Abstract:
A compact yet low-cost zoom lens system being particularly suited for use with small portable information terminal equipment is provided. The zoom lens system includes, in order from an object side thereof, first, third and fourth lens groups G 1,  G 3  and G 4,  respectively, that have positive refracting powers and a second lens group G 2  that has negative refracting power. Lens group G 1  remains fixed during zooming and lens groups G 2  and G 3  move during zooming and lens group G 4  is movable during zooming. the zoom lens system should satisfy condition (1) regarding the power of lens group G 3,  condition (2) regarding the amount of movement of lens group G 3  during zooming condition (3) regarding the composite power of lens groups G 3  and G 4,  and condition (10) regarding the actual value of the back focus.

Description:
This is a Continuation-in-Part of: National Appln. No. 09/172,263 filed Oct. 14, 1998 now U.S. Pat. No. 6,185,048. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to a zoom lens system, and more particularly to a compact yet low-cost zoom lens system used with cameras using an electronic image pickup means such as camcorders, digital cameras, supervisory cameras, portable telephones, personal computers, etc. 
     To achieve size and weight reductions of a consumer-oriented zoom lens system in this field, a specific zoom lens system has been proposed, which comprises four lens groups, i.e., a positive lens group, a negative lens group, a positive lens group and a positive lens group in order from an object side thereof, as typically disclosed in JP-A&#39;s 4-43311 and 4-78806. For zooming, the second negative lens group moves on an optical axis while the first and third lens groups remain fixed. The fourth lens group moves to make correction for a fluctuation in the position of an image plane in association with zooming. A further size reduction is achievable by a specific zoom lens system wherein, as typically disclosed in JP-A&#39;s 6-94997 and 6-194572, a third lens group moves from an image plane side to an object side of the system during zooming from a wide-angle end to a telephoto end of the system. Such zoom lens systems have a relatively high zoom ratio of the order of 8 to 12. However, these zoom lens systems are still insufficient for zoom lens systems having a lower zoom ratio while weight is placed on ever smaller size and ever lower cost, because of a large number of lenses. 
     In the zoom lens systems set forth in JP-A&#39;s 6-94997 and 6-194572, a great part of the zooming action is shared by the second lens group. To keep an image point substantially constant in this case, the lateral magnification of the second lens group must be in the range of about −1 from the wide-angle end to the telephoto end. At a zoom ratio lower than that, however, the amount of movement of the second lens group can become so small that size reductions can be achieved. It is thus efficient to reduce the space allowed between the first and second lens groups as much as possible for the purpose of size reductions. 
     To permit the second lens group to have a lateral magnification of about −1 while the space between the first and second lens groups is kept as narrow as possible, however, it is required to increase the power of the first lens group with respect to the second lens group. This then causes an entrance pupil to be located at a farther position where the height of an off-axis ray passing through the first lens group increases, resulting in an increase in the size of the lens system in the first lens group and, hence, an increase in the thickness of the lenses in the first lens group. Further, the curvature of each lens in the first lens group must be increased to make sure of the edge thickness of each lens, resulting in a further increase in the thickness of each lens in the first lens group. 
     SUMMARY OF THE INVENTION 
     In view of the aforesaid problems associated with the prior art, an object of the present invention is to achieve further size and cost reductions of such zoom lens systems. 
     One particular object of the present invention is to provide a zoom lens system comprising four lens groups, wherein size reductions are achieved without increasing the power of the first lens group with respect to the second lens group while satisfactory zoom ratios are maintained. 
     Another particular object of the present invention is to use a reduced number of lenses thereby achieving a compact zoom lens best suited for use with digital cameras, portable telephones, personal computers, etc. This zoom lens system is designed to achieve a substantially telecentric emergent bundle while taking an image pickup element such as a CCD or CMOS into consideration, and obtain such a back focus as to allow optical elements such as low-pass filters and bundle-splitting elements to be located in the system, if required. In addition, the ability of the zoom lens system to form images is considerably improved. 
     According to one aspect of the present invention, the aforesaid objects are achieved by the provision of a zoom lens system comprising, in order from an object side thereof, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from the object side to an image plane side of the system during zooming from a wide-angle end to a telephoto end of the system, a third lens group that has positive refracting power and moves from the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, provided that the zoom lens system satisfies the following conditions (1) and (10): 
     
       
         0.5 &lt;|F   2   /F   3 |&lt;1.2  (1) 
       
