Abstract:
Taking lens apparatus has zoom lens system, focusing light from object to form optical image, and image-sensing device, converting optical image into electric signal. Lens system has: first lens unit having a positive optical power, composed of three or fewer lens elements including at least one negative lens element and at least one positive lens element; second lens unit having negative optical power and moving to be on image-plane side of its position in shortest-focal-length condition; and one or more succeeding lens units. This system varies magnification by varying distances between lens units, and fulfills 0.92&lt;FW/IH&lt;1.85, ND&lt;1.53, and VD&gt;78, where FW represents focal length of lens system in shortest-focal-length condition, IH represents maximum image height, ND represents refractive index for d line of positive lens element included in first lens unit, and VD represents Abbe number for d line of same positive lens element.

Description:
This application is based on applications Nos. H11-308390 and 2000-291686 filed in Japan on Oct. 29, 1999 and Sep. 26, 2000, respectively, the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a taking lens apparatus, and particularly to a taking lens apparatus that optically takes in an image of a subject through an optical system and that outputs the image as an electric signal by means of an image-sensing device (i.e. a taking lens apparatus for use as the principal component of a digital camera, video camera, or camera built in or externally fitted to a personal computer, mobile computer, portable telephone, personal digital assistant (PDA), or the like), and more particularly to a taking lens apparatus provided with a compact high-zoom-ratio zoom lens system. 
     2. Description of the Prior Art 
     In recent years, as personal computers become more and more popular, digital still cameras, which permit easy acquisition of images, have been becoming increasingly popular. As digital still cameras become more and more popular, models offering increasingly high zoom ratios are sought after, and accordingly there is a growing demand for increasingly compact and high-zoom-ratio taking lens systems. On the other hand, as image-sensing devices with more and more pixels are developed, increasingly high-performance taking lens systems are sought after. 
     However, no known conventional zoom lens system satisfactorily meets these conflicting requirements of compactness and a high zoom ratio combined with high optical performance. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a taking lens apparatus provided with a compact, high-zoom-ratio, but nevertheless high-performance zoom lens system. 
     To achieve the above object, according to one aspect of the present invention, a taking lens apparatus is provided with: a zoom lens system for focusing the light from an object so as to form an optical image; and an image-sensing device for converting the optical image formed by the zoom lens system into an electric signal. Here, the zoom lens system is provided with, from the object side: a first lens unit having a positive optical power and composed of three or fewer lens elements in total including at least one negative lens element and at least one positive lens element; a second lens unit having a negative optical power and moving, during zooming, in such a way as to be located always on the image-plane side of the position in which the second lens unit is located in the shortest-focal-length condition; and one or more succeeding lens units. This zoom lens system permits the magnification to be varied by varying the distances between the lens units, and fulfills the following conditions: 
     0.92&lt;FW/IH&lt;1.85; 
     ND&lt;1.53; and 
     VD&gt;78, 
     where FW represents the focal length of the zoom lens system in the shortest-focal-length condition; IH represents the maximum image height; ND represents the refractive index for the d line of the positive lens element mentioned above as at least one included in the first lens unit; and VD represents the Abbe number for the d line of the positive lens element mentioned above as at least one included in the first lens unit. 
     According to another aspect of the present invention, a taking lens apparatus is provided with: a zoom lens system for focusing the light from an object so as to form an optical image; an image-sensing device for converting the optical image formed by the zoom lens system into an electric signal; and an optical low-pass filter, disposed in the optical path on the object side of the image-sensing device, for optically controlling a predetermined spatial frequency component included in the optical image formed by the zoom lens system. Here, the zoom lens system is provided with, from the object side: a first lens unit having a positive optical power and composed of three or fewer lens elements in total including at least one negative lens element and at least one positive lens element; a second lens unit having a negative optical power and moving, during zooming, in such a way as to be located always on the image-plane side of the position in which the second lens unit is located in the shortest-focal-length condition; and one or more succeeding lens units. This zoom lens system permits the magnification to be varied by varying the distances between those lens units, and fulfills the following conditions: 
     0.92&lt;FW/IH&lt;1.85; 
     ND&lt;1.53; and 
     VD&gt;78, 
     where FW represents the focal length of the zoom lens system in the shortest-focal-length condition; IH represents the maximum image height; ND represents the refractive index for the d line of the positive lens element mentioned above as at least one included in the first lens unit; and VI) represents the Abbe number for the d line of the positive lens element mentioned above as at least one included in the first lens unit. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     This and other objects and features of the present invention will become clear from the following description, taken in conjunction with the preferred embodiments with reference to the accompanying drawings in which: 
     FIG. 1 is a lens construction diagram of a first embodiment (Example 1) of the invention; 
     FIG. 2 is a lens construction diagram of a second embodiment (Example 2) of the invention; 
     FIG. 3 is a lens construction diagram of a third embodiment (Example 3) of the invention; 
     FIG. 4 is a lens construction diagram of a fourth embodiment (Example 4) of the invention; 
     FIG. 5 is a lens construction diagram of a fifth embodiment (Example 5) of the invention; 
     FIG. 6 is a lens construction diagram of a sixth embodiment (Example 6) of the invention; 
     FIGS. 7A to  7 I are diagrams showing the aberrations observed in Example 1; 
     FIGS. 8A to  8 I are diagrams showing the aberrations observed in Example 2; 
     FIGS. 9A to  9 I are diagrams showing the aberrations observed in Example 3; 
     FIGS. 10A to  10 I are diagrams showing the aberrations observed in Example 4; 
     FIGS. 11A to  11 I are diagrams showing the aberrations observed in Example 5; 
     FIGS. 12A to  12 I are diagrams showing the aberrations observed in Example 6; and 
     FIG. 13 is a schematic diagram illustrating the outline of the optical construction of a taking lens apparatus embodying the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, taking lens apparatuses embodying the present invention will be described with reference to the drawings. A taking lens apparatus takes in an image of a subject optically, and outputs it as an electric signal. Taking lens apparatuses are used as a principal component in cameras for taking still or moving pictures of a subject (for example, digital cameras, video cameras, and cameras built in or externally fitted to personal computers, mobile computers, portable telephones, personal digital assistants (PDAs) and the like). For example, as shown in FIG. 13, a taking lens apparatus is composed of, from the object (i.e. the subject to be shot) side, a taking lens system (TL) for forming an optical image of the object, a plane-parallel plate (LPF) serving as a low-pass filter or the like, and an image-sensing device (SR) for converting the optical image formed by the taking lens system (TL) into an electric signal. 
     All of the embodiments described hereinafter employ as the taking lens system (TL) a zoom lens system composed of a plurality of lens units. This zoom lens system is so constructed that at least two of its constituent lens units can move along the optical axis (AX) in such a way as to vary the distances between the individual lens units and thereby vary the magnification. As the image-sensing device (SR), for example, a solid-state image-sensing device such as a CCD (charge-coupled device) or CMOS (complementary metal-oxide semiconductor) having a plurality of pixels is used, by which the optical image formed by the zoom lens system is converted into an electric signal. The optical image to be formed by the zoom lens system is passed through the optical low-pass filter (LPF), which has a predetermined cut-off frequency characteristic determined by the pixel pitch of the image-sensing device. This helps adjust the spatial frequency characteristics of the optical image in such a way as to minimize so-called turning noise that occurs when the optical image is converted into an electric signal. The electric signal produced by the image-sensing device (SR) is subjected to predetermined digital image processing, image compression processing, or other as required, and is then recorded as a digital image signal on a storage device (such as a semiconductor memory or optical disk) or, depending on applications, transmitted to an external device by way of a cable or after being converted into an infrared signal. 
     FIGS. 1 to  6  are lens construction diagrams of the zoom lens system employed in a first to a sixth embodiment, respectively, of the invention, each illustrating the lens arrangement at the wide-angle end [W] (i.e. in the shortest-focal-length condition). In each lens construction diagram, an arrow mj (j=1, 2, . . . ) schematically indicates the movement of the j-th lens unit (Grj) during zooming from the wide-angle end [W] to the telephoto end [T] (i.e. the longest-focal-length condition). Moreover, in each lens construction diagram, ri (i=1, 2, 3, . . . ) indicates the i-th surface as counted from the object side, and a surface ri marked with an asterisk (*) is an aspherical surface; di (i=1, 2, 3, . . . ) indicates the i-th axial distance as counted from the object side, though only those which vary with zooming are shown here. 
