibits an unduly strong inclination toward the under side. In contrast, if the value of Condition (4) is equal to or greater than its upper limit, the second lens unit needs to be moved through so long a distance for zooming that the front-end lens unit needs to have an unduly large diameter. 
     Note that, although the embodiments described above deal only with cases where frame-format conversion is achieved in a taking optical system by adding a conversion optical system thereto with the configuration of the main optical system left untouched, it is also possible, for example, to modify part of the configuration of the main optical system without changing its principal characteristics, and then add a conversion optical system thereto. Example of methods that allow the principal characteristics of the main optical system to be left untouched include so-called bending, whereby the radius of curvature of the single lens element constituting the main optical system is changed without changing its optical power, and addition of an aspherical surface or a diffractive optical surface. Also categorized into methods that allow the principal characteristics of the main optical system to be left untouched is addition thereto of a spherical lens, cemented lens, aspherical lens, diffractive optical lens, or the like having, in any case, a weak power for the purpose of improving image plane characteristics. 
     Modifying part of the configuration of the main optical system as described above is effective in improving optical performance particularly in the configuration for the larger frame-format. Because the configuration for the larger frame-format is used with an image sensing device having a larger number of pixels, and is accordingly required to offer higher optical performance than that for the smaller frame-format. Moreover, although the embodiments described above deal only with cases where the main optical system and the conversion optical system are both composed solely of refractive surfaces, it is also possible to adopt, depending on the requirements imposed by the image taking apparatus into which the taking optical system is incorporated, an arrangement having a mirror disposed in the optical path so as to turn the optical path, or an arrangement including a diffractive optical element. 
     Moreover, although the embodiments described above provide only examples of taking optical systems for use with image sensing devices having different frame-formats, the techniques underlying them are applicable also to taking optical systems designed for use with both an image sensing device having a smaller frame-format and a silver-halide film having a larger frame-format, or to taking optical systems designed for use with both conventional 35 mm silver-halide film and new-generation silver-halide film (i.e. APS film used in the Advanced Photo System). 
     Embodiments 6 to 8 
     FIGS. 21 and 22, FIGS. 23 and 24, and FIGS. 25 and 26 show the lens arrangement of the taking optical systems of a sixth to an eighth embodiment, respectively, of the invention. Note that, in each diagram, arrows schematically indicate the movement of the lens units, which will be described later, during zooming from the wide-angle end to the telephoto end. Arrows with a broken line indicate that the lens unit is kept in a fixed position during zooming. Moreover, each diagram shows the lens arrangement of the taking optical system during zooming, as observed at the wide-angle end. 
     The taking optical system of the sixth embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), has the construction as shown in FIG.  21 . In this figure, the left-hand side is the object side and the right-hand side is the image side. This lens system is built as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Here, the first lens unit Gr 1  is referred to as the “first object-side lens unit”. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the sixth embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm), has a construction as shown in FIG. 22, and is thus constructed basically in the same manner as in FIG. 21 except that, in the former, the first lens unit is replaced with another one in the zoom range between the middle-focal-length position and the telephoto end described later. Here, the first lens units is referred to as the “second object-side lens unit”. The other lens units placed behind the first lens unit in FIGS. 21 and 22 have the same construction and are moved in the same way during zooming. 
     The taking optical system of the seventh embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), has the construction as shown in FIG.  23 . In this figure, the left-hand side is the object side and the right-hand side is the image side. This lens system is built as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 1  and Gr 3  are stationary and Gr 2  and Gr 4  are movable. Here, the first lens unit Gr 1  is referred to as the “first object-side lens unit”. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the seventh embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm), has a construction as shown in FIG. 24, and is thus constructed basically in the same manner as in FIG. 23 except that, in the former, the first lens unit is replaced with another one in the zoom range between the middle-focal-length position and the telephoto end described later. Here, the first lens unit is referred to as the “second object-side lens unit”. The other lens units placed behind the first lens unit in FIGS. 23 and 24 have the same construction and are moved in the same way during zooming. 
     The taking optical system of the eighth embodiment, when configured for a first frame-format (a smaller frame-format, of which the height Y in a direction perpendicular to the optical axis=3.1 mm), has the construction as shown in FIG.  25 . In this figure, the left-hand side is the object side and the right-hand side is the image side. This lens system is built as a four-unit zoom lens system of a positive-negative-positive-positive configuration composed of, from the object side, a first lens unit Gr 1 , a second lens unit Gr 2 , a third lens unit Gr 3 , and a fourth lens unit Gr 4 , of which Gr 3  is stationary and Gr 1 , Gr 2 , and Gr 4  are movable. Here, the first lens unit Gr 1  is referred to as the “first object-side lens unit”. Gr 1  consists of three lens elements G 1 , G 2 , and G 3 ; Gr 2  consists of three lens elements G 4 , G 5 , and G 6 ; Gr 3  consists of two lens elements G 7  and G 8  and an aperture stop S; and Gr 4  consists of three lens elements G 9 , G 10 , and G 11 . In addition, a low-pass filter LPF shaped like a flat plate is disposed at the image-side end of the taking optical system. 
     On the other hand, the taking optical system of the eighth embodiment, when configured for a second frame-format (a larger frame-format, of which the height Y in a direction perpendicular to the optical axis=4.0 mm), has a construction as shown in FIG. 26, and is thus constructed basically in the same manner as in FIG. 25 except that, in the former, the first lens unit is replaced with another one in the zoom range between the middle-focal-length position and the telephoto end described later. Here, the first lens unit is referred to as the “second object-side lens unit”. The other lens units placed behind the first lens unit in FIGS. 25 and 26 have the same construction and are moved in the same way during zooming 
     In any of these embodiments, other things being equal, the taking optical system is larger when configured for the second frame-format than when configured for the first frame-format. Therefore, exchanging the first lens unit yields no advantage, because, as explained earlier in the description of the prior art, the size of the entire taking optical system is determined by its size when configured for the larger frame-format. 
     Incidentally, in zoom-type taking optical systems, like those of the embodiments of the present invention, during zooming from the wide-angle end to the telephoto end, the lens units are moved in such a way that the distance between the first and second lens units increases and that the distance between the second lens unit and the lens units placed behind it, including the aperture stop, decreases. In general, the diameter of such a zoom-type taking optical system as a whole depends on the diameter of the front-end lens unit thereof. Here, by adopting an arrangement that can be adapted to the second frame-format by exchanging the first lens unit in the zoom range between the middle-focal-length position and the telephoto end of the configuration for the first frame-format, it is possible to reduce the increased distance between the first and second lens units and thereby place the first lens unit closer to the second lens unit, and as a result, now that the distance between the second lens unit and the lens units placed behind it, including the aperture stop, is reduced, it is possible to position the entrance pupil closer. This helps achieve a considerable reduction in the diameter of the front-end lens unit. 
     What is important here is that, in order for the second lens unit to offer the same zoom solution irrespective of whether the first lens unit is exchanged or not, the second lens unit needs to offer substantially the same magnification. That is, in either case, the image point position of the first lens unit (the second object-side lens unit) with respect to the second lens unit as observed in the zoom range between the wide-angle end and the telephoto end when the taking optical system is configured for the second frame-format needs to coincide with the image point position of the first lens unit (the first object-side lens unit) with respect to the second lens unit as observed in the zoom range between the middle-focal-length position and the telephoto end when configured for the first frame-format. 
     As described above, by adopting an arrangement that can be adapted to the second frame-format by exchanging the first lens unit in the zoom range between the middle-focal-length position and the telephoto end of the configuration for the first frame-format, it is possible to realize a taking optical system that can cope with both the first frame-format and the second frame-format without sacrificing its size when configured for the first frame-format. Moreover, this permits the zoom solution of the lens units disposed behind the first lens unit to remain invariable, and thus contributes greatly to the standardization of the structures of lens barrels. 
     The conditions which are preferably fulfilled by the taking optical systems will be described below. In the embodiments 6 to 8 described above, it is preferable that the taking optical system fulfill Condition (5) below. 
     
       
         0.65 &lt;f   1   b/f   1   s&lt; 0.95  (5) 
       
     
     wherein 
     f 1 s represents the focal length of the first object-side lens unit; and 
     f 1 b represents the focal length of the second object-side lens unit. 
     Condition (5) defines the ratio of the focal length of the second object-side lens unit to that of the first object-side lens unit, and thus defines the condition to be fulfilled to achieve proper aberration correction and to set the above-described image point of the first lens unit in an appropriate position. If the value of Condition (5) is equal to or less than its lower limit, the focal length of the second object-side lens unit is too short relative to that of the first object-side lens unit, and thus it is difficult to obtain satisfactory peripheral imaging performance at the wide-angle end, and it is difficult to secure a sufficient distance between the first and second lens units at the wide-angle end to set the image point of the first lens unit in an appropriate position. In contrast, if the value of Condition (5) is equal to or greater than its upper limit, the focal length of the second object-side lens unit is too long relative to that of the first object-side lens unit, and thus the distance between the first and second lens units is unduly long at the wide-angle end. This inconveniently leads to an increase in the total length of the entire taking optical system and to an increase in the diameter of the front-end lens unit. 
     In the embodiments 6 to 8, it is preferable that the taking optical system fulfill Condition (6) below. 
     