     
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     where F i  is a focal length of an i-th lens group, and f B(min)  is a value obtained when a length, as calculated on an air basis, from a final surface of a powered lens in said zoom lens system to an image plane is minimized in an overall zooming zone. 
     According to another aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said zoom lens system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from an object side to an image plane side of said zoom lens system during zooming from a wide-angle end to a telephoto end of said zoom lens system, a third lens group that has positive refracting power and moves from the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, provided that the zoom lens system satisfies the following conditions (2) and (10): 
     
       
         0.49 &lt;|L   3   /L   2 |&lt;1  (2) 
       
     
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     where L i  is an amount of movement of an i-th lens group from the wide-angle end to the telephoto end, and f B(min)  is a value obtained when a length, as calculated on an air basis, from a final surface of a powered lens in said zoom lens system to an image plane is minimized in an overall zooming zone. 
     According to yet another aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said zoom lens system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from an object side to an image plane side of said zoom lens system during zooming from a wide-angle end to a telephoto end of said zoom lens system, a third lens group that has positive refracting power and moves from the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, provided that said zoom lens system satisfies the following conditions (3) and (10): 
     
       
         2&lt;( F   3, 4W )/ IH &lt;3.3  (3) 
       
     
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     where (F 3, 4W ) is a composite focal length of said third and fourth lens groups at the wide-angle end, IH is a radius of an image circle, and f B(min)  is a value obtained when a length, as calculated on an air basis, from a final surface of a powered lens in said zoom lens system to an image plane is minimized in an overall zooming zone. 
     According to a further aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said zoom lens system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from an object side to an image plane side of said zoom lens system during zooming from a wide-angle end to a telephoto end of said zoom lens system, a third lens group that has positive refracting power and moves constantly from the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, wherein said third lens group comprises a doublet consisting of a positive lens and a negative lens, and said fourth lens group comprises one positive lens, provided that said zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     where f B(min)  is a value obtained when a length, as calculated on an air basis, from a final surface of a powered lens in said zoom lens system to an image plane is minimized in an overall zooming zone. 
     A detailed explanation will now be made of why the aforesaid arrangements are used, and how they work. 
     In the information equipment field with built-in electronic image pickup means such as not only camcorders and digital cameras but also portable telephones and personal computers, too, demand for consumer-oriented, compact yet low-cost zoom lens systems has gone up recently. To meet such demand, JP-A&#39;s 6-94997 and 6-194572 have come up with such zoom lens systems as already noted. As previously mentioned, these have a zoom ratio of the order of 8 to 12, and a great part of the zooming action is shared by the second lens group. To keep an image point substantially constant in this case, the lateral magnification of the second lens group must be within the range of about −1 from the wide-angle end to the telephoto end. 
     At a zoom ratio lower than that, however, the amount of movement of the second lens group can become so small that size reductions can be achieved. It is thus efficient to reduce the space allowed between the first and second lens groups as much as possible for the purpose of size reductions. 
     To permit the second lens group to have a lateral magnification of about −1 while the space between the first and second lens groups is kept as narrow as possible, however, it is required to increase the power of the first lens group with respect to the second lens group. This then causes an entrance pupil to be located at a farther position where the height of an off-axis ray passing through the first lens group increases, resulting in an increase in the size of the lens system in the first lens group and, hence, an increase in the thickness of the lenses in the first lens group. Further, the curvature of each lens in the first lens group must be increased to make sure of the edge thickness of each lens, resulting in a further increase in the thickness of each lens in the first lens group. 
     In accordance with the present invention, this problem can be averted by allocating a great part of the burden of the zooming action to the third lens group, whereby a satisfactory zoom ratio and compactness are achieved with no considerable change in the power ratio between the first and second lens groups. To allow the third lens group to have a great zooming action, it is then required that the third lens group have relatively large power, as defined by condition (1). When the lower limit of 0.5 in condition (1) is not reached or when the power of the third lens group becomes weak with respect to the power of the second lens group, the amount of movement of the third lens group during zooming becomes too large. With this, the amount of movement of the second lens group to keep the image plane at a constant position becomes large, failing to achieve compactness. When the upper limit of 1.2 is exceeded or when the power of the third lens group with respect to the second lens group becomes too strong, the amount of astigmatism produced at the third lens group becomes too large, and the distance between the third lens group and an object point therefor becomes too short. This in turn makes it impossible to provide a sufficient space between the second and third lens groups. For the insertion of an image pickup element package such as a CCD or CMOS, an IR cut filter, low-pass filter or the like in the optical system, it is required that a back focus f B  be at least 2.5 min. At a back focus f B  of greater than 4.5 mm, on the other hand, compactness is unachievable. For this reason, it is required to satisfy the following condition (10): 
     