     In all the embodiments, the zoom lens system is composed of, from the object side, a first lens unit (Gr 1 ) having a positive optical power, a second lens unit (Gr 2 ) having a negative optical power, and at least one succeeding lens unit (Gr 3 , . . . ) that follows them. During zooming from the wide-angle end [W] to the telephoto end [T], the second lens unit (Gr 2 ) moves in such a way as to be located always on the image-plane side of the position where it is located at the wide-angle end [W]. This causes the distances between the individual lens units to vary and thereby causes the magnification to vary. Since this zoom lens system is designed for use in a camera (for example, a digital still camera) provided with a solid-state image-sensing device (for example, a CCD), on the image-plane side thereof is disposed the plane-parallel plate (LPF), which is made of glass and serves as a low-pass filter or the like. In all the embodiments, the first lens unit (Gr 1 ) is composed of three or fewer lens elements in total including at least one negative lens element and at least one positive lens element, and the third lens unit (Gr 3 ) includes an aperture stop (SP) at the object-side end thereof. The lens construction of each embodiment will be described in detail below. 
     First Embodiment (FIG. 1, positive-negative-positive-positive) 
     In the first embodiment, the zoom lens system is a four-lens-unit type of a positive-negative-positive-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the object side cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a negative meniscus lens element concave to the image-plane side, a biconcave negative lens element, and a positive meniscus lens element convex to the object side (having aspherical surfaces on both sides). The third lens unit (Gr 3 ) is composed of an aperture stop (SP) and a cemented lens element consisting of a biconvex positive lens element and a negative meniscus lens element concave to the object side cemented together. The fourth lens unit (Gr 4 ) is composed of a positive meniscus lens element convex to the object side, a biconcave negative lens element (having aspherical surfaces on both sides), and a positive meniscus lens element convex to the object side. During zooming, all these lens units move for zooming. 
     Second Embodiment (FIG. 2, positive-negative-positive-positive) 
     In the second embodiment, the zoom lens system is a four-lens-unit type of a positive-negative-positive-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a biconvex positive lens element cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a negative meniscus lens element concave to the image-plane side, a biconcave negative lens element, and a positive meniscus lens element convex to the object side (having aspherical surfaces on both sides). The third lens unit (Gr 3 ) is composed of an aperture stop (SP) and a cemented lens element consisting of a biconvex positive lens element and a negative meniscus lens element concave to the object side cemented together. The fourth lens unit (Gr 4 ) is composed of a positive meniscus lens element convex to the object side, a negative meniscus lens element concave to the image-plane side (having aspherical surfaces on both sides), and a positive meniscus lens element convex to the object side. During zooming, all these lens units move for zooming. 
     Third Embodiment (FIG. 3, positive-negative-positive-negative-positive) 
     In the third embodiment, the zoom lens system is a five-lens-unit type of a positive-negative-positive-negative-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the object side cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a negative meniscus lens element concave to the image-plane side (having aspherical surfaces on both sides), a biconcave negative lens element, a biconvex positive lens element, and a negative meniscus lens element concave to the object side. The third lens unit (Gr 3 ) is composed of an aperture stop (SP), a biconvex positive lens element, a biconcave negative lens element (having aspherical surfaces on both sides), and a biconvex positive lens element. The fourth lens unit (Gr 4 ) is composed of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the image-plane side. The fifth lens unit (Gr 5 ) is composed of a biconvex positive lens element, a biconcave negative lens element, and a positive meniscus lens element convex to the object side. During zooming, all these lens units move for zooming. 
     Fourth Embodiment (FIG. 4, positive-negative-positive-negative-positive-positive) 
     In the fourth embodiment, the zoom lens system is a six-lens-unit type of a positive-negative-positive-negative-positive-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a biconvex positive lens element cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a negative meniscus lens element concave to the image-plane side, a biconcave negative lens element, a biconvex positive lens element (having aspherical surfaces on both sides), and a negative meniscus lens element concave to the object side. The third lens unit (Gr 3 ) is composed of an aperture stop (SP), a positive meniscus lens element convex to the object side, a biconcave negative lens element (having aspherical surfaces on both sides), and a biconvex positive lens element. The fourth lens unit (Gr 4 ) is composed of a biconcave negative lens element and a positive meniscus lens element convex to the object side. The fifth lens unit (Gr 5 ) is composed of a positive meniscus lens element convex to the object side. The sixth lens unit (Gr 6 ) is composed of a cemented lens element consisting of a biconvex positive lens element and a biconcave negative lens element cemented together. During zooming, whereas the first to fifth lens units (Gr 1  to Gr 5 ) move for zooming, the sixth, i.e. last, lens unit (Gr 6 ), as well as the plane-parallel plate (LPF), remains in a fixed position. 
     Fifth Embodiment (FIG. 5, positive-negative-positive-negative-positive) 
     In the fifth embodiment, the zoom lens system is a five-lens-unit type of a positive-negative-positive-negative-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the object side cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side, a biconcave negative lens element, and a biconvex positive lens element cemented together, and a negative meniscus lens element concave to the object side (having an aspherical surface on the image-plane side). The third lens unit (Gr 3 ) is composed of an aperture stop (SP), a cemented lens element consisting of a positive meniscus lens element convex to the object side, a biconvex positive lens element, and a biconcave negative lens element cemented together, a positive meniscus lens element convex to the object side (having an aspherical surface on the image-plane side), and a biconvex positive lens element. The fourth lens unit (Gr 4 ) is composed of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the object side. The fifth lens unit (Gr 5 ) is composed of a positive meniscus lens element convex to the object side. During zooming, whereas the first to fourth lens units (Gr 1  to Gr 4 ) move for zooming, the fifth, i.e. last, lens unit (Gr 5 ), as well as the plane-parallel plate (LPF), remains in a fixed position. 
     Sixth Embodiment (FIG. 6, positive-negative-positive-positive) 
     In the sixth embodiment, the zoom lens system is a four-lens-unit type of a positive-negative-positive-positive construction. Each lens unit is composed of optical elements that are arranged, from the object side, as follows. The first lens unit (Gr 1 ) is composed of a cemented lens element consisting of a negative meniscus lens element concave to the image-plane side and a positive meniscus lens element convex to the object side cemented together, and a positive meniscus lens element convex to the object side. The second lens unit (Gr 2 ) is composed of a negative meniscus lens element concave to the image-plane side (having an aspherical surface on the image-plane side), and a cemented lens element consisting of a biconcave negative lens element and a positive meniscus lens element convex to the object side (having an aspherical surface on the image-plane side) cemented together. The third lens unit (Gr 3 ) is composed of an aperture stop (SP) and a cemented lens element consisting of a biconvex positive lens element and a negative meniscus lens element concave to the object side cemented together. The fourth lens unit (Gr 4 ) is composed of a biconvex positive lens element and a biconcave negative lens element (having aspherical surfaces on both sides). During zooming, whereas the second and fourth lens units (Gr 2  and Gr 4 ) move for zooming, the first and third lens units (Gr 1  and Gr 3 ) remain in fixed positions. 
     In all the embodiments described above, during zooming from the wide-angle end [W] to the telephoto end [T], the second lens unit (Gr 2 ) moves in such a way as to be located always on the image-plane side of the position where it is located at the wide-angle end [W]. Thus, at the wide-angle end [W], the second lens unit (Gr 2 ) is located in the most object-side position throughout the entire zoom range. Such movement of the second lens unit (Gr 2 ) is peculiar to a camera (for example, a digital still camera) provided with a solid-state image-sensing device (for example, a CCD). Designed for such application, the zoom lens system here should preferably fulfill the conditions that will be described below. It is to be noted that even fulfilling those conditions singly helps achieve the effects corresponding to the fulfilled conditions but, needless to say, fulfilling as many of them as possible is preferable for best results in terms of optical performance, compactness, and other aspects. 
     It is preferable that condition (1) noted below be fulfilled. If the lower limit of condition (1) is transgressed, the lens elements that are disposed at the front need to be given unduly large diameters. This makes the camera unduly large, and in addition makes correction of distortion unduly difficult. By contrast, if the upper limit of condition (1) is transgressed, the zoom lens system comes to have an unduly long total length. This makes the camera unduly large. 
     