       
         0.45 &lt;Zb/Zs&lt; 0.85  (6) 
       
     
     wherein 
     Zb represents the zoom ratio of the taking optical system, when configured for the second frame-format; and 
     Zs represents the zoom ratio of the taking optical system, when configured for the first frame-format. 
     If the value of Condition (6) is equal to or less than its lower limit, the zoom ratio of the taking optical system, when configured for the second frame-format, is too low, and thus it is impossible to gain an appreciable advantage by exchanging the first lens unit. In contrast, if the value of Condition (6) is equal to or greater than its upper limit, the zoom ratio of the taking optical system, when configured for the second frame-format, is too high, and thus, as described previously, the taking optical system is unduly large relative to the first frame-format. 
     In the embodiments 6 to 8, it is preferable that the taking optical system, when configured for the first frame-format, fulfill Condition (7) below. 
     
       
         0.85 &lt;|f 2 |/fws&lt; 1.55  (7) 
       
     
     wherein 
     f 2  represents the focal length of the second lens unit; and 
     fws represents the focal length of the entire taking optical system, when configured for the first frame-format, as observed at the wide-angle end. 
     If the value of Condition (7) is equal to or less than its lower limit, the focal length of the second lens unit is too short, i.e. the optical power thereof is too strong, and thus, irrespective of whether the taking optical system is configured for the first frame-format or for the second frame-format with the first lens unit exchanged, it is difficult to correct the negative distortion occurring at the wide-angle end, and in addition curvature of field exhibits an unduly strong inclination toward the under side. In contrast, if the value of Condition (7) is equal to or greater than its upper limit, the second lens unit needs to be moved through so long a distance for zooming that the front-end lens unit needs to have an unduly large diameter. 
     In the embodiments 6 to 8, it is preferable that the taking optical system fulfill Condition (8) below. 
     
       
         0.5 &lt;Ys/Yb&lt; 0.95  (8) 
       
     
     wherein 
     Ys represents the maximum image height of the first frame-format; and 
     Yb represents the maximum image height of the second frame-format. 
     Condition (8) defines the conversion magnification of the frame-format. If the value of Condition (8) is equal to or less than its lower limit, the ratio between the two frame-formats is so high that the total length of the taking optical system is unduly long. In contrast, if the value of Condition (8) is equal to or greater than its upper limit, the ratio between the frame-formats is so low that exchanging the first lens unit yields no appreciable advantage. 
     Note that, although the embodiments described above deal only with cases where frame-format conversion is achieved in a taking optical system by exchanging the first lens unit thereof with the configuration of the lens units placed behind it left untouched, it is also possible, for example, to modify part of the configuration of the lens units placed behind the first lens unit without changing their principal characteristics, and then exchange the first lens unit. Example of methods that allow the principal characteristics of the lens units placed behind the first lens unit to be left untouched include so-called bending, whereby the radii of curvature of the single lens elements constituting the lens units placed behind the first lens unit are changed without changing their optical powers, and addition of an aspherical surface or a diffractive optical surface. Also categorized into methods that allow the principal characteristics of the lens units placed behind the first lens unit to be left untouched is addition thereto of a spherical lens, cemented lens, aspherical lens, diffractive optical lens, or the like having, in any case, a weak power for the purpose of improving image plane characteristics. 
     Modifying part of the configuration of the lens units placed behind the first lens unit as described above is effective in improving optical performance particularly in the configuration for the larger frame-format. Because the configuration for the larger frame-format is used with an image sensing device having a larger number of pixels, and is accordingly required to offer higher optical performance than that for the smaller frame-format. Moreover, although the embodiments described above deal only with cases where the taking optical system is composed solely of refractive surfaces, it is also possible to adopt, depending on the requirements imposed by the image taking apparatus into which the taking optical system is incorporated, an arrangement having a mirror disposed in the optical path so as to turn the optical path, or an arrangement including a diffractive optical element. 
     Moreover, although the embodiments described above provide only examples of taking optical systems for use with image sensing devices having different frame-formats, the techniques underlying them are applicable also to taking optical systems designed for use with both an image sensing device having a smaller frame-format and a silver-halide film having a larger frame-format, or to taking optical systems designed for use with both conventional 35 mm silver-halide film and new-generation silver-halide film (i.e. APS film used in the Advanced Photo System). 
     EXAMPLES 
     Hereinafter, examples of taking optical systems embodying the present invention will be presented with reference to their construction data, graphic representations of aberrations, and other data. Examples 1 to 8 presented below correspond to the first to eighth embodiments, respectively, described above. Tables 1, 3, 5, 7, 9, 12, 14, and 16 list the construction data of Examples 1 to 8, respectively, when configured for the first frame-format, thus corresponding to the lens arrangements shown in FIGS. 1,  3 ,  5 ,  7 ,  9 ,  21 ,  23 , and  25 , respectively. Tables 2, 4, 6, 8, 10, 13, 15, and 17 list the construction data of Examples 1 to 8, respectively, when configured for the second frame-format, thus corresponding to the lens arrangements shown in FIGS. 2,  4 ,  6 ,  8 ,  10 ,  22 ,  24 , and  26 , respectively. 
     In the construction data of these Examples, ri (i=1, 2, 3, . . . ) represents the ith surface counted from the object side and its radius of curvature, di (i=1, 2, 3, . . . ) represents the ith axial distance counted from the object side, and Ni (i=1, 2, 3, . . . ) and vi (i=1, 2, 3, . . . ) respectively represent the refractive index for the d line and the Abbe number of the ith lens element counted from the object side. 
     In the construction data of Examples 1 to 5, for each of the focal length f of the entire taking optical system, the F number FNO of the entire taking optical system, the distance between the first and second lens units, the distance between the second and third lens units, the distance between the third and fourth lens units, and the distance between the last lens unit of the main optical system and the low-pass filter (or the conversion optical system), three values are given which are observed at, from left, the wide-angle end (W), the middle-focal-length position (M), and the telephoto end (T). 
     In the construction data of Examples 6 to 8, for each of the focal length f of the entire taking optical system, the F number FNO of the entire taking optical system, the distance between the first and second lens units, the distance between the second and third lens units, the distance between the third and fourth lens units, and the distance between the last lens unit of the taking optical system and the low-pass filter, three values are given which are observed at, from left, the wide-angle end (W), the middle-focal-length position (M), and the telephoto end (T). 
     Note that, in all of Examples, a surface whose radius of curvature is marked with an asterisk (*) is an aspherical surface, whose surface shape is defined by the following formulae: 
     
       
           X=X   0   +ΣA   i   Y   i   (a) 
       
     
     
       
           X   0   =CY   2 /{1+(1 −εC   2   Y   2 ) ½ }  (b) 
       
     
     wherein 
     X represents the displacement from the reference surface along the optical axis; 
     Y represents the height in a direction perpendicular to the optical axis; 
     C represents the paraxial curvature; 
     ε represents the quadric surface parameter; and 
     A i  represents the aspherical coefficient of the ith order. 
     FIGS. 11A to  11 I,  13 A to  13 I,  15 A to  15 I,  17 A to  17 I,  19 A to  19 I,  27 A to  27 I,  29 A to  29 I, and  31 A to  31 I are graphic representations of the aberrations observed in the taking optical systems of Examples 1 to 8, respectively, when configured for the first frame-format; and FIGS. 12A to  12 I,  14 A to  14 I,  16 A to  16 I,  18 A to  18 I,  20 A to  20 I,  28 A to  28 I,  30 A to  30 I, and  32 A to  32 I are graphic representations of the aberrations observed in the taking optical systems of Examples 1 to 8, respectively, when configured for the second frame-format. Of these diagrams, FIGS. 11A to  11 C,  12 A to  12 C,  13 A to  13 C,  14 A to  14 C,  15 A to  15 C,  16 A to  16 C,  17 A to  17 C,  18 A to  18 C,  19 A to  19 C,  20 A to  20 C,  27 A to  27 C,  28 A to  28 C,  29 A to  29 C,  30 A to  30 C,  31 A to  31 C, and  32 A to  32 C show the aberrations observed at the wide-angle end [W]; FIGS. 11D to  11 F,  12 D to  12 F,  13 D to  13 F,  14 D to  14 F,  15 D to  15 F,  16 D to  16 F,  17 D to  17 F,  18 D, to  18 F,  19 D to  19 F,  20 A to  20 F,  27 D to  27 F,  28 D to  28 F,  29 D to  29 F,  30 D to  30 F,  31 D to  31 F, and  32 D to  32 F show the aberrations observed at the middle focal length [M]; FIGS. 11G to  11 I,  12 G to  12 I,  13 G to  13 I,  14 G to  14 I,  15 G to  15 I,  16 G to  16 I,  17 G to  17 I,  18 G to  18 I,  19 G to  19 I,  20 G to  20 I,  27 G to  27 I,  28 G to  28 I,  29 G to  29 I,  30 G to  30 I,  31 G to  31 I, and  32 G to  32 I show the aberrations observed at the telephoto end [T]. In the spherical aberration diagrams, the solid line (d) represents the spherical aberration observed for the d line and the broken line (SC) represents the sine condition. In the astigmatism diagrams, the solid line (DS) represents the astigmatism observed on the sagittal plane and the broken line (DM) represents the astigmatism observed on the meridional plane. 
     Examples 1 to 5, when configured for the first or second frame-format, fulfill corresponding one or ones of Conditions (1) to (4) described previously. 
     Examples 6 to 8, when configured for the first or second frame-format, fulfill corresponding one or ones of Conditions (5) to (8) described previously. 
     