       
         2.5 mm&lt; f   B (min)&lt;4.8 mm  (10) 
       
     
     Here f B  (min) is a value obtained when the length, as calculated on an air basis, from the final surface of the powered lens in the zoom lens system to the image plane is minimized in the overall zooming zone. Intended by the term “powered lens” used herein is a lens whose refracting power is not zero. 
     When the lower limit of 2.5 mm in condition (10) is not reached, it is impossible to make sure of any space in which a filter such as an IR cut filter is built. When the upper limit of 4.8 mm is exceeded, on the other hand, the zoom lens system becomes too large. This condition is important to reduce the size of an optical system used with a portable telephone, a notebook type PC or the like. 
     More preferably, the zoom lens system of the present invention should satisfy the following condition (4): 
     
       
         0.6 &lt;|F   2   /F   3 |&lt;1  (4) 
       
     
     In the present invention, it is required that the amount of movement of the third lens group during zooming be increased so as to allocate a relatively large zooming action to the third lens group, as defined by condition (2). Thus, condition (2) gives a definition of the ratio of the amount of movement between the second and third lens groups from the wide-angle end to the telephoto end. Falling below the lower limit of 0.49 in condition (2) is not preferable because the amount of movement of the third lens group with respect to the second lens group becomes too small to allocate a sufficient zooming action to the third lens group. Exceeding the upper limit of 1 is again not preferable because the amount of movement of the third lens group with respect to the second lens group increases with the results that there is an excessive fluctuation in astigmatism, coma and other aberrations produced at the third lens group during zooming while the distance between the third lens group and an object point therefor at the telephoto end becomes too short. Consequently, no sufficient space can be provided between the second and third lens groups. 
     For a four-lens-group or a +−++ power profile zoom lens system such as one contemplated herein, it is required to increase the composite power of the third and fourth lens groups, as defined by condition (3). This is because it is effective for reducing the overall length of the zoom lens system that the powers of the third and fourth lens groups for relaying a virtual image formed by the first and second lens groups to an image pickup plane be increased to reduce the distance between the position of the virtual image by the first and second lens groups and the image pickup plane. When the upper limit of 3.3 in condition (3) is exceeded or when the composite focal length of the third and fourth lens groups at the wide-angle end becomes large relative to the radius of the image circle (image height) IH (when the power becomes weak), no sufficient compactness is achieved for the aforesaid reason. Falling below the lower limit of 2 in condition (3) is not preferred. This is because the composite focal length of the third and fourth lens groups at the wide-angle end becomes small relative to the radius of the image circle with the results that astigmatism produced at the third and fourth lens groups becomes too large, while the distance between the third lens group and an object point therefor becomes too short. Consequently, no sufficient space can be provided between the second and third lens groups. 
     For a zoom lens system such as one contemplated herein, it is preferable to perform focusing with the fourth lens group where the angle of incidence of an axial bundle is relatively small, because aberrational fluctuations during focusing are limited. Since the fourth lens group has a relatively small lens diameter and is light in weight, there is an additional advantage that the driving torque for focusing can be reduced. 
     It is also favorable for reducing the overall length of the zoom lens system that as much of the composite power of the third and fourth lens groups as possible is allocated to the third lens group. In this embodiment, therefore, relatively large power is allocated to the third lens group rather than to the fourth lens group, as defined by the following condition (5) giving a definition of the ratio of the focal length of the third lens group with respect to the focal length of the fourth lens group. 
     
       
         0.3 &lt;F   3   /F   4 &lt;0.8  (5) 
       
     
     where F i  is a focal length of an i-th lens group. By meeting condition (5) or making the ratio of the focal length of the third lens group with respect to the focal length of the fourth lens group smaller than the upper limit of 0.8 therein, it is possible to achieve more compactness than would be possible with the prior art. Falling below the lower limit of 0.3 in condition (5) is not preferable because the ratio of the focal length of the third lens group with respect to the focal length of the fourth lens group becomes small, with the results that the power of the fourth lens group becomes too weak, and the amount of movement of the fourth lens group for focusing becomes too large. There is thus a large aberrational fluctuation in association with focusing. 
     In the present invention, the power of the fourth lens group is relatively weaker than that of the third lens group; that is, it is desired for achieving compactness to construct the fourth lens group of one positive lens. 
     To reduce an astigmatism fluctuation due to zooming, it is desired that at least one surface in the fourth lens group be provided by an aspherical surface. 
     Preferably in the present invention, the following condition (6) is satisfied: 
     