       
         0.92&lt;FW/IH&lt;1.85  (1) 
       
     
     where 
     FW represents the focal length of the zoom lens system as a whole at the wide-angle end [W]; and 
     IH represents the maximum image height. 
     It is preferable that conditions (2) and (3) noted below be fulfilled. Conditions (2) and (3) define the conditions that ensure effective use of anomalous dispersion glass in a zoom lens system designed for use in a camera provided with a solid-state image-sensing device. If the upper limit of condition (2) or the lower limit of condition (3) is transgressed, it is unduly difficult to correct lateral chromatic aberration, and thus it is unduly difficult to obtain satisfactory optical performance over the entire zoom range. 
     
       
         ND&lt;1.53  (2) 
       
     
      VD&gt;78  (3) 
     where 
     ND represents the refractive index for the d line of the positive lens element mentioned above as at least one included in the first lens unit (Gr 1 ); and 
     VD represents the Abbe number for the d line of the positive lens element mentioned above as at least one included in the first lens unit (Gr 1 ). 
     It is preferable that, as in any of the embodiments described previously, the first lens unit (Gr 1 ) be composed of three lens elements that are, from the object side, a negative lens element convex to the object side, a positive lens element convex to the object side, and a positive lens element convex to the object side. This lens arrangement is effective in properly correcting various aberrations with the first lens unit (Gr 1 ), and is effective also in reducing the total length of the zoom lens system. 
     It is preferable that, as in any of the embodiments described previously, the third lens unit (Gr 3 ) be given a positive optical power. Giving the third lens unit (Gr 3 ) a positive optical power permits the light beam that has been made to diverge by the second lens unit (Gr 2 ) to be made to converge by the third lens unit (Gr 3 ). This helps reduce the total length of the zoom lens system. 
     Generally, a solid-state image-sensing device (such as a CCD) designed for use in a digital still camera, video camera, or the like has microlenses provided individually in front of light-sensing elements in order to enhance their light-collecting ability. To make the most of the characteristics of the microlenses, it is essential to make a light beam incident thereon substantially parallel to the optical axes thereof (i.e. substantially perpendicularly to the light-sensing surface of the light-sensing elements). To achieve this, it is necessary to use a taking lens system that is so constructed as to be telecentric toward the image-plane side. From this perspective, it is preferable that, as in any of the embodiments described previously, the lens unit disposed at the image-plane-side end (i.e. the last lens unit) be given a positive optical power. Giving the last lens unit a positive optical power permits a light beam to be incident on the solid-state image-sensing device substantially perpendicularly to the light-sensing surface thereof. Thus, it is possible to make the most of the performance of the solid-state image-sensing device. 
     It is preferable that condition (4) noted below be fulfilled. If the lower limit of condition (4) is transgressed, the lens elements disposed at the front need to be given unduly large diameters. This makes the camera unduly large. By contrast, if the upper limit of condition (4) is transgressed, coma aberration becomes so large as to cause unduly large astigmatism. 
     