       
         
               
             
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Construction Data of Example 1 (for the first frame-format) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 f = 5.1 mm˜12.0 mm˜29.4 mm 
               
               
                 (Focal Length of the Entire Optical System) 
               
               
                 FNO = 2.28˜2.51˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
               
                 r1 = 39.361 
               
               
                   
                 d1 = 0.800 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 25.444 
               
               
                   
                 d2 = 3.932 
                 N2 = 1.48749 
                 ν2 = 70.44 
               
               
                 r3 = −92.731 
               
               
                   
                 d3 = 0.100 
               
               
                 r4 = 18.735 
               
               
                   
                 d4 = 1.976 
                 N3 = 1.65364 
                 ν3 = 55.78 
               
               
                 r5 = 35.205 
               
             
          
           
               
                   
                 d5 = 0.500˜8.755˜14.831 
               
             
          
           
               
                 r6* = 49.390 
                   
                   
                   
               
               
                   
                 d6 = 0.750 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 7.170 
               
               
                   
                 d7 = 4.459 
               
               
                 r8 = −9.753 
               
               
                   
                 d8 = 0.700 
                 N5 = 1.48749 
                 ν5 = 70.44 
               
               
                 r9 = 12.601 
               
               
                   
                 d9 = 1.268 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
               
                 r10 = 57.770 
               
             
          
           
               
                   
                 d10 = 14.831˜6.576˜0.500 
               
             
          
           
               
                 r11 = ∞ (Aperture Stop) 
               
             
          
           
               
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 15.739 
               
               
                   
                 d12 = 1.546 
                 N7 = 1.75450 
                 ν7 = 51.57 
               
               
                 r13 = −113.832 
               
               
                   
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
               
                 r14* = 41.438 
               
             
          
           
               
                   
                 d14 = 4.732˜2.453˜0.200 
               
             
          
           
               
                 r15 = 6.813 
                   
                   
                   
               
               
                   
                 d15 = 3.315 
                 N9 = 1.63237 
                 ν9 = 48.67 
               
               
                 r16 = −34.984 
               
               
                   
                 d16 = 1.181 
               
               
                 r17* = −49.645 
               
               
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 9.148 
               
               
                   
                 d18 = 1.869 
               
               
                 r19 = 11.635 
               
               
                   
                 d19 = 2.378 
                 N11 = 1.54012 
                 ν11 = 63.99 
               
               
                 r20 = −15.552 
               
             
          
           
               
                   
                 d20 = 1.359˜3.641˜5.877 
               
             
          
           
               
                 r21 = ∞ 
                   
                   
                   
               
               
                   
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.26307 × 10 −4   
               
               
                 A6 = 0.24482 × 10 −5   
               
               
                 A8 = −0.30163 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = −0.92198 × 10 −5   
               
               
                 A6 = 0.24720 × 10 −5   
               
               
                 A8 = 0.22450 × 10 −6   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.30309 × 10 −4   
               
               
                 A6 = 0.27800 × 10 −5   
               
               
                 A8 = −0.29431 × 10 −6   
               
               
                 A10 = 0.11555 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = −0.47983 × 10 −3   
               
               
                 A6 = 0.34008 × 10 −5   
               
               
                 A8 = −0.15789 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.49212 × 10 −3   
               
               
                 A6 = 0.16988 × 10 −4   
               
               
                 A8 = 0.50803 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Construction Data of Example 1 (for the second frame-format) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 f = 6.6 mm˜15.5 mm˜38.1 mm 
               
               
                 (Focal Length of the Entire Optical System) 
               
               
                 FNO = 2.93˜3.24˜3.72 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
               
                 r1 = 39.361 
                   
                   
                   
               
               
                   
                 d1 = 0.800 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 25.444 
               
               
                   
                 d2 = 3.932 
                 N2 = 1.48749 
                 ν2 = 70.44 
               
               
                 r3 = −92.731 
               
               
                   
                 d3 = 0.100 
               
               
                 r4 = 18.735 
               
               
                   
                 d4 = 1.976 
                 N3 = 1.65364 
                 ν3 = 55.78 
               
               
                 r5 = 35.205 
               
             
          
           
               
                   
                 d5 = 0.500˜8.755˜14.831 
               
             
          
           
               
                 r6* = 49.390 
                   
                   
                   
               
               
                   
                 d6 = 0.750 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 7.170 
               
               
                   
                 d7 = 4.459 
               
               
                 r8 = −9.753 
               
               
                   
                 d8 = 0.700 
                 N5 = 1.48749 
                 ν5 = 70.44 
               
               
                 r9 = 12.601 
               
               
                   
                 d9 = 1.268 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
               
                 r10 = 57.770 
               
             
          
           
               
                   
                 d10 = 14.831˜6.576˜0.500 
               
             
          
           
               
                 r11 = ∞ (Aperture Stop) 
               
             
          
           
               
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 15.739 
               
               
                   
                 d12 = 1.546 
                 N7 = 1.75450 
                 ν7 = 51.57 
               
               
                 r13 = −113.832 
               
               
                   
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
               
                 r14* = 41.438 
               
             
          
           
               
                   
                 d14 = 4.732˜2.453˜0.200 
               
             
          
           
               
                 r15 = 6.813 
                   
                   
                   
               
               
                   
                 d15 = 3.315 
                 N9 = 1.63237 
                 ν9 = 48.67 
               
               
                 r16 = −34.984 
               
               
                   
                 d16 = 1.181 
               
               
                 r17* = −49.645 
               
               
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 9.148 
               
               
                   
                 d18 = 1.869 
               
               
                 r19 = 11.635 
               
               
                   
                 d19 = 2.378 
                 N11 = 1.54012 
                 ν11 = 63.99 
               
               
                 r20 = −15.552 
               
             
          
           
               
                   
                 d20 = 0.400˜2.679˜4.932 
               
             
          
           
               
                 r21 = 71.678 
                   
                   
                   
               
               
                   
                 d21 = 0.800 
                 N12 = 1.75450 
                 ν12 = 51.57 
               
               
                 r22 = 6.056 
               
               
                   
                 d22 = 0.121 
               
               
                 r23 = 6.248 
               
               
                   
                 d23 = 2.244 
                 N13 = 1.57058 
                 ν13 = 39.32 
               
               
                 r24 = 33.647 
               
               
                   
                 d24 = 1.000 
               
               
                 r25 = ∞ 
               
               
                   
                 d25 = 3.400 
                 N14 = 1.51680 
                 ν14 = 64.20 
               
               
                 r26 = ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.26307 × 10 −4   
               
               
                 A6 = 0.24482 × 10 −5   
               
               
                 A8 = −0.30163 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = −0.92198 × 10 −5   
               
               
                 A6 = 0.24720 × 10 −5   
               
               
                 A8 = 0.22450 × 10 −6   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.30309 × 10 −4   
               
               
                 A6 = 0.27800 × 10 −5   
               
               
                 A8 = −0.29431 × 10 −6   
               
               
                 A10 = 0.11555 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = −0.47983 × 10 −3   
               
               
                 A6 = 0.34008 × 10 −5   
               
               
                 A8 = −0.15789 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.49212 × 10 −3   
               
               
                 A6 = 0.16988 × 10 −4   
               
               
                 A8 = 0.50803 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Construction Data of Example 2 (for the first frame-format) 
               
               
                   
               
             
             
               
                 f = 5.1 mm˜12.0 mm˜29.4 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.28˜2.51˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 44.384 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                 ν1 = 21.00 
               
               
                  r2 = 
                 26.902 
               
               
                   
                   
                  d2 = 3.548 
                  N2 = 1.48749 
                 ν2 = 70.44 
               
               
                  r3 = 
                 −87.224 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 18.690 
               
               
                   
                   
                  d4 = 1.903 
                  N3 = 1.71785 
               
               
                  r5 = 
                 34.111 
               
             
          
           
               
                   
                  d5 = 0.500˜8.898˜15.092 
               
             
          
           
               
                  r6* = 
                 53.697 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                 ν3 = 49.77 
               
               
                  r7* = 
                 7.151 
               
               
                   
                   
                  d7 = 4.412 
               
               
                  r8 = 
                 −9.136 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
               
               
                  r9 = 
                 14.748 
               
               
                   
                   
                  d9 = 1.249 
                  N6 = 1.83350 
                 ν4 = 21.00 
               
               
                 r10 = 
                 166.857 
               
             
          