       
         0.4&lt;|β 2T |&lt;1  (6) 
       
     
     Here β 2T  is a lateral magnification of the second lens group at the telephoto end. 
     Condition (6) gives a definition of the absolute value of the lateral magnification of the second lens group at the telephoto end. When the lower limit of 0.4 is not reached or when the absolute value of the lateral magnification of the second lens group at the telephoto end becomes small, no lens compactness can be achieved because the zooming action of the second lens group becomes insufficient, and the power of the first lens group becomes too weak. When the upper limit of 1 is exceeded or when the absolute value of the lateral magnification of the second lens group at the telephoto end becomes large, no compactness can again be achieved because the zooming action of the third lens group becomes insufficient, and the power of the first lens group becomes too strong, resulting an increase in the size of the lens system in the first lens group. 
     Preferably, the third lens group contributes to a size reduction of the zoom lens system by increasing its power without varying its image-forming magnification. It is then preferable that the principal point of the third lens group is located as close to the object side as possible, thereby avoiding interference between the second and third lens groups at the telephoto end of the system, which may be caused when the distance between the third lens group and an object point for the third lens group is short. For this reason, it is preferable that the third lens group is made up of three lenses or, in order from an object side thereof, a positive lens, a positive lens and a negative lens. To make correction for spherical aberrations, it is further preferable that an aspherical surface is used for at least one surface in the third lens group. 
     By using an aspherical surface for at least one surface in the second lens group, it is possible to make better correction for fluctuations in astigmatism and coma in association with zooming. 
     In the present invention, the burden of correction of aberrations on the first and second lens groups can be relieved because the third lens group shares a relatively great part of the zooming action as previously mentioned, and so the first lens group may be made up of one positive lens. It is then preferable that the lens in the second lens group that is located nearest to an object side thereof is made up of a negative lens having relatively large dispersion so as to make correction for chromatic aberration of magnification produced at the first lens group. This is defined by the following condition (7) that gives a definition of the Abbe&#39;s number of the negative lens in the second lens group that is located nearest to the object side thereof. 
     
       
         ν 21 &lt;40  (7) 
       
     
     where ν 21  is an Abbe&#39;s number of the negative lens in the second lens group that is located nearest to the object side thereof. 
     To make correction for chromatic aberration of magnification produced at the positive lens in the first lens group as mentioned above, it is preferable that the Abbe&#39;s number of the negative lens located nearest to the object side of the second lens group does not exceed the upper limit of 40 in condition (7). If the following condition (8) is satisfied, it is then possible to make better correction for the chromatic aberration of magnification. 
     
       
         ν 21 &lt;35  (8) 
       