       
         0.06&lt;FW/F 1 &lt;0.21  (4) 
       
     
     where 
     FW represents the focal length of the zoom lens system as a whole at the wide-angle end [W]; and 
     F 1  represents the focal length of the first lens unit (Gr 1 ). 
     It is preferable that, as in any of the embodiments described previously, in the first lens unit (Gr 1 ), a negative lens element convex to the object side and a positive lens element convex to the object side be cemented together. Cementing these lens elements together helps simplify the shape of the lens frame and in addition reduce error-causing factors (that is, the errors attributable to the gap between the lenses can be minimized by cementing them together). This makes it easy to give the zoom lens system high optical performance. 
     It is preferable that, as in any of the embodiments described previously, the first lens unit (Gr 1 ) move toward the object side during zooming from the wide-angle end [W] to the telephoto end [T]. Moving the first lens unit (Gr 1 ) toward the object side permits the heights at which rays of light pass therethrough to vary with zooming. This makes it possible to distribute properly the burden of aberration correction among the lens units, and thus makes it easy to give the zoom lens system high optical performance. 
     It is preferable that, as in any of the embodiments described previously, the third lens unit (Gr 3 ) move toward the object side during zooming from the wide-angle end [W] to the telephoto end [T]. Moving the third lens unit (Gr 3 ) toward the object side helps alleviate the burden of aberration correction associated with zooming on the third lens unit (Gr 3 ) and any lens unit succeeding it. This makes it easy to give the zoom lens system high optical performance. 
     It is preferable that condition (5) noted below be fulfilled. If the lower limit of condition (5) is transgressed, the third lens unit (Gr 3 ) has too weak an optical power. This is advantageous to aberration correction, but requires an undue increase in the movement stroke of the third lens unit (Gr 3 ). This makes the total length of the zoom lens system and the diameters of the lens elements disposed at the front unduly large. By contrast, if the upper limit of condition (5) is transgressed, the third lens unit (Gr 3 ) has too strong an optical power. This is advantageous to reducing the total length of the zoom lens system, but makes the inclination of the image plane toward the over side unduly large. 
     
       
         0.12&lt;FW/F 3 &lt;0.56  (5) 
       
     
     where 
     FW represents the focal length of the zoom lens system as a whole at wide-angle end [W]; and 
     F 3  represents the focal length of the third lens unit (Gr 3 ). 
     It is preferable that condition (6) noted below be fulfilled. If the lower limit of condition (6) is transgressed, coma aberration becomes so large as to cause unduly large high-order lateral chromatic aberration. By contrast, if the upper limit of condition (6) is transgressed, coma aberration becomes so large as to cause unduly large astigmatism. 
     
       
         0.03&lt;FW/FR&lt;0.55  (6) 
       
     
     where 
     FW represents the focal length of the zoom lens system as a whole at wide-angle end [W]; and 
     FR represents the focal length of the lens unit disposed at the image-plane-side end. 
     In the first to sixth embodiments described hereinbefore, all the lens units are composed solely of refractive lens elements, i.e. lens elements that deflect the light incident thereon by refraction (in other words, lens elements in which deflection of light occurs at the interface surface between media having different refractive indices). However, these lens units may include one or more lens elements of any other type, e.g. diffractive lens elements that deflect the light incident thereon by diffraction, refractive/diffractive hybrid-type lens elements that deflect the light incident thereon by combined effect of diffraction and refraction, or gradient-index lens elements that deflect the light incident thereon by varying refractive indices distributed within a medium. 
     Moreover, in any of the embodiments described hereinbefore, a surface having no optical power (for example, a reflecting, refracting, or diffracting surface) may be disposed in the optical path so as to turn the optical path in front of, behind, or within the zoom lens system. Where to turn the optical path may be determined as required. Turning the optical path appropriately helps make the camera look slimmer. It is also possible even to realize a construction that keeps the thickness of the camera constant even when the zoom lens system performs zooming or when the zoom lens system is so constructed as to be collapsible. For example, by disposing a mirror behind the first lens unit (Gr 1 ), which remains in a fixed position during zooming, in such a way that the reflecting surface of the mirror turns the optical path 90 degrees there, it is possible to keep the front-to-rear length of the zoom lens system fixed and thereby make the camera slimmer. 
     Furthermore, in any of the embodiments described hereinbefore, as the optical low-pass filter having the shape of a plane-parallel plate and disposed between the final surface of the zoom lens system and the image-sensing device, it is also possible to use a birefringence-type low-pass filter made of quartz or the like and having a predetermined crystal axis thereof aligned appropriately, a phase-type low-pass filter that exploits the effect of diffraction to achieve a desired optical cut-off frequency characteristic, or the like. 
     EXAMPLES 
     Hereinafter, practical examples of the construction of the zoom lens system employed in taking lens apparatuses embodying the present invention will be described with reference to their construction data and other data. Examples 1 to 6 described below correspond to the first to sixth embodiments, respectively, described previously, and therefore the lens arrangement diagrams (FIGS. 1 to  6 ), which show the lens construction of the first to sixth embodiments, also show the lens construction of Examples 1 to 6, respectively. 
     Tables 1 to 6 list the construction data of Examples 1 to 6, respectively. In the construction data of each example, ri (i=1, 2, 3, . . . ) represents the radius of curvature of the i-th surface as counted from the object side, di (i=1, 2, 3, . . . ) represents the i-th axial distance as counted from the object side, and Ni (i=1, 2, 3, . . . ) and vi (i=1, 2, 3, . . . ) respectively represent the refractive index (Nd) for the d line and the Abbe number (vd) of the i-th optical element as counted from the object side. In the construction data, for each of those axial distances that vary with zooming (i.e. variable axial distances), three values are listed, which are, from left, the axial distances as observed at the wide-angle end [W] (in the shortest-focal-length condition), at the middle [M] (in the middle-focal-length condition), and at the telephoto end [T] (in the longest-focal-length condition). Also listed are the focal length (f) and the f/number (FNO) of the zoom lens system as a whole as observed in each of the three focal length conditions [W], [M], and [T] mentioned just above. Table 7 lists the values of conditions (1) to (6) as actually observed in each example. 
     A surface whose radius of curvature ri is marked with an asterisk (*) is an aspherical surface, of which the surface shape is defined by formula (AS) below. The data of each aspherical surface are also listed together with other data in the construction data. 
     
       
         X(H)=(C·H 2 )/( 1+{square root over (1+L −ε·C 2 +L ·H 2 +L )}) +(A 4·H 4 +A6·H 6 +A8·H 8 +A10·H 10 )  (AS) 
       