           
               
                   
                 d10 = 15.092˜6.694˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 16.402 
               
               
                   
                   
                 d12 = 1.569 
                  N7 = 1.75450 
               
               
                 r13 = 
                 −73.572 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                 ν5 = 23.82 
               
               
                 r14* = 
                 47.167 
               
             
          
           
               
                   
                 d14 = 4.771˜2.465˜0.200 
               
             
          
           
               
                 r15 = 
                 6.930 
                   
                   
                   
               
               
                   
                   
                 d15 = 3.195 
                  N9 = 1.64598 
               
               
                 r16 = 
                 −49.092 
               
               
                   
                   
                 d16 = 1.247 
               
               
                 r17* = 
                 −259.880 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν6 = 23.82 
               
               
                 r18* = 
                 8.606 
               
               
                   
                   
                 d18 = 2.029 
               
               
                 r19 = 
                 10.973 
               
               
                   
                   
                 d19 = 2.385 
                 N11 = 1.48757 
               
               
                 r20 = 
                 −15.859 
               
             
          
           
               
                   
                 d20 = 1.336˜3.642˜5.907 
               
             
          
           
               
                 r21 = 
                 ∞ 
                   
                   
                   
               
               
                   
                   
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν7 = 64.20 
               
               
                 r22 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.50768 × 10 −4   
               
               
                 A6 = 
                  0.27040 × 10 −5   
               
               
                 A8 = 
                 −0.32896 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.26886 × 10 −5   
               
               
                 A6 = 
                  0.24656 × 10 −5   
               
               
                 A8 = 
                  0.28044 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.29944 × 10 −4   
               
               
                 A6 = 
                  0.23942 × 10 −5   
               
               
                 A8 = 
                 −0.26510 × 10 −6   
               
               
                 A10 = 
                  0.10143 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.43785 × 10 −3   
               
               
                 A6 = 
                 −0.85525 × 10 −6   
               
               
                 A8 = 
                 −0.55200 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.49210 × 10 −3   
               
               
                 A6 = 
                  0.12730 × 10 −4   
               
               
                 A8 = 
                  0.66578 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Construction Data of Example 2 (for the second frame-format) 
               
               
                   
               
             
             
               
                 f = 6.6 mm˜15.5 mm˜38.1 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.9˜3.22˜3.72 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 44.384 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                 ν1 = 21.00 
               
               
                  r2 = 
                 26.902 
               
               
                   
                   
                  d2 = 3.548 
                  N2 = 1.48749 
               
               
                  r3 = 
                 −87.224 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 18.690 
               
               
                   
                   
                  d4 = 1.903 
                  N3 = 1.71785 
               
               
                  r5 = 
                 34.111 
               
             
          
           
               
                   
                  d5 = 0.500˜8.898˜15.092 
               
             
          
           
               
                  r6* = 
                 53.697 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                 ν2 = 49.77 
               
               
                  r7* = 
                 7.151 
               
               
                   
                   
                  d7 = 4.412 
               
               
                  r8 = 
                 −9.136 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
               
               
                  r9 = 
                 14.748 
               
               
                   
                   
                  d9 = 1.249 
                  N6 = 1.83350 
                 ν3 = 21.00 
               
               
                 r10 = 
                 166.857 
               
             
          
           
               
                   
                 d10 = 15.092˜6.694˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 16.402 
               
               
                   
                   
                 d12 = 1.569 
                  N7 = 1.75450 
               
               
                 r13 = 
                 −73.572 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                 ν4 = 23.82 
               
               
                 r14* = 
                 47.167 
               
             
          
           
               
                   
                 d14 = 4.771˜2.465˜0.200 
               
             
          
           
               
                 r15 = 
                 6.930 
                   
                   
                   
               
               
                   
                   
                 d15 = 3.195 
                  N9 = 1.64598 
               
               
                 r16 = 
                 −49.092 
               
               
                   
                   
                 d16 = 1.247 
               
               
                 r17* = 
                 −259.880 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν5 = 23.82 
               
               
                 r18* = 
                 8.606 
               
               
                   
                   
                 d18 = 2.029 
               
               
                 r19 = 
                 10.973 
               
               
                   
                   
                 d19 = 2.385 
                 N11 = 1.48757 
               
               
                 r20 = 
                 −15.859 
               
             
          
           
               
                   
                 d20 = 0.100˜2.405˜4.671 
               
             
          
           
               
                 r21 = 
                 49.436 
                   
                   
                   
               
               
                   
                   
                 d21 = 0.600 
                 N12 = 1.75450 
               
               
                 r22 = 
                 5.976 
               
               
                   
                   
                 d22 = 0.102 
               
               
                 r23 = 
                 6.145 
               
               
                   
                   
                 d23 = 1.807 
                 N13 = 1.57277 
               
               
                 r24 = 
                 28.181 
               
               
                   
                   
                 d24 = 1.000 
               
               
                 r25 = 
                 ∞ 
               
               
                   
                   
                 d25 = 3.400 
                 N14 = 1.51680 
                 ν6 = 64.20 
               
               
                 r26 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.50768 × 10 −4   
               
               
                 A6 = 
                  0.27040 × 10 −5   
               
               
                 A8 = 
                 −0.32896 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.26886 × 10 −5   
               
               
                 A6 = 
                  0.24656 × 10 −5   
               
               
                 A8 = 
                  0.28044 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.29944 × 10 −4   
               
               
                 A6 = 
                  0.23942 × 10 −5   
               
               
                 A8 = 
                 −0.26510 × 10 −6   
               
               
                 A10 = 
                  0.10143 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.43785 × 10 −3   
               
               
                 A6 = 
                 −0.85525 × 10 −6   
               
               
                 A8 = 
                 −0.55200 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.49210 × 10 −3   
               
               
                 A6 = 
                  0.12730 × 10 −4   
               
               
                 A8 = 
                  0.66578 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 Construction Data of Example 3 (for the first frame-format) 
               
               
                   
               
             
             
               
                 f = 5.1 mm˜12.0 mm˜29.4 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.28˜2.51˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 38.100 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 25.197 
               
               
                   
                   
                  d2 = 4.072 
                  N2 = 1.48749 
                  ν2 = 70.44 
               
               
                  r3 = 
                 −98.604 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 19.021 
               
               
                   
                   
                  d4 = 2.041 
                  N3 = 1.63412 
                  ν3 = 56.85 
               
               
                  r5 = 
                 36.020 
               
             
          
           
               
                   
                  d5 = 0.500˜8.861˜14.981 
               
             
          
           
               
                  r6* = 
                 49.675 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 7.233 
               
               
                   
                   
                  d7 = 4.595 
               
               
                  r8 = 
                 −9.793 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
                  ν5 = 70.44 
               
               
                  r9 = 
                 12.800 
               
               
                   
                   
                  d9 = 1.273 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 60.435 
               
             
          
           
               
                   
                 d10 = 14.981˜6.620˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 15.868 
               
               
                   
                   
                 d12 = 1.517 
                  N7 = 1.75450 
                  ν7 = 51.57 
               
               
                 r13 = 
                 −296.209 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r14* = 
                 35.961 
               
             
          
           
               
                   
                 d14 = 4.773˜2.488˜0.200 
               
             
          
           
               
                 r15 = 
                 6.619 
                   
                   
                   
               
               
                   
                   
                 d15 = 3.473 
                  N9 = 1.56380 
                  ν9 = 47.92 
               
               
                 r16 = 
                 −24.792 
               
               
                   
                   
                 d16 = 1.309 
               
               
                 r17* = 
                 −23.223 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 
                 11.411 
               
               
                   
                   
                 d18 = 1.585 
               
               
                 r19 = 
                 12.595 
               
               
                   
                   
                 d19 = 2.498 
                 N11 = 1.58242 
                 ν11 = 60.28 
               
               
                 r20 = 
                 −13.465 
               
             
          
           
               
                   
                 d20 = 1.343˜3.628˜5.916 
               
             
          
           
               
                 r21 = 
                 ∞ 
                   
                   
                   
               
               
                   
                   
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.29472 × 10 −4   
               
               
                 A6 = 
                  0.19378 × 10 −5   
               
               
                 A8 = 
                 −0.23877 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.60653 × 10 −5   
               
               
                 A6 = 
                  0.20752 × 10 −5   
               
               
                 A8 = 
                  0.17680 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.32613 × 10 −4   
               
               
                 A6 = 
                  0.21765 × 10 −5   
               
               
                 A8 = 
                 −0.22337 × 10 −6   
               
               
                 A10 = 
                  0.89525 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.50533 × 10 −3   
               
               
                 A6 = 
                  0.65302 × 10 −5   
               
               
                 A8 = 
                 −0.26699 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.46260 × 10 −3   
               
               
                 A6 = 
                  0.18637 × 10 −4   
               
               
                 A8 = 
                  0.25741 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Construction Data of Example 3 (for the second frame-format) 
               
               
                   
               
             