     
     When, as contemplated herein, the third lens group is made up of three lenses, i.e., a positive lens, a positive lens and a negative lens in order from an object side thereof, a principal point throughout the third lens group should be located as close to the object side as possible for the achievement of compactness. It is then preferable that both the positive lenses are convex on object sides thereof and the negative lens is strongly concave on an image plane side thereof. The performance of the convex surfaces (opposing to the object side) of the two positive lenses having strong refracting power and the performance of the concave surface (opposing to the image side) of the negative lens are often adversely affected by an error of decentration of such lenses with respect to optical axes at the time of lens fabrication. For this reason, it is preferable that the positive lens on the image plane side and negative lens are cemented together, and that when the third lens group is held in a lens holder barrel, the positive lens on the object side and the doublet are held by the lens holder barrel while their convex surfaces opposing to the object side are abutting at their peripheries or some points on the lens holder barrel. 
     According to one specific aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of the system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from the object side to an image plane side of the system during zooming from a wide-angle end to a telephoto end of the system, a third lens group that has positive refracting power and moves constantly form the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, wherein said third lens group comprises a doublet consisting of a positive lens and a negative lens, and said fourth lens group comprises one positive lens, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     In this embodiment, during zooming from the wide-angle end to the telephoto end, the second lens group having negative refracting power can move from the object side to the image plane side while the third lens group having positive refracting power can move from the image plane side to the object side, so that the burden of zooming so far shared by the second lens group can be allocated to the second and third lens groups. It is thus possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. In other words, by allocating a great part of the zooming action to the third lens group, it is possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. 
     Reference is then made to what action and effect are obtained when the third lens group comprises a doublet consisting of a positive lens and a negative lens. When the third lens group is designed as a group movable during zooming, the burden on the third lens group of correction of aberrational fluctuations in association with zooming does not only become heavy, but it is also required to make good correction for chromatic aberrations. For this reason, it is necessary for the third lens group to comprise at least a positive lens component and a negative lens component. Relative decentration between the positive and negative lenses gives rise to a considerable deterioration in the image-forming capability. This decentration between the positive and negative lenses can be easily reduced by using the doublet consisting of a positive lens and a negative lens in the third lens group. It is thus possible to allocate a great part of the zooming action to the third lens group, make good correction for chromatic aberrations, and make an image quality drop due to decentration unlikely to occur. In this embodiment, the burden of zooming so far shared by the second lens group is allocated to the second and third lens groups so that the burden of correction of aberrations on the fourth lens group can be successfully reduced. By constructing the fourth lens group of one positive lens, it is possible to achieve compactness while the image-forming capability is kept. 
     In the instant embodiment, it is preferable that an aspherical surface is used for at least one surface of the positive lens in the fourth lens group. 
     When the fourth lens group is constructed of one positive lens, it is preferable that the fourth lens group has one aspherical surface therein because the burden of zooming can be allocated to the second and third lens groups and correction of aberrations shared by the fourth lens group can be well performed, resulting in the achievement of cost and size reductions. It is here to be noted that the aspherical surface may be formed by a so-called glass pressing process, a so-called hybrid process wherein a thin resin layer is stacked on a glass or other substrate, or a plastic molding process. 
     According to another specific aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of the system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from the object side to an image plane side of the system during zooming from a wide-angle end to a telephoto end of the system, a third lens group that has positive refracting power and moves constantly form the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, wherein each of said second lens group and said third lens group comprises a doublet consisting of a positive lens and a negative lens, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     In this embodiment, during zooming from the wide-angle end to the telephoto end, the second lens group having negative refracting power can move from the object side to the image plane side while the third lens group having positive refracting power can move from the image plane side to the object side, so that the burden of zooming so far shared by the second lens group can be allocated to the second and third lens groups. It is thus possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. In other words, by allocating a great part of the zooming action to the third lens group, it is possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. 
     Reference is then made to what action and effect are obtained when the third lens group comprises a doublet consisting of a positive lens and a negative lens. When the third lens group is designed as a group movable during zooming, the burden on the third lens group of correction of aberration fluctuations in association with zooming does not only become heavy, but it is also required to make good correction for chromatic aberrations. For this reason, it is necessary for the third lens group to comprise at least a positive lens component and a negative lens component. Relative decentration between the positive and negative lenses then gives rise to a considerable deterioration in the image-forming capability. This decentration between the positive and negative lenses can be easily reduced by using the doublet consisting of a positive lens and a negative lens in the third lens group. It is thus possible to allocate a great part of the zooming action to the third lens group, make good correction for chromatic aberrations, and make an image quality drop due to decentration unlikely to occur. Although the burden of zooming on the second lens group is reduced, yet the burden on the second lens group of correction of aberrational fluctuations in association with zooming is still heavy because the second lens group is a group movable during zooming. It is thus required to make good correction for chromatic aberrations. For this reason, it is necessary for the second lens group to comprise at least a positive lens component and a negative lens component. Relative decentration between the positive and negative lenses then gives rise to a considerable deterioration in the image-forming capability. This decentration between the positive and negative lenses can be easily reduced by using the doublet consisting of a positive lens and a negative lens in the second lens group. It is thus possible to make an image quality drop due to decentration unlikely to occur. 