     
     where 
     X(H) represents the displacement along the optical axis at the height H (with respect to the vertex); 
     H represents the height in a direction perpendicular to the optical axis; 
     C represents the paraxial curvature; 
     ε represents the quadric surface parameter; and 
     Ai represents the aspherical surface coefficient of the i-th order. 
     FIGS. 7A-7I,  8 A- 8 I,  9 A- 9 I,  10 A- 10 I,  11 A- 11 I, and  12 A- 12 I are diagrams showing the aberrations observed in Examples 1 to 6, respectively. Of these diagrams, FIGS. 7A-7C,  8 A- 8 C,  9 A- 9 C,  10 A- 10 C,  11 A- 11 C, and  12 A- 12 C show the aberrations observed at the wide-angle end [W], FIGS. 7D-7F,  8 D- 8 F,  9 D- 9 F,  10 D- 10 F,  11 D- 11 F, and  12 D- 12 F show the aberrations observed at the middle [M], and FIGS. 7G-7I,  8 G- 8 I,  9 G- 91 ,  10 G- 10 I,  11 G- 11 I, and  12 G- 12 I show the aberrations observed at the telephoto end [T]. Of these diagrams, FIGS. 7A,  7 D,  7 G,  8 A,  8 D,  8 G,  9 A,  9 D,  9 G,  10 A,  10 D,  10 G,  11 A,  11 D,  11 G,  12 A,  12 D, and  12 G show spherical aberration and the sine condition, FIGS. 7B,  7 E,  7 H,  8 B,  8 E,  8 H,  9 B,  9 E,  9 H,  10 B,  10 E,  10 H,  11 B,  11 E,  11 H,  12 B,  12 E, and  12 H show astigmatism, and FIGS. 7C,  7 F,  7 I,  8 C,  8 F,  8 I,  9 C,  9 F,  9 I,  10 C,  10 F,  10 I,  11 C,  11 F,  11 I,  12 C,  12 F, and  12 I show distortion. In each diagram, Y′ represents the maximum image height. In the diagrams showing spherical aberration, a solid line (d) indicates the spherical aberration for the d line, a dash-and-dot line (g) indicates the spherical aberration for the g line, a dash-dot-dot line (c) indicates the spherical aberration for the c line, and a broken line (SC) indicates the sine condition. In the diagrams showing astigmatism, a broken line (DM) indicates the astigmatism for the d line as observed on the meridional plane, and a solid line (DS) indicates the astigmatism for the d line as observed on the sagittal plane. In the diagrams showing distortion, a solid line indicates the distortion (%) for the d line. 
     As described above, according to the present invention, it is possible to realize a taking lens apparatus provided with a compact, high-zoom-ratio, but nevertheless high-performance zoom lens system. By applying the present invention in digital cameras, video cameras, and cameras built in or externally fitted to personal computers, mobile computers, portable telephones, personal digital assistants (PDAs), and the like, it is possible to achieve satisfactory compactness, high zoom ratios, and high optical performance in such devices. 
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Example 1 
               
               
                 f = 7.17 ˜ 19.39 ˜ 27.44, FN0 = 2.98 ˜ 3.58 ˜ 3.69 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 41.634 
                 d1 = 1.100 
                 N1 = 1.83350 
                 ν1 = 21.00 
               
               
                 r2 = 25.936 
                 d2 = 3.780 
                 N2 = 1.75450 
                 ν2 = 51.57 
               
               
                 r3 = 131.591 
                 d3 = 0.100 
               
               
                 r4 = 19.149 
                 d4 = 3.089 
                 N3 = 1.49310 
                 ν3 = 83.58 
               
             
          
           
               
                 r5 = 48.179 
                 d5 = 0.900 ˜ 10.875 ˜ 14.065 
               
             
          
           
               
                 r6 = 26.434 
                 d6 = 0.750 
                 N4 = 1.75450 
                 ν4 = 51.57 
               
               
                 r7 = 5.738 
                 d7 = 3.604 
               
               
                 r8 = −16.645 
                 d8 = 0.650 
                 N5 = 1.69680 
                 ν5 = 56.47 
               
               
                 r9 = 13.081 
                 d9 = 0.500 
               
               
                 r10* = 11.585 
                 d10 = 2.500 
                 N6 = 1.84506 
                 ν6 = 23.66 
               
             
          
           
               
                 r11* = 81.076 
                 d11 = 10.832 ˜ 3.527 ˜ 1.500 
               
             
          
           
               
                 r12 = ∞(SP) 
                 d12 = 1.000 
                   
                   
               
               
                 r13 = 43.905 
                 d13 = 2.090 
                 N7 = 1.72916 
                 ν7 = 54.67 
               
               
                 r14 = −8.586 
                 d14 = 0.700 
                 N8 = 1.85000 
                 ν8 = 40.04 
               
             
          
           
               
                 r15 = −39.965 
                 d15 = 2.298 ˜ 0.300 ˜ 0.300 
               
             
          
           
               
                 r16 = 6.982 
                 d16 = 3.500 
                 N9 = 1.58913 
                 ν9 = 61.11 
               
               
                 r17 = 53.652 
                 d17 = 1.472 
               
               
                 r18* = −329.100 
                 d18 = 1.859 
                 N10 = 1.84506 
                 ν10 = 23.66 
               
               
                 r19* = 15.146 
                 d19 = 1.200 
               
               
                 r20 = 8.679 
                 d20 = 2.650 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
             
          
           
               
                 r21 = 125.894 
                 d21 = 5.406 ˜ 9.036 ˜ 9.816 
               
             
          
           
               
                 r22 = ∞ 
                 d22 = 3.000 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r23 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 10th Surface (r10) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.55964 × 10 −4   
               
               
                 A6 = −0.13119 × 10 −5   
               
               
                 A8 = −0.18275 × 10 −6   
               
               
                 Aspherical Surface Data of the 11th Surface (r11) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.52847 × 10 −4   
               
               
                 A6 = −0.10695 × 10 −5   
               
               
                 A8 = −0.18285 × 10 −6   
               
               
                 Aspherical Surface Data of the 18th Surface (r18) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.73476 × 10 −3   
               
               
                 A6 = −0.20772 × 10 −4   
               
               
                 A8 = −0.12834 × 10 −6   
               
               
                 Aspherical Surface Data of the 19th Surface (r19) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.16025 × 10 −2   
               
               
                 A6 =   0.58744 × 10 −5   
               
               
                 A8 =   0.15147 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Example 2 
               
               
                 f = 5.40 ˜ 13.90 ˜ 31.00, FN0 = 2.91 ˜ 3.42 ˜ 3.69 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 61.137 
                 d1 = 1.100 
                 N1 = 1.80518 
                 ν1 = 25.43 
               
               
                 r2 = 27.581 
                 d2 = 5.000 
                 N2 = 1.49310 
                 ν2 = 83.58 
               
               
                 r3 = −105.275 
                 d3 = 0.100 
               
               
                 r4 = 20.146 
                 d4 = 2.667 
                 N3 = 1.78100 
                 ν3 = 44.55 
               
             
          
           
               
                 r5 = 36.805 
                 d5 = 0.850 ˜ 10.983 ˜ 18.820 
               
             
          
           
               
                 r6 = 24.459 
                 d6 = 0.750 
                 N4 = 1.75450 
                 ν4 = 51.57 
               
               
                 r7 = 5.771 
                 d7 = 3.683 
               
               
                 r8 = −13.089 
                 d8 = 0.650 
                 N5 = 1.61800 
                 ν5 = 63.39 
               
               
                 r9 = 14.445 
                 d9 = 0.500 
               
               
                 r10* = 12.512 
                 d10 = 2.455 
                 N6 = 1.84506 
                 ν6 = 23.66 
               
             
          
           
               
                 r11* = 90.973 
                 d11 = 15.836 ˜ 6.454 ˜ 1.500 
               
             
          
           
               
                 r12 = ∞(SP) 
                 d12 = 1.000 
                   
                   
               