             
               
                 f = 7.3 mm˜17.2 mm˜42.0 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 3.26˜3.58˜4.12 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 38.100 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 25.197 
               
               
                   
                   
                  d2 = 4.072 
                  N2 = 1.48749 
                  ν2 = 70.44 
               
               
                  r3 = 
                 −98.604 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 19.021 
               
               
                   
                   
                  d4 = 2.041 
                  N3 = 1.63412 
                  ν3 = 56.85 
               
               
                  r5 = 
                 36.020 
               
             
          
           
               
                   
                  d5 = 0.500˜8.861˜14.981 
               
             
          
           
               
                  r6* = 
                 49.673 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 7.233 
               
               
                   
                   
                  d7 = 4.595 
               
               
                  r8 = 
                 −9.793 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
                  ν5 = 70.44 
               
               
                  r9 = 
                 12.800 
               
               
                   
                   
                  d9 = 1.273 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 60.435 
               
             
          
           
               
                   
                 d10 = 14.981˜6.620˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 15.868 
               
               
                   
                   
                 d12 = 1.517 
                  N7 = 1.75450 
                  ν7 = 51.57 
               
               
                 r13 = 
                 −296.209 
               
               
                   
                   
                 d13 = 0.010 
               
               
                 r14 = 
                 −296.203 
               
               
                   
                   
                 d14 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r15* = 
                 35.961 
                   
                   
                   
               
             
          
           
               
                   
                 d15 = 4.773˜2.488˜0.200 
               
             
          
           
               
                 r16 = 
                 6.619 
                   
                   
                   
               
               
                   
                   
                 d16 = 3.473 
                  N9 = 1.56380 
                  ν9 = 47.92 
               
               
                 r17 = 
                 −24.792 
               
               
                   
                   
                 d17 = 1.309 
               
               
                 r18* = 
                 −23.223 
               
               
                   
                   
                 d18 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r19* = 
                 11.411 
               
               
                   
                   
                 d19 = 1.585 
               
               
                 r20 = 
                 12.595 
               
               
                   
                   
                 d20 = 2.498 
                 N11 = 1.58242 
                 ν11 = 60.28 
               
               
                 r21 = 
                 −13.465 
                   
                   
                   
               
             
          
           
               
                   
                 d21 = 0.400˜2.685˜4.973 
               
             
          
           
               
                 r22 = 
                 41.840 
                   
                   
                   
               
               
                   
                   
                 d22 = 0.800 
                 N12 = 1.75450 
                 ν12 = 51.57 
               
               
                 r23 = 
                 5.885 
               
               
                   
                   
                 d23 = 0.245 
               
               
                 r24 = 
                 6.199 
               
               
                   
                   
                 d24 = 2.016 
                 N13 = 1.59891 
                 ν13 = 35.03 
               
               
                 r25 = 
                 16.340 
               
               
                   
                   
                 d25 = 1.000 
               
               
                 r26 = 
                 ∞ 
               
               
                   
                   
                 d26 = 3.400 
                 N14 = 1.51680 
                 ν14 = 64.20 
               
               
                 r27 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.29472 × 10 −4   
               
               
                 A6 = 
                  0.19378 × 10 −5   
               
               
                 A8 = 
                 −0.23877 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.60653 × 10 −5   
               
               
                 A6 = 
                  0.20752 × 10 −5   
               
               
                 A8 = 
                  0.17680 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 15th Surface (r15) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.32613 × 10 −4   
               
               
                 A6 = 
                  0.21765 × 10 −5   
               
               
                 A8 = 
                 −0.22337 × 10 −6   
               
               
                 A10 = 
                  0.89525 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.50533 × 10 −3   
               
               
                 A6 = 
                  0.65302 × 10 −5   
               
               
                 A8 = 
                 −0.26699 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 19th Surface (r19) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.46260 × 10 −3   
               
               
                 A6 = 
                  0.18637 × 10 −4   
               
               
                 A8 = 
                  0.25741 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 Construction Data of Example 4 (for the first frame-format) 
               
               
                   
               
             
             
               
                 f = 5.1 mm˜12.0 mm˜29.4 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.3˜2.53˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 51.292 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 28.707 
               
               
                   
                   
                  d2 = 3.874 
                  N2 = 1.49411 
                  ν2 = 69.48 
               
               
                  r3 = 
                 −88.318 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 19.533 
               
               
                   
                   
                  d4 = 2.187 
                  N3 = 1.74573 
                  ν3 = 51.87 
               
               
                  r5 = 
                 38.766 
               
             
          
           
               
                   
                  d5 = 0.500˜8.903˜15.126 
               
             
          
           
               
                  r6* = 
                 76.536 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 7.248 
               
               
                   
                   
                  d7 = 4.289 
               
               
                  r8 = 
                 −9.577 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
                  ν5 = 70.44 
               
               
                  r9 = 
                 14.103 
               
               
                   
                   
                  d9 = 1.327 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 119.341 
               
             
          
           
               
                   
                 d10 = 15.126˜6.723˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 14.886 
               
               
                   
                   
                 d12 = 1.645 
                  N7 = 1.76163 
                  ν7 = 50.36 
               
               
                 r13 = 
                 −54.790 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r14* = 
                 47.323 
               
             
          
           
               
                   
                 d14 = 4.717˜2.400˜0.200 
               
             
          
           
               
                 r15 = 
                 7.049 
                   
                   
                   
               
               
                   
                   
                 d15 = 3.069 
                  N9 = 1.65030 
                  ν9 = 49.41 
               
               
                 r16 = 
                 −87.401 
               
               
                   
                   
                 d16 = 1.297 
               
               
                 r17* = 
                 107.653 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 
                 7.817 
               
               
                   
                   
                 d18 = 1.736 
               
               
                 r19 = 
                 10.410 
               
               
                   
                   
                 d19 = 2.338 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
               
                 r20 = 
                 −16.932 
               
             
          
           
               
                   
                 d20 = 1.351˜3.667˜5.867 
               
             
          
           
               
                 r21 = 
                 ∞ 
                   
                   
                   
               
               
                   
                   
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.15037 × 10 −3   
               
               
                 A6 = 
                 −0.41303 × 10 −6   
               
               
                 A8 = 
                 −0.67332 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.11096 × 10 −3   
               
               
                 A6 = 
                  0.25794 × 10 −5   
               
               
                 A8 = 
                  0.16455 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.30579 × 10 −4   
               
               
                 A6 = 
                  0.34943 × 10 −5   
               
               
                 A8 = 
                 −0.41149 × 10 −6   
               
               
                 A10 = 
                  0.16505 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.46605 × 10 −3   
               
               
                 A6 = 
                  0.42583 × 10 −6   
               
               
                 A8 = 
                 −0.17528 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.39333 × 10 −3   
               
               
                 A6 = 
                  0.12845 × 10 −4   
               
               
                 A8 = 
                  0.65431 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Construction Data of Example 4 (for the second frame-format) 
               
               
                   
               
             
             
               
                 f = 6.0 mm˜14.1 mm˜34.6 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.73˜3.0˜3.4 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 51.292 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 28.707 
               
               
                   
                   
                  d2 = 3.874 
                  N2 = 1.49411 
                  ν2 = 69.48 
               
               
                  r3 = 
                 −88.318 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 19.533 
               
               
                   
                   
                  d4 = 2.187 
                  N3 = 1.74575 
                  ν3 = 51.87 
               
               
                  r5 = 
                 38.766 
               
             
          
           
               
                   
                  d5 = 0.500˜8.903˜15.126 
               
             
          
           
               
                  r6* = 
                 76.536 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 7.248 
               
               
                   
                   
                  d7 = 4.289 
               
               
                  r8 = 
                 −9.577 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.48749 
                  ν5 = 70.44 
               
               
                  r9 = 
                 14.103 
               
               
                   
                   
                  d9 = 1.327 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 119.341 
               
             
          
           
               
                   
                 d10 = 15.126˜6.723˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 14.886 
               
               
                   
                   
                 d12 = 1.645 
                  N7 = 1.76163 
                  ν7 = 50.36 
               
               
                 r13 = 
                 −54.790 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r14* = 
                 47.323 
               
             
          
           
               
                   
                 d14 = 4.717˜2.400˜0.200 
               
             
          
           
               
                 r15 = 
                 7.049 
                   
                   
                   
               
               
                   
                   
                 d15 = 3.069 
                  N9 = 1.65030 
                  ν9 = 49.41 
               
               
                 r16 = 
                 −87.401 
               
               
                   
                   
                 d16 = 1.297 
               
               
                 r17* = 
                 107.653 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 
                 7.817 
               
               
                   
                   
                 d18 = 1.736 
               
               
                 r19 = 
                 10.410 
               
               
                   
                   
                 d19 = 2.338 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
               
                 r20 = 
                 −16.932 
               
             
          
           
               
                   
                 d20 = 0.400˜2.717˜4.917 
               
             
          
           
               
                 r21 = 
                 117.244 
                   
                   
                   
               
               
                   
                   
                 d21 = 0.800 
                 N12 = 1.75450 
                 ν12 = 51.57 
               
               
                 r22 = 
                 6.400 
               
               
                   