     According to yet another specific embodiment of the present invention, there is provided a zoom lens system comprising, in order from an object side of the system, a first lens group that has positive refracting power and remains fixed during zooming, a second lens group that has negative refracting power and moves from the object side to an image plane side of the system during zooming from a wide-angle end to a telephoto end of the system, a third lens group that has positive refracting power and moves constantly form the image plane side to the object side during zooming from the wide-angle end to the telephoto end and a fourth lens group that has positive refracting power and is movable during zooming, wherein said third lens group comprises, in order from an object side thereof, a positive lens and a doublet consisting of a positive lens and a negative lens, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     In this embodiment, during zooming from the wide-angle end to the telephoto end, the second lens group having negative refracting power can move from the object side to the image plane side while the third lens group having positive refracting power can move from the image plane side to the object side, so that the burden of zooming so far shared by the second lens group can be allocated to the second and third lens groups. It is thus possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. In other words, by allocating a great part of the zooming action to the third lens group, it is possible to achieve compactness while a satisfactory zoom ratio is maintained, without increasing the power ratio of the first lens group to the second lens group. Further, since the third lens group is made up of, in order from the object side, a positive lens, a positive lens and a negative lens, a principal point throughout the third lens group can be located on the object side for the achievement of a further size reduction. Stated otherwise, the negative lens is required for correction of chromatic aberration, and two positive lenses are located to obtain strong positive power and achieve a size reduction (simple structure) of the third lens group itself. Furthermore, this power profile (positive-positive-negative in order from the object side) of third lens group allows various aberrations to be well corrected with a reduced number of lenses. In addition, the principal point throughout the third lens group is located on the object side so that the principal point positions of the second and third lens groups can effectively be brought close to each other at the telephoto end of the system, thereby achieving a further size reduction of the system. 
     According to a further specific aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said system, a first lens group having positive refracting power, a second lens group having negative refracting power, a third lens group having positive refracting power and a fourth lens group having positive refracting power, wherein during zooming, a space between said first and second lens groups, a space between said second and third lens groups and a space between said third and fourth lens groups vary independently, said third lens group comprises, in order from an object side thereof, a double-convex positive lens, and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens, and said fourth lens group comprises a double-convex lens having a large curvature on an object side surface thereof, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     In this embodiment, the third lens group is constructed of, in order from the object side, a positive lens convex on an object side thereof and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens, so that a principal point throughout the third lens group can be located closer to the object side, thereby achieving a size reduction of the lens system. Use of the doublet consisting of a positive meniscus lens and a negative meniscus lens can reduce a performance drop due to decentration. Since the third lens group has such an arrangement, the fourth lens group can be constructed of one single lens. By using a double-convex lens having a large curvature on an object side thereof as the single lens, it is possible to make a light ray incident on the image plane substantially telecentric and obtain a satisfactory back focus while the number of lenses in the third and fourth lens groups is reduced to the minimum, thereby achieving the aforesaid another object of the present invention. 
     According to a still further specific aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said system, a first lens group having positive refracting power, a second lens group having negative refracting power, a third lens group having positive refracting power and a fourth lens group having positive refracting power, wherein during zooming, a space between said first and second lens groups, a space between said second and third lens groups and a space between said third and fourth lens groups vary independently, said first lens group comprises one positive lens, said second lens group comprise three lenses or, in order from an object side thereof, a single lens and a doublet consisting of a negative lens and a positive lens, said third lens group comprises three lenses or, in order from an object side thereof, a single lens and a doublet consisting of a positive lens and a negative lens, and said fourth lens group comprises one positive lens, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     With this arrangement, it is possible to achieve a positive-negative-positive-positive power profile zoom lens system that can have good image-forming capability with a reduced number of lenses and so can be well suited for use with digital cameras. By allowing the burden of correction of aberrations to be concentrated on the second and third lens groups, each of the first and fourth lens groups taking no great part in correction of aberrations can be constructed of one positive lens. By allowing the second lens group sharing a great part of correction of aberrations to be constructed of, in order from the object side, a single lens and a doublet consisting of a negative lens and a positive lens, it is possible to reduce, with a minimum number of lenses, various aberrations inclusive of chromatic aberrations produced at the second lens group alone, thereby achieving a further size reduction. Use of the doublet consisting of a negative lens and a positive lens in the second lens group can reduce a performance drop due to decentration. By allowing the third lens group sharing a great part of the burden of correction of aberrations to be constructed of, in order from the object side, a single lens and a doublet consisting of a positive lens and a negative lens, it is possible to reduce, with a minimum number of lenses, various aberrations inclusive of chromatic aberrations produced at the third lens group alone, thereby achieving a further size reduction. Use of the doublet consisting of a positive lens and a negative lens in the third lens group can reduce a performance drop due to decentration. 
     In this embodiment, it is preferable to make the power of the first lens group weak because the amount of aberrations produced at the first lens group can be so reduced that the burden of correction of aberrations produced at the first lens group on the second and third lens groups can be relieved. Further, it is preferable that this embodiment satisfies the following condition (9): 
      8 &lt;F   1   /IH &lt;20  (9) 
     where F 1  is a focal length of the first lens group, and IH is an image height (a length from the center to the periphery of an image or the radius of an image circle). Falling below the lower limit of 8 in condition (9) is not preferable because the amount of aberrations produced at the first lens group increases. When the upper limit of 20 is exceeded, on the other hand, the power of the first lens group becomes weak, failing to obtain a satisfactory zoom ratio or achieve size reductions. 
     According to a still further specific aspect of the present invention, there is provided a zoom lens system comprising, in order from an object side of said system, a first lens group having positive refracting power, a second lens group having negative refracting power, a third lens group having positive refracting power and a fourth lens group having positive refracting power, wherein during zooming, a space between said first and second lens groups, a space between said second and third lens groups and a space between said third and fourth lens groups vary independently, said first lens group comprises two lenses or a positive lens and a negative lens, and said second or third lens group comprises a doublet consisting of at least one set of a positive lens and a negative lens, provided that the zoom lens system satisfies the following condition (10): 
     