               
                 r13 = 40.325 
                 d13 = 2.093 
                 N7 = 1.72916 
                 ν7 = 54.67 
               
               
                 r14 = −9.013 
                 d14 = 0.700 
                 N8 = 1.85000 
                 ν8 = 40.04 
               
             
          
           
               
                 r15 = −39.711 
                 d15 = 3.033 ˜ 0.700 ˜ 0.300 
               
             
          
           
               
                 r16 = 6.951 
                 d16 = 3.500 
                 N9 = 1.58913 
                 ν9 = 61.11 
               
               
                 r17 = 65.236 
                 d17 = 1.589 
               
               
                 r18* = 1136.648 
                 d18 = 1.709 
                 N10 = 1.84506 
                 ν10 = 23.66 
               
               
                 r19* = 11.961 
                 d19 = 1.200 
               
               
                 r20 = 8.223 
                 d20 = 2.650 
                 N11 = 1.48749 
                 ν11 = 70.44 
               
             
          
           
               
                 r21 = 144.688 
                 d21 = 3.650 ˜ 6.938 ˜ 8.580 
               
             
          
           
               
                 r22 = ∞ 
                 d22 = 3.000 
                 N12 = 1.51680 
                 ν12 = 64.20 
               
               
                 r23 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 10th Surface (r10) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.10832 × 10 −3   
               
               
                 A6 = −0.16138 × 10 −5   
               
               
                 A8 = −0.18581 × 10 −6   
               
               
                 Aspherical Surface Data of the 11th Surface (r11) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.95767 × 10 −4   
               
               
                 A6 = −0.72129 × 10 −6   
               
               
                 A8 = −0.20064 × 10 −6   
               
               
                 Aspherical Surface Data of the 18th Surface (r18) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.70719 × 10 −3   
               
               
                 A6 = −0.28509 × 10 −4   
               
               
                 A8 =   0.85712 × 10 −7   
               
               
                 Aspherical Surface Data of the 19th Surface (r19) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.16595 × 10 −2   
               
               
                 A6 = −0.33283 × 10 −5   
               
               
                 A8 =   0.52834 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Example 3 
               
               
                 f = 7.14 ˜ 23.15 ˜ 68.60, FN0 = 2.33 ˜ 3.00 ˜ 3.70 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 81.973 
                 d1 = 1.400 
                 N1 = 1.84700 
                 ν1 = 24.84 
               
               
                 r2 = 61.207 
                 d2 = 5.961 
                 N2 = 1.49310 
                 ν2 = 83.58 
               
               
                 r3 = 856.502 
                 d3 = 0.100 
               
               
                 r4 = 45.555 
                 d4 = 4.773 
                 N3 = 1.49310 
                 ν3 = 83.58 
               
             
          
           
               
                 r5 = 103.248 
                 d5 = 0.900 ˜ 30.274 ˜ 52.572 
               
             
          
           
               
                 r6* = 32.565 
                 d6 = 1.800 
                 N4 = 1.77250 
                 ν4 = 49.77 
               
               
                 r7* = 10.160 
                 d7 = 6.937 
               
               
                 r8 = −34.736 
                 d8 = 1.100 
                 N5 = 1.71218 
                 ν5 = 47.10 
               
               
                 r9 = 32.109 
                 d9 = 0.100 
               
               
                 r10 = 23.896 
                 d10 = 3.352 
                 N6 = 1.84666 
                 ν6 = 23.82 
               
               
                 r11 = −113.596 
                 d11 = 2.273 
               
               
                 r12 = −15.197 
                 d12 = 1.077 
                 N7 = 1.49310 
                 ν7 = 83.58 
               
             
          
           
               
                 r13 = −35.767 
                 d13 = 30.489 ˜ 7.350 ˜ 0.500 
               
             
          
           
               
                 r14 = ∞(SP) 
                 d14 = 0.0 
                   
                   
               
               
                 r15 = 12.732 
                 d15 = 2.253 
                 N8 = 1.75847 
                 ν8 = 50.89 
               
               
                 r16 = −343.551 
                 d16 = 4.695 
               
               
                 r17* = −26.163 
                 d17 = 1.500 
                 N9 = 1.67227 
                 ν9 = 30.69 
               
               
                 r18* = 12.288 
                 d18 = 0.685 
               
               
                 r19 = 13.470 
                 d19 = 2.599 
                 N10 = 1.48749 
                 ν10 = 70.44 
               
             
          
           
               
                 r20 = −17.432 
                 d20 = 1.898 ˜ 3.215 ˜ 15.554 
               
             
          
           
               
                 r21 = 3425.596 
                 d21 = 0.899 
                 N11 = 1.63197 
                 ν11 = 31.41 
               
               
                 r22 = 22.225 
                 d22 = 0.827 
               
               
                 r23 = −596.274 
                 d23 = 1.500 
                 N12 = 1.75450 
                 ν12 = 51.57 
               
             
          
           
               
                 r24 = −54.401 
                 d24 = 0.460 ˜ 0.321 ˜ 9.254 
               
             
          
           
               
                 r25 = 20.563 
                 d25 = 4.140 
                 N13 = 1.75450 
                 ν13 = 51.57 
               
               
                 r26 = −33.868 
                 d26 = 0.129 
               
               
                 r27 = −29.329 
                 d27 = 2.800 
                 N14 = 1.64867 
                 ν14 = 29.97 
               
               
                 r28 = 26.044 
                 d28 = 0.101 
               
               
                 r29 = 27.832 
                 d29 = 4.882 
                 N15 = 1.79850 
                 ν15 = 22.60 
               
             
          
           
               
                 r30 = 876.079 
                 d30 = 1.000 ˜ 7.634 ˜ 6.206 
               
             
          
           
               
                 r31 = ∞ 
                 d31 = 3.000 
                 N16 = 1.51680 
                 ν16 = 64.20 
               
               
                 r32 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 6th Surface (r6) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.34691 × 10 −5   
               
               
                 A6 = −0.73603 × 10 −7   
               
               
                 A8 =   0.53336 × 10 −9   
               
               
                 Aspherical Surface Data of the 7th Surface (r7) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.23921 × 10 −4   
               
               
                 A6 = −0.24238 × 10 −6   
               
               
                 A8 = −0.37119 × 10 −8   
               
               
                 Aspherical Surface Data of the 17th Surface (r17) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.29274 × 10 −3   
               
               
                 A6 =   0.76183 × 10 −5   
               
               
                 A8 = −0.95192 × 10 −7   
               
               
                 Aspherical Surface Data of the 18th Surface (r18) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.12200 × 10 −3   
               
               
                 A6 =   0.82935 × 10 −5   
               
               
                 A8 = −0.10737 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Example 4 
               
               
                 f = 7.14 ˜ 20.01 ˜ 49.03, FN0 = 2.50 ˜ 3.03 ˜ 3.66 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 111.111 
                 d1 = 1.400 
                 N1 = 1.79850 
                 ν1 = 22.60 
               