                   
                 d22 = 0.100 
               
               
                 r23 = 
                 6.592 
               
               
                   
                   
                 d23 = 2.286 
                 N13 = 1.64387 
                 ν13 = 44.47 
               
               
                 r24 = 
                 45.168 
               
               
                   
                   
                 d24 = 1.000 
               
               
                 r25 = 
                 ∞ 
               
               
                   
                   
                 d25 = 3.400 
                 N14 = 1.51680 
                 ν14 = 64.20 
               
               
                 r26 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.15037 × 10 −3   
               
               
                 A6 = 
                 −0.41303 × 10 −6   
               
               
                 A8 = 
                 −0.67332 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.11096 × 10 −3   
               
               
                 A6 = 
                  0.25794 × 10 −5   
               
               
                 A8 = 
                  0.16455 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.30579 × 10 −4   
               
               
                 A6 = 
                  0.34943 × 10 −5   
               
               
                 A8 = 
                 −0.41149 × 10 −6   
               
               
                 A10 = 
                  0.16505 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.46605 × 10 −3   
               
               
                 A6 = 
                  0.42583 × 10 −6   
               
               
                 A8 = 
                 −0.17528 × 10 −8   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.39333 × 10 −3   
               
               
                 A6 = 
                  0.12845 × 10 −4   
               
               
                 A8 = 
                  0.65431 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 Construction Data of Example 5 (for the first frame-format) 
               
               
                   
               
             
             
               
                 f = 3.8 mm˜9.0 mm˜21.7 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 2.34˜2.52˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 33.893 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 20.854 
               
               
                   
                   
                  d2 = 2.933 
                  N2 = 1.48749 
                  ν2 = 70.44 
               
               
                  r3 = 
                 3458.532 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 18.532 
               
               
                   
                   
                  d4 = 2.028 
                  N3 = 1.75409 
                  ν3 = 51.58 
               
               
                  r5 = 
                 52.594 
               
             
          
           
               
                   
                  d5 = 0.500˜7.990˜13.134 
               
             
          
           
               
                  r6* = 
                 54.228 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 5.734 
               
               
                   
                   
                  d7 = 3.716 
               
               
                  r8 = 
                 −9.442 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.51435 
                  ν5 = 54.87 
               
               
                  r9 = 
                 10.231 
               
               
                   
                   
                  d9 = 1.262 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 82.356 
               
             
          
           
               
                   
                 d10 = 13.134˜5.644˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 12.294 
               
               
                   
                   
                 d12 = 1.696 
                  N7 = 1.70084 
                  ν7 = 26.54 
               
               
                 r13 = 
                 −12.693 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r14* = 
                 22.033 
               
             
          
           
               
                   
                 d14 = 3.925˜2.101˜0.200 
               
             
          
           
               
                 r15 = 
                 6.741 
                   
                   
                   
               
               
                   
                   
                 d15 = 5.913 
                  N9 = 1.50423 
                  ν9 = 59.67 
               
               
                 r16 = 
                 −9.980 
               
               
                   
                   
                 d16 = 1.116 
               
               
                 r17* = 
                 −6.796 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 
                 −127.113 
               
               
                   
                   
                 d18 = 0.100 
               
               
                 r19 = 
                 12.962 
               
               
                   
                   
                 d19 = 3.236 
                 N11 = 1.61322 
                 ν11 = 48.97 
               
               
                 r20 = 
                 −7.908 
               
             
          
           
               
                   
                 d20 = 1.731˜3.554˜5.455 
               
             
          
           
               
                 r21 = 
                 ∞ 
                   
                   
                   
               
               
                   
                   
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.17992 × 10 −3   
               
               
                 A6 = 
                  0.21097 × 10 −5   
               
               
                 A8 = 
                 −0.60366 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.10422 × 10 −3   
               
               
                 A6 = 
                  0.71873 × 10 −5   
               
               
                 A8 = 
                  0.67492 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.20982 × 10 −4   
               
               
                 A6 = 
                  0.10888 × 10 −4   
               
               
                 A8 = 
                 −0.19610 × 10 −5   
               
               
                 A10 = 
                  0.12639 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.82030 × 10 −3   
               
               
                 A6 = 
                  0.27014 × 10 −4   
               
               
                 A8 = 
                 −0.40805 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.26263 × 10 −3   
               
               
                 A6 = 
                  0.42079 × 10 −4   
               
               
                 A8 = 
                 −0.49132 × 10 −5   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
             
               
               
               
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
               
             
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Construction Data of Example 5 (for the second frame-format) 
               
               
                   
               
             
             
               
                 f = 6.6 mm˜15.7 mm˜37.8 mm 
               
               
                 (Focal length of the Entire Optical System) 
               
               
                 FNO = 4.11˜4.43˜5.0 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number (νd) 
               
               
                   
               
             
          
           
               
                  r1 = 
                 33.893 
                   
                   
                   
               
               
                   
                   
                  d1 = 0.800 
                  N1 = 1.83350 
                  ν1 = 21.00 
               
               
                  r2 = 
                 20.854 
               
               
                   
                   
                  d2 = 2.933 
                  N2 = 1.48749 
                  ν2 = 70.44 
               
               
                  r3 = 
                 3458.532 
               
               
                   
                   
                  d3 = 0.100 
               
               
                  r4 = 
                 18.532 
               
               
                   
                   
                  d4 = 2.028 
                  N3 = 1.75409 
                  ν3 = 51.58 
               
               
                  r5 = 
                 52.594 
               
             
          
           
               
                   
                  d5 = 0.500˜7.990˜13.134 
               
             
          
           
               
                  r6* = 
                 54.228 
                   
                   
                   
               
               
                   
                   
                  d6 = 0.750 
                  N4 = 1.77250 
                  ν4 = 49.77 
               
               
                  r7* = 
                 5.734 
               
               
                   
                   
                  d7 = 3.716 
               
               
                  r8 = 
                 −9.442 
               
               
                   
                   
                  d8 = 0.700 
                  N5 = 1.51435 
                  ν5 = 54.87 
               
               
                  r9 = 
                 10.231 
               
               
                   
                   
                  d9 = 1.262 
                  N6 = 1.83350 
                  ν6 = 21.00 
               
               
                 r10 = 
                 82.356 
               
             
          
           
               
                   
                 d10 = 13.134˜5.644˜0.500 
               
             
          
           
               
                 r11 = 
                 ∞ (Aperture Stop) 
               
             
          
           
               
                   
                   
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 
                 12.294 
               
               
                   
                   
                 d12 = 1.696 
                  N7 = 1.70084 
                  ν7 = 26.54 
               
               
                 r13 = 
                 −12.693 
               
               
                   
                   
                 d13 = 1.000 
                  N8 = 1.84666 
                  ν8 = 23.82 
               
               
                 r14* = 
                 22.033 
               
             
          
           
               
                   
                 d14 = 3.925˜2.101˜0.200 
               
             
          
           
               
                 r15 = 
                 6.741 
                   
                   
                   
               
               
                   
                   
                 d15 = 5.913 
                  N9 = 1.50423 
                  ν9 = 59.67 
               
               
                 r16 = 
                 −9.980 
               
               
                   
                   
                 d16 = 1.116 
               
               
                 r17* = 
                 −6.796 
               
               
                   
                   
                 d17 = 1.000 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 
                 −127.113 
               
               
                   
                   
                 d18 = 0.100 
               
               
                 r19 = 
                 12.962 
               
               
                   
                   
                 d19 = 3.236 
                 N11 = 1.61322 
                 ν11 = 48.97 
               
               
                 r20 = 
                 −7.908 
               
             
          
           
               
                   
                 d20 = 0.400˜2.224˜4.125 
               
             
          
           
               
                 r21 = 
                 33.371 
                   
                   
                   
               
               
                   
                   
                 d21 = 0.800 
                 N12 = 1.75450 
                 ν12 = 51.57 
               
               
                 r22 = 
                 5.500 
               
               
                   
                   
                 d22 = 0.660 
               
               
                 r23 = 
                 6.120 
               
               
                   
                   
                 d23 = 1.747 
                 N13 = 1.71069 
                 ν13 = 26.02 
               
               
                 r24 = 
                 8.790 
               
               
                   
                   
                 d24 = 1.000 
               
               
                 r25 = 
                 ∞ 
               
               
                   
                   
                 d25 = 3.400 
                 N14 = 1.51680 
                 ν14 = 64.20 
               
               
                 r26 = 
                 ∞ 
               
               
                   
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.17992 × 10 −3   
               
               
                 A6 = 
                  0.21097 × 10 −5   
               
               
                 A8 = 
                 −0.60366 × 10 −7   
               
             
          
           
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.10422 × 10 −3   
               
               
                 A6 = 
                  0.71873 × 10 −5   
               
               
                 A8 = 
                  0.67492 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.20982 × 10 −4   
               
               
                 A6 = 
                  0.10888 × 10 −4   
               
               
                 A8 = 
                 −0.19610 × 10 −5   
               
               
                 A10 = 
                  0.12639 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                 −0.82030 × 10 −3   
               