       
         2.5 mm&lt; f   B(min) &lt;4.8 mm  (10) 
       
     
     In this embodiment, the first lens group is constructed of two lenses, i.e., a positive lens and a negative lens, whereby chromatic aberrations produced at the first lens group can be reduced irrespective of the power of the first lens group. This in turn allows the subsequent burden of correction of aberrations to be relieved, resulting in a size reduction of the optical system. By using the doublet consisting of a positive lens and a negative lens in the second or third lens group, it is then possible to reduce chromatic aberrations produced at other lens groups and prevent a deterioration in the image-forming capability due to decentration, etc. Consequently, it is possible to achieve an optical system favorable in view of the number of lenses, fabrication cost, and size reductions. 
     More preferably, the zoom lens systems explained so far should satisfy the following condition (11): 
     
       
         2.5 mm&lt; f   B(max) &lt;4.8 mm  (11) 
       
     
     where f B(max)  is a value obtained when a length, as calculated on an air basis, from a final surface of a powered lens in said zoom lens system to an image plane is maximized in an overall zooming zone. 
     The above explanation holds for the lower limit of 2.5 mm in condition (11). At less than this lower limit, problems such as interference arise when an image pickup element package, an IR cut filter, a low-pass filter or the like is built in the optical system. At greater than the upper limit of 4.8 mm, on the other hand, any compactness is unachievable. This condition is effective to prevent any increase in the size of the zoom lens when built in a small portable information terminal such as a portable telephone or a notebook type PC. 
     More preferably, the upper limit of condition (10) should be 4.0 mm in consideration of compactness. 
     More preferably, the upper limit of condition (11), too, should be 4.8 mm in consideration of compactness. 
     Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification. 
     The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 a  and  1   b  are a sectional schematic views illustrative of Example 1 of the zoom lens according to the invention. 
     FIGS. 2 a  and  2   b  are a sectional schematic views illustrative of Example 2 of the zoom lens according to the invention. 
     FIGS. 3 a  and  3   b  are a sectional schematic views illustrative of Example 3 of the zoom lens according to the invention. 
     FIGS. 4 a  and  4   b  are a sectional schematic views illustrative of Example 4 of the zoom lens according to the invention. 
     FIGS. 5 a  and  5   b  are a sectional schematic views illustrative of Example 5 of the zoom lens according to the invention. 
     FIGS. 6 a  and  6   b  are a sectional schematic views illustrative of Example 6 of the zoom lens according to the invention. 
     FIG. 7 is a sectional schematic of Example 7 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 8 is a sectional schematic of Example 8 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 9 is a sectional schematic of Example 9 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 10 is a sectional schematic of Example 10 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 11 is a sectional schematic of Example 11 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 12 is a sectional schematic of Example 12 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 13 is a sectional schematic of Example 13 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 14 is a sectional schematic of Example 14 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 15 is a sectional schematic of Example 15 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 16 is a sectional schematic of Example 16 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 17 is a sectional schematic of Example 17 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 18 is a sectional schematic of Example 18 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 19 is a sectional schematic of Example 19 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 20 is a sectional schematic of Example 20 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 21 is a sectional schematic of Example 21 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 22 is a sectional schematic of Example 22 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 23 is a sectional schematic of Example 23 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 24 is a sectional schematic of Example 24 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 25 is a sectional schematic of Example 25 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 26 is a sectional schematic of Example 26 of the zoom lens system according to the invention at a wide-angle end thereof. 
     FIG. 27 is a view of a holder barrel structure for the third lens group in Example 11, and Example 21. 
     FIGS. 28 a - 28   d  are aberration diagrams of Example 1 at a wide-angle end thereof. 
     FIGS. 29 a - 29   d  are aberration diagrams of Example 1 at an intermediate focal length. 
     FIGS. 30 a - 30   d  are aberration diagrams of Example 1 at a telephoto end thereof. 
     FIGS. 31 a - 31   e  are aberration diagrams of Example 17 at a wide-angle end thereof. 
     FIGS. 32 a - 32   e  are aberration diagrams of Example 17 at a telephoto end thereof. 
     FIG. 33 is a front perspective view of an electronic camera wherein the zoom lens system of the invention is incorporated in the form of an objective optical system. 
     FIG. 34 is a rear perspective view of an electronic camera wherein the zoom lens system of the invention is incorporated in the form of an objective optical system. 