               
                 r2 = 85.390 
                 d2 = 4.303 
                 N2 = 1.49310 
                 ν2 = 83.58 
               
               
                 r3 = −1831.972 
                 d3 = 0.100 
               
               
                 r4 = 43.431 
                 d4 = 4.988 
                 N3 = 1.49310 
                 ν3 = 83.58 
               
             
          
           
               
                 r5 = 130.083 
                 d5 = 0.900˜ 24.171 ˜ 43.681 
               
             
          
           
               
                 r6 = 35.035 
                 d6 = 1.200 
                 N4 = 1.75450 
                 ν4 = 51.57 
               
               
                 r7 = 10.040 
                 d7 = 4.791 
               
               
                 r8 = −96.605 
                 d8 = 1.100 
                 N5 = 1.75450 
                 ν5 = 51.57 
               
               
                 r9 = 15.175 
                 d9 = 1.925 
               
               
                 r10* = 25.398 
                 d10 = 3.981 
                 N6 = 1.84666 
                 ν6 = 23.82 
               
               
                 r11* = 43.373 
                 d11 = 1.258 
               
               
                 r12 = −15.932 
                 d12 = 1.000 
                 N7 = 1.48749 
                 ν7 = 70.44 
               
             
          
           
               
                 r13 = −134.899 
                 d13 = 20.871 ˜ 5.426 ˜ 0.600 
               
             
          
           
               
                 r14 = ∞(SP) 
                 d14 = 0.600 
                   
                   
               
               
                 r15 = 11.251 
                 d15 = 2.129 
                 N8 = 1.75450 
                 ν8 = 51.57 
               
               
                 r16 = 422.558 
                 d16 = 4.585 
               
               
                 r17* = −39.509 
                 d17 = 1.500 
                 N9 = 1.70395 
                 ν9 = 26.41 
               
               
                 r18* = 12.891 
                 d18 = 0.596 
               
               
                 r19 = 12.874 
                 d19 = 2.614 
                 N10 = 1.48749 
                 ν10 = 70.44 
               
             
          
           
               
                 r20 = −14.240 
                 d20 = 1.806 ˜ 1.837 ˜ 3.682 
               
             
          
           
               
                 r21 = −8157.937 
                 d21 = 0.800 
                 N11 = 1.71649 
                 ν11 = 25.74 
               
               
                 r22 = 13.228 
                 d22 = 0.445 
               
               
                 r23 = 13.631 
                 d23 = 1.919 
                 N12 = 1.48749 
                 ν12 = 70.44 
               
             
          
           
               
                 r24 = 668.856 
                 d24 = 3.002 ˜ 1.300 ˜ 12.240 
               
             
          
           
               
                 r25 = 31.322 
                 d25 = 1.691 
                 N13 = 1.79850 
                 ν13 = 22.60 
               
             
          
           
               
                 r26 = 217.261 
                 d26 = 0.500 ˜ 9.743 ˜ 7.994 
               
             
          
           
               
                 r27 = 18.461 
                 d27 = 4.643 
                 N14 = 1.79850 
                 ν14 = 22.60 
               
               
                 r28 = −11.955 
                 d28 = 0.460 
                 N15 = 1.83724 
                 ν15 = 30.17 
               
               
                 r29 = 21.532 
                 d29 = 1.000 
               
               
                 r30 = ∞ 
                 d30 = 3.000 
                 N16 = 1.51680 
                 ν16 = 64.20 
               
               
                 r31 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 10th Surface (r10) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.34767 × 10 −4   
               
               
                 A6 =   0.63939 × 10 −7   
               
               
                 A8 = −0.15659 × 10 −8   
               
               
                 Aspherical Surface Data of the 11th Surface (r11) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.11239 × 10 −3   
               
               
                 A6 = −0.50907 × 10 −4   
               
               
                 A8 = −0.20881 × 10 −8   
               
               
                 Aspherical Surface Data of the 17th Surface (r17) 
               
               
                 ε= 1.00000 
               
               
                 A4 = −0.53164 × 10 −3   
               
               
                 A6 =   0.11706 × 10 −4   
               
               
                 A8 = −0.13639 × 10 −6   
               
               
                 Aspherical Surface Data of the 18th Surface (r18) 
               
               
                 ε 1.00000 
               
               
                 A4 = −0.23930 × 10 −3   
               
               
                 A6 =   0.14046 × 10 −4   
               
               
                 A8 = −0.15638 × 10 −6   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Example 5 
               
               
                 f = 7.53 ˜ 25.47 ˜ 50.62, FN0 = 2.49 ˜ 3.05 ˜ 3.60 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 61.849 
                 d1 = 1.200 
                 N1 = 1.78578 
                 ν1 = 23.00 
               
               
                 r2 = 49.954 
                 d2 = 3.953 
                 N2 = 1.49310 
                 ν2 = 83.58 
               
               
                 r3 = 270.579 
                 d3 = 0.100 
               
               
                 r4 = 58.704 
                 d4 = 2.800 
                 N3 = 1.49310 
                 ν3 = 83.58 
               
             
          
           
               
                 r5 = 162.001 
                 d5 = 1.000 ˜ 30.382 ˜ 47.888 
               
             
          
           
               
                 r6 = 35.027 
                 d6 = 0.800 
                 N4 = 1.75450 
                 ν4 = 51.57 
               
               
                 r1 = 9.368 
                 d7 = 7.570 
               
               
                 r8 = −36.274 
                 d8 = 0.800 
                 N5 = 1.75450 
                 ν5 = 51.57 
               
               
                 r9 = 62.467 
                 d9 = 3.501 
                 N6 = 1.84831 
                 ν6 = 29.79 
               
               
                 r10 = −17.800 
                 d10 = 0.520 
               
               
                 r11 = −15.004 
                 d11 = 0.800 
                 N7 = 1.71236 
                 ν7 = 53.1 
               
             
          
           
               
                 r12* = −98.611 
                 d12 = 28.057 ˜ 4.668 ˜ 1.000 
               
             
          
           
               
                 r13 = ∞(SP) 
                 d13 = 0.800 
                   
                   
               
               
                 r14 = 12.908 
                 d14 = 1.790 
                 N8 = 1.85000 
                 ν8 = 40.04 
               
               
                 r15 = 62.919 
                 d15 = 4.104 
               
               
                 r16 = 13.503 
                 d16 = 2.925 
                 N9 = 1.64205 
                 ν9 = 56.40 
               
               
                 r17 = −14.608 
                 d17 = 0.800 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
               
                 r18 = 9.386 
                 d18 = 0.275 
               
               
                 r19 = 7.311 
                 d19 = 1.352 
                 N11 = 1.48853 
                 ν11 = 70.29 
               