               
                 A6 = 
                  0.27014 × 10 −4   
               
               
                 A8 = 
                 −0.40805 × 10 −6   
               
             
          
           
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
             
          
           
               
                 ε = 
                  0.10000 × 10 
               
               
                 A4 = 
                  0.26263 × 10 −3   
               
               
                 A6 = 
                  0.42079 × 10 −4   
               
               
                 A8 = 
                 −0.49132 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 Values Corresponding to Conditions (1) to (4) 
               
             
          
           
               
                   
                 |fc/Yb| 
                 βc 
                 (Yb/Ys)/βc 
                 |f2|/fws 
               
               
                   
                   
               
             
          
           
               
                   
                 Example 1 
                 6.42 
                 1.29 
                 1.00 
                 1.37 
               
               
                   
                 Example 2 
                 6.69 
                 1.29 
                 1.00 
                 1.39 
               
               
                   
                 Example 3 
                 5.15 
                 1.43 
                 0.90 
                 1.38 
               
               
                   
                 Example 4 
                 9.17 
                 1.18 
                 1.09 
                 1.38 
               
               
                   
                 Example 5 
                 3.34 
                 1.74 
                 1.00 
                 1.59 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 Construction Data of Example 6 (for the first frame-format) 
               
               
                 f = 5.1 mm˜12.0 mm˜29.5 mm (Focal Length of the 
               
               
                 Entire Optical System) 
               
               
                 FN0 = 2.04˜2.34˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 60.282 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 24.393 
                 d2 = 3.953 
                 N2 = 1.71402 
                 ν2 = 53.04 
               
               
                 r3 = 906.240 
                 d3 = 0.100 
               
               
                 r4 = 19.593 
                 d4 = 2.514 
                 N3 = 1.82317 
                 ν3 = 42.49 
               
             
          
           
               
                 r5 = 46.718 
                 d5 = 0.500˜7.378˜12.321 
               
             
          
           
               
                 r6* = 299.608 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 8.414 
                 d7 = 5.893 
               
               
                 r8 = −7.590 
                 d8 = 0.857 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 38.990 
                 d9 = 1.278 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −18.635 
                 d10 = 12.321˜5.443˜0.500 
               
             
          
           
               
                 r11 = ∞(Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 7.684 
                 d12 = 2.101 
                 N7 = 1.84902 
                 ν7 = 33.39 
               
               
                 r13 = 30.947 
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14* = 8.532 
                 d14 = 4.868˜2.651˜0.200 
               
             
          
           
               
                 r15 = 7.957 
                 d15 = 3.139 
                 N9 = 1.78283 
                 ν9 = 47.19 
               
               
                 r16 = −25.917 
                 d16 = 0.100 
               
               
                 r17* = 525.290 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 6.887 
                 d18 = 0.100 
               
               
                 r19 = 6.336 
                 d19 = 5.568 
                 N11 = 1.51030 
                 ν11 = 56.67 
               
             
          
           
               
                 r20 = −68.590 
                 d20 = 1.000˜3.217˜5.668 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.21709 × 10 −3   
               
               
                 A6 = −0.18329 × 10 −5   
               
               
                 A8 = 0.10898 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.10916 × 10 −3   
               
               
                 A6 = 0.29366 × 10 −5   
               
               
                 A8 = −0.55087 × 10 −7   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.30221 × 10 −3   
               
               
                 A6 = 0.94148 × 10 −5   
               
               
                 A8 = −0.46090 × 10 −6   
               
               
                 A10 = 0.22390 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.19557 × 10 −3   
               
               
                 A6 = −0.26628 × 10 −4   
               
               
                 A8 = 0.42985 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.96285 × 10 −3   
               
               
                 A6 = −0.18887 × 10 −4   
               
               
                 A8 = 0.84935 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 Construction Data of Example 6 (for the second frame-format) 
               
               
                 f = 6.8 mm˜16.7 mm˜26.1 mm (Focal Length of the 
               
               
                 Entire Optical System) 
               
               
                 FN0 = 2.15˜2.62˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 50.490 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 21.305 
                 d2 = 3.953 
                 N2 = 1.71402 
                 ν2 = 53.04 
               
               
                 r3 = 209.898 
                 d3 = 0.100 
               
               
                 r4 = 17.259 
                 d4 = 2.514 
                 N3 = 1.82317 
                 ν3 = 42.49 
               
             
          
           
               
                 r5 = 44.790 
                 d5 = 0.700˜6.527˜8.874 
               
             
          
           
               
                 r6* = 299. 608 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 8.414 
                 d7 = 5.893 
               
               
                 r8 = −7.590 
                 d8 = 0.857 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 38.990 
                 d9 = 1.278 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −18.635 
                 d10 = 8.674˜2.847˜0.500 
               
             
          
           
               
                 r11 = ∞(Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 7.684 
                 d12 = 2.101 
                 N7 = 1.84902 
                 ν7 = 33.39 
               
               
                 r13 = 30.947 
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14* = 8.532 
                 d14 = 3.890˜1.302˜0.200 
               
             
          
           
               
                 r15 = 7.957 
                 d15 = 3.139 
                 N9 = 1.78283 
                 ν9 = 47.19 
               
               
                 r16 = −25.917 
                 d16 = 0.100 
               
               
                 r17* = 525.290 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 6.887 
                 d18 = 0.100 
               
               
                 r19 = 6.336 
                 d19 = 5.568 
                 N11 = 1.51030 
                 ν11 = 56.67 
               
             
          
           
               
                 r20 = −68.590 
                 d20 = 1.978˜4.566˜5.668 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.21709 × 10 −3   
               
               
                 A6 = −0.18329 × 10 −5   
               
               
                 A8 = 0.10898 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.10916 × 10 −3   
               
               
                 A6 = 0.29366 × 10 −5   
               
               
                 A8 = −0.55087 × 10 −7   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.30221 × 10 −3   
               
               
                 A6 = 0.94148 × 10 −5   
               
               
                 A8 = −0.46090 × 10 −6   
               
               
                 A10 = 0.22390 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.19557 × 10 −3   
               
               
                 A6 = −0.26628 × 10 −4   
               
               
                 A8 = 0.42985 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.96285 × 10 −3   
               
               
                 A6 = −0.18887 × 10 −4   
               
               
                 A8 = 0.84935 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 14 
               
             
             
               
                   
               
               
                 Construction Data of Example 7 (for the first frame-format) 
               
               
                 f = 5.1 mm˜12.0 mm˜29.5 mm (Focal Length of 
               
               
                 the Entire Optical System) 
               
               
                 FN0 = 2.95˜3.33˜3.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 71.588 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν = 21.00 
               
               
                 r2 = 25.624 
                 d2 = 3.040 
                 N2 = 1.75450 
                 ν2 = 51.57 
               
               
                 r3 = −228.108 
                 d3 = 0.100 
               
               
                 r4 = 16.398 
                 d4 = 2.088 
                 N3 = 1.75450 
                 ν3 = 51.57 
               
             
          
           
               
                 r5 = 36.054 
                 d5 = 0.500˜6.767˜11.422 
               
             
          
           
               
                 r6* = 331.726 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 6.964 
                 d7 = 3.281 
               
               
                 r8 = −7.055 
                 d8 = 0.700 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 17.529 
                 d9 = 1.305 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −20.010 
                 d10 = 11.422˜5.155˜0.500 
               
             
          
           
               
                 r11 = ∞(Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 17.211 
                 d12 = 1.748 
                 N7 = 1.64939 
                 ν7 = 40.02 
               
               
                 r13 = −8.162 
                 d13 = 0.500 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14 = −26.221 
                 d14 = 5.358˜2.714˜0.200 
               
             
          
           
               
                 r15 = 6.566 
                 d15 = 2.884 
                 N9 = 1.59898 
                 ν9 = 59.07 
               
               
                 r16 = −51.162 
                 d16 = 1.371 
               
               
                 r17* = 56.257 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 8.477 
                 d18 = 2.119 
               
               
                 r19 = 11.481 
                 d19 = 1.866 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
             
          
           
               
                 r20 = −130.207 
                 d20 = 1.000˜3.644˜6.158 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.53164 × 10 −3   
               
               
                 A6 = −0.48611 × 10 −5   
               
               
                 A8 = 0.38580 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.52331 × 10 −3   
               
               
                 A6 = 0.10727 × 10 −4   
               
               
                 A8 = 0.10211 × 10 −5   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = −0.35095 × 10 −3   
               
               
                 A6 = −0.22893 × 10 −4   
               
               
                 A8 = 0.31631 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.81168 × 10 −3   
               
               
                 A6 = −0.66566 × 10 −5   
               
               
                 A8 = 0.17258 × 10 −5   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 15 
               
             
             
               
                   
               
               
                 Construction Data of Example 7 (for the second frame-format) 
               
               
                 f = 6.7 mm˜16.5 mm˜25.9mm (Focal Length of the 
               
               
                 Entire Optical System) 
               