     FIG. 35 is a sectional schematic of one embodiment of the electronic camera wherein the zoom lens system of the invention is incorporated in the form of an objective optical system. 
     FIG. 36 is a front perspective view of an uncovered personal computer wherein the zoom lens system of the invention is incorporated in the form of an objective optical system. 
     FIG. 37 is a sectional schematic of a phototaking optical system in a personal computer. 
     FIG. 38 is a side schematic of one state shown in FIG.  36 . 
     FIG. 39 is a front and side view of a portable telephone wherein the zoom lens system of the invention is incorporated in the form of an objective optical system, and a sectional schematic of a phototaking optical system therein. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Examples 1 to 26 of the zoom lens system according to the present invention are given. Lens data regarding the zoom lens system of each example will be given later. 
     FIGS. 1 a  and  1   b  are schematic views illustrative of one sectional arrangement of Example 1. Example 1 is made up of, in order from an object side thereof, a first positive lens group G 1 , a second negative lens group G 2 , a stop S, a third positive lens group G 3 , and a fourth positive lens group G 4 . The first lens group G 1  remains fixed during zooming, the second lens group G 2  moves from the object side to an image plane side of the system during zooming from a wide-angle end thereof to a telephoto end thereof, the third lens group G 3  moves from the image plane side to the object side during zooming from the wide-angle end to the telephoto end, and the fourth lens group G 4  moves to keep an image plane at a constant position during zooming. 
     The first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof and a double-convex lens. The two lenses are separated from each other. The second lens group G 2  is made up of, in order from an object side thereof, a double-concave lens and a positive meniscus lens convex on an object side thereof, with an aspherical surface being used for an image-side surface of the positive meniscus lens. The third lens group G 3  is made up of, in order from an object side thereof, a double-convex lens and a negative meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface of the double-convex lens. The fourth lens group G 4  is made up of one double-convex convex lens. Also, the zoom lens system of Example 1 satisfies the aforesaid condition (a). 
     FIGS. 2 a  and  2   b  are schematic views illustrative of one lens arrangement of Example 2. The overall power profile and zooming movements in Example 2 are the same as in Example 1. 
     A first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on object side thereof, and a double-convex lens. The two lenses are separated from each other. A second lens group G 2  is made up of, in order from an object side thereof, a double-concave lens, a negative meniscus lens convex on an object side thereof, and a positive meniscus lens convex on an object side thereof. The negative and positive meniscus lenses are cemented together, with an aspherical surface being used for an image-side surface of the positive meniscus lens. A third lens group G 3  is made up of, in order from an object side thereof, a double-convex lens, a positive meniscus lens convex on an object side thereof, and a negative meniscus lens convex on an object side thereof. The positive and negative meniscus lenses are cemented together, with an aspherical surface being used for an object-side surface of the double-convex lens. A fourth lens group G 4  is made up of one double-convex lens. Also, the zoom lens system of Example 2 satisfies the aforesaid condition (a). 
     FIGS. 3 a  and  3   b  are schematic views illustrative of one lens arrangement of Example 3. The overall power profile and zooming movements in Example 3 are the same as in Example 1. 
     A first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof, and a double-convex lens. The two lenses are cemented together. A second lens group G 2  is made up of, in order from an object side thereof, a double-concave lens, and a positive lens, with an aspherical surface being used for an image-side surface of the positive lens. A third lens group G 3  is made up of, in order from an object side thereof, a double-convex lens, a positive meniscus lens convex on an object side thereof, and a negative meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface of the double-convex lens. A fourth lens group G 4  is made up of one double-convex lens, with an aspherical surface being used for an object-side surface thereof. Also, the zoom lens system of Example 3 satisfies the aforesaid condition (a). 
     FIGS. 4 a  and  4   b  are schematic views illustrative of one lens arrangement of Example 4. The overall power profile and zooming movements in Example 4 are the same as in Example 1. 
     A first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof, and a double-convex lens. The two lenses are separated from each other. A second lens group G 2  is made up of, in order from an object side thereof, a double-concave lens, and a positive meniscus lens convex on an object side thereof, with an aspherical surface being used for an image-side surface of the positive meniscus lens. A third lens group G 3  is made up of, in order from an object side thereof, a double-convex lens, a positive meniscus lens convex on an object side thereof, and a negative meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface of the double-convex lens. A fourth lens group G 4  is made up of one double-convex lens. Also, the zoom