               
                 r20* = 14.663 
                 d20 = 1.488 
               
               
                 r21 = 35.435 
                 d21 = 1.462 
                 N12 = 1.79850 
                 ν12 = 22.60 
               
             
          
           
               
                 r22 = −37.996 
                 d22 = 1.000 ˜ 6.964 ˜ 4.489 
               
             
          
           
               
                 r23 = 25.595 
                 d23 = 0.800 
                 N13 = 1.81916 
                 ν13 = 42.89 
               
               
                 r24 = 10.073 
                 d24 = 2.866 
               
               
                 r25 = 11.166 
                 d25 = 1.263 
                 N14 = 1.79850 
                 ν14 = 22.60 
               
             
          
           
               
                 r26 = 13.792 
                 d26 = 1.980 ˜ 1.521 ˜ 8.160 
               
             
          
           
               
                 r27 = 33.413 
                 d27 = 1.371 
                 N15 = 1.84666 
                 ν15 = 23.82 
               
               
                 r28 = 145.103 
                 d28 = 1.102 
               
               
                 r29 = ∞ 
                 d29 = 3.000 
                 N16 = 1.51680 
                 ν16 = 64.20 
               
               
                 r30 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 12th Surface (r12) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.47667 × 10 −4   
               
               
                 A6 = −0.83476 × 10 −7   
               
               
                 A8 = −0.19331 × 10 −8   
               
               
                 Aspherical Surface Data of the 20th Surface (r20) 
               
               
                 ε = 1.00000 
               
               
                 A4 = 0.52640 × 10 −3   
               
               
                 A6 = 0.39582 × 10 −5   
               
               
                 A8 = 0.74569 × 10 −7   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Example 6 
               
               
                 f = 5.3 ˜ 12.6 ˜ 50.1, FN0 = 2.68 ˜ 2.99 ˜ 3.60 
               
             
          
           
               
                 Radius of 
                 Axial 
                 Refractive 
                 Abbe 
               
               
                 Curvature 
                 Distance 
                 Index 
                 Number 
               
               
                   
               
               
                 r1 = 52.184 
                 d1 = 0.800 
                 N1 = 1.84666 
                 ν1 = 23.82 
               
               
                 r2 = 31.633 
                 d2 = 4.921 
                 N2 = 1.49310 
                 ν2 = 83.58 
               
               
                 r3 = 737.681 
                 d3 = 0.100 
               
               
                 r4 = 29.287 
                 d4 = 3.401 
                 N3 = 1.75450 
                 ν3 = 51.57 
               
             
          
           
               
                 r5 = 76.097 
                 d5 = 0.700 ˜ 13.461 ˜ 26.604 
               
             
          
           
               
                 r6 = 67.989 
                 d6 = 0.900 
                 N4 = 1.75450 
                 ν4 = 51.57 
               
               
                 r7* = 6.835 
                 d7 = 4.527 
               
               
                 r8 = −63.145 
                 d8 = 0.800 
                 N5 = 1.63854 
                 ν5 = 55.62 
               
               
                 r9 = 12.522 
                 d9 = 2.492 
                 N6 = 1.84666 
                 ν6 = 23.82 
               
             
          
           
               
                 r10* = 70.342 
                 d10 = 26.404 ˜ 13.643 ˜ 0.500 
               
             
          
           
               
                 r11 = ∞(SP) 
                 d11 = 1.000 
                   
                   
               
               
                 r12 = 32.480 
                 d12 = 2.226 
                 N7 = 1.58267 
                 ν7 = 46.43 
               
               
                 r13 = −14.911 
                 d13 = 0.800 
                 N8 = 1.84666 
                 ν8 = 23.82 
               
             
          
           
               
                 r14 = −40.873 
                 d14 = 7.030 ˜ 4.412 ˜ 0.800 
               
             
          
           
               
                 r15 = 7.288 
                 d15 = 6.052 
                 N9 = 1.58267 
                 ν9 = 46.46 
               
               
                 r16 = −14.170 
                 d16 = 0.108 
               
               
                 r17* = −19.169 
                 d17 = 1.201 
                 N10 = 1.84666 
                 ν10 = 23.82 
               
             
          
           
               
                 r18* = 24.411 
                 d18 = 1.341 ˜ ˜ 3.960 ˜ 7.572 
               
             
          
           
               
                 r19 = ∞ 
                 d19 = 3.000 
                 N11 = 1.51680 
                 ν11 = 64.20 
               
               
                 r20 = ∞ 
               
             
          
           
               
                 Aspherical Surface Data of the 7th Surface (r7) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.30920 × 10  −5   
               
               
                 A6 = −0.15275 × 10 −5   
               
               
                 A8 =   0.13017 × 10 −6   
               
               
                 A10 = −0.36324 × 10 −8   
               
               
                 Aspherical Surface Data of the 10th Surface (r10) 
               
               
                 ε = 1.00000 
               
               
                 A4 = −0.92062 × 19 −4   
               
               
                 A6 = −0.10571 × 10 −5   
               
               
                 A8 =   0.40713 × 10 −7   
               
               
                 A10 = −0.87049 × 10 −9   
               
               
                 Aspherical Surface Data of the 17th Surface (r17) 
               
               
                 ε = 1.00000 
               
               
                 A4 = 0.30299 × 10 −3   
               
               
                 A6 = −0.13575 × 10 −4   
               
               
                 A8 = −0.51291 × 10 −6   
               
               
                 A10 = 0.16304 × 10 −7   
               
               
                 Aspherical Surface Data of the 18th Surface (r18) 
               
               
                 ε = 1.00000 
               
               
                 A4 =   0.10542 × 10 −2   
               
               
                 A6 =   0.10270 × 10 −4   
               
               
                 A8 = −0.11812 × 10 −5   
               
               
                 A10 =   0.59254 × 10 −7   
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Actual Values of Conditions (1) to (6) 
               
             
          
           
               
                   
                 (1) 
                 (2) 
                 (3) 
                 (4) 
                 (5) 
                 (6) 
               
               
                 Example 
                 FW/IH 
                 ND 
                 VD 
                 FW/F1 
                 FW/F3 
                 FW/FR 
               
               
                   
               
               
                 1 
                 1.63 
                 1.49310 
                 83.58 
                 0.194 
                 0.169 
                 0.498 
               
               
                 2 
                 1.80 
                 1.49310 
                 83.58 
                 0.136 
                 0.140 
                 0.361 
               
               
                 3 
                 1.37 
                 1.49310 
                 83.58 
                 0.072 
                 0.348 
                 0.282 
               
               
                 4 
                 1.30 
                 1.49310 
                 83.58 
                 0.082 
                 0.434 
                 0.044 
               
               
                 5 
                 1.37 
                 1.49310 
                 83.58 
                 0.078 
                 0.503 
                 0.148 
               
               
                 6 
                 1.58 
                 1.49310 
                 83.58 
                 0.108 
                 0.110 
                 0.297