               
                 FN0 = 3.07˜3.60˜3.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 68.797 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 23.685 
                 d2 = 3.040 
                 N2 = 1.75450 
                 ν2 = 51.57 
               
               
                 r3 = −295.130 
                 d3 = 0.100 
               
               
                 r4 = 14.636 
                 d4 = 2.088 
                 N3 = 1.75450 
                 ν3 = 51.57 
               
             
          
           
               
                 r5 = 36.561 
                 d5 = 0.700˜6.093˜8.316 
               
             
          
           
               
                 r6* = 331.726 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 6.964 
                 d7 = 3.281 
               
               
                 r8 = −7.055 
                 d8 = 0.700 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 17.529 
                 d9 = 1.305 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −20.010 
                 d10 = 8.116˜2.723˜0.500 
               
             
          
           
               
                 r11 = ∞(Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 17.211 
                 d12 = 1.748 
                 N7 = 1.64939 
                 ν7 = 40.02 
               
               
                 r13 = −8.162 
                 d13 = 0.500 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14 = −26.221 
                 d14 = 4.156˜1.252˜0.200 
               
             
          
           
               
                 r15 = 6.566 
                 d15 = 2.884 
                 N9 = 1.59898 
                 ν9 = 59.07 
               
               
                 r16 = −51.162 
                 d16 = 1.371 
               
               
                 r17* = 56.257 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 8.477 
                 d18 = 2.119 
               
               
                 r19 = 11.481 
                 d19 = 1.866 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
             
          
           
               
                 r20 = −130.207 
                 d20 = 2.202˜5.106˜6.158 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.53164 × 10 −3   
               
               
                 A6 = −0.48611 × 10 −5   
               
               
                 A8 = 0.38580 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.52331 × 10 −3   
               
               
                 A6 = 0.10727 × 10 −4   
               
               
                 A8 = 0.10211 × 10 −5   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = =0.35095 × 10 −3   
               
               
                 A6 = −0.22893 × 10 −4   
               
               
                 A8 = 0.31631× 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.81168 × 10 −3   
               
               
                 A6 = −0.66566 × 10 −5   
               
               
                 A8 = 0.17258 × 10 −5   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 16 
               
             
             
               
                   
               
               
                 Construction Data of Example 8 (for the first frame-format) 
               
               
                 f = 5.1 mm˜12.0 mm˜29.5 mm (Focal Length of the 
               
               
                 Entire Optical System) 
               
               
                 FNO = 2.15˜2.46˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 48.042 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 27.540 
                 d2 = 3.848 
                 N2 = 1.48749 
                 ν2 = 70.44 
               
               
                 r3 = 125.425 
                 d3 = 0.100 
               
               
                 r4 = 19.606 
                 d4 = 2.663 
                 N3 = 1.75450 
                 ν3 = 51.57 
               
             
          
           
               
                 r5 = 44.341 
                 d5 = 0.909˜9.146˜15.048 
               
             
          
           
               
                 r6* = −125.878 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 8.661 
                 d7 = 5.379 
               
               
                 r8 = −6.344 
                 d8 = 0.743 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 170.925 
                 d9 = 1.109 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −13.808 
                 d10 = 9.830˜4.621˜0.500 
               
             
          
           
               
                 r11 = ∞ (Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 6.833 
                 d12 = 1.797 
                 N7 = 1.84910 
                 ν7 = 33.85 
               
               
                 r13 = 19.895 
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14* = 7.569 
                 d14 = 3.919˜1.936˜0.200 
               
             
          
           
               
                 r15 = 8.280 
                 d15 = 3.123 
                 N9 = 1.75450 
                 ν9 = 51.57 
               
               
                 r16 = −24.676 
                 d16 = 0.100 
               
               
                 r17* = 68.278 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 6.577 
                 d18 = 0.100 
               
               
                 r19 = 6.360 
                 d19 = 5.645 
                 N11 = 1.57545 
                 ν11 = 56.48 
               
             
          
           
               
                 r20 = −56.054 
                 d20 = 1.095˜3.078˜4.814 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.35660 × 10 −3   
               
               
                 A6 = −0.48752 × 10 −5   
               
               
                 A8 = 0.32922 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.17663 × 10 −3   
               
               
                 A6 = 0.46973 × 10 −5   
               
               
                 A8 = −0.33901 × 10 −6   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.44879 × 10 −3   
               
               
                 A6 = 0.14888 × 10 −4   
               
               
                 A8 = −0.85281 × 10 −6   
               
               
                 A10 = 0.57505 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.62336 × 10 −4   
               
               
                 A6 = −0.24680 × 10 −4   
               
               
                 A8 = 0.43821 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.70776 × 10 −3   
               
               
                 A6 = −0.20433 × 10 −4   
               
               
                 A8 = 0.80230 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 17 
               
             
             
               
                   
               
               
                 Construction Data of Example 8 (for the second frame-format) 
               
               
                 f = 6.1 mm˜16.3 mm˜25.5 mm (Focal Length of the 
               
               
                 Entire Optical System) 
               
               
                 FN0 = 2.28˜2.66˜2.88 (F-Numbers) 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index (Nd) 
                 Number(νd) 
               
               
                   
               
               
                 r1 = 39.393 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 23.154 
                 d2 = 3.848 
                 N2 = 1.48749 
                 ν2 = 70.44 
               
               
                 r3 = −365.665 
                 d3 = 0.100 
               
               
                 r4 = 17.689 
                 d4 = 2.663 
                 N3 = 1.75450 
                 ν3 = 51.57 
               
             
          
           
               
                 r5 = 50.349 
                 d5 = 0.835˜8.235˜10.806 
               
             
          
           
               
                 r6* = −125.878 
                 d6 = 1.200 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 8.661 
                 d7 = 5.379 
               
               
                 r8 = −6.344 
                 d8 = 0.743 
                 N5 = 1.77250 
                 ν5 = 49.77 
               
               
                 r9 = 170.925 
                 d9 = 1.109 
                 N6 = 1.83350 
                 ν6 = 21.00 
               
             
          
           
               
                 r10 = −13.808 
                 d10 = 6.897˜2.615˜0.500 
               
             
          
           
               
                 r11 = ∞(Aperture Stop) 
                 d11 = 0.500 
                   
                   
               
               
                 r12 = 6.833 
                 d12 = 1.797 
                 N7 = 1.84910 
                 ν7 = 33.85 
               
               
                 r13 = 19.895 
                 d13 = 1.000 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14* = 7.569 
                 d14 = 2.918˜1.023˜0.200 
               
             
          
           
               
                 r15 = 8.280 
                 d15 = 3.123 
                 N9 = 1.75450 
                 ν9 = 51.57 
               
               
                 r16 = −24.676 
                 d16 = 0.100 
               
               
                 r17* = 68.278 
                 d17 = 1.200 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18* = 6.577 
                 d18 = 0.100 
               
               
                 r19 = 6.360 
                 d19 = 5.645 
                 N11 = 1.57545 
                 ν11 = 56.48 
               
             
          
           
               
                 r20 = −56.054 
                 d20 = 2.096˜3.991˜4.814 
               
             
          
           
               
                 r21 = ∞ 
                 d21 = 3.400 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r22 = ∞ 
               
             
          
           
               
                 Aspherical Coefficients of 6th Surface (r6) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.35660 × 10 −3   
               
               
                 A6 = −0.48752 × 10 −5   
               
               
                 A8 = 0.32922 × 10 −7   
               
               
                 Aspherical Coefficients of 7th Surface (r7) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.17663 × 10 −3   
               
               
                 A6 = 0.46973 × 10 −5   
               
               
                 A8 = −0.33901 × 10 −6   
               
               
                 Aspherical Coefficients of 14th Surface (r14) 
               
               
                 ε = 0.1000 × 10 
               
               
                 A4 = 0.44879 × 10 −3   
               
               
                 A6 = 0.14888 × 10 −4   
               
               
                 A8 = −0.85281 × 10 −6   
               
               
                 A10 = 0.57505 × 10 −7   
               
               
                 Aspherical Coefficients of 17th Surface (r17) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.62336 × 10 −4   
               
               
                 A6 = −0.24680 × 10 −4   
               
               
                 A8 = 0.43821 × 10 −6   
               
               
                 Aspherical Coefficients of 18th Surface (r18) 
               
               
                 ε = 0.10000 × 10 
               
               
                 A4 = 0.70776 × 10 −3   
               
               
                 A6 = −0.20433 × 10 −4   
               
               
                 A8 = 0.80230 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 18 
               
             
             
               
                   
               
               
                 Values Corresponding to Conditions (5) to (8) 
               
             
          
           
               
                   
                 f1b/f1s 
                 Zb/Zs 
                 |f2|/fws 
                 Ys/Yb 
               
               
                   
                   
               
             
          
           
               
                   
                 Example 6 
                 0.89 
                 0.67 
                 1.22 
                 0.78 
               
               
                   
                 Example 7 
                 0.88 
                 0.67 
                 1.07 
                 0.78 
               
               
                   
                 Example 8 
                 0.87 
                 0.67 
                 1.15 
                 0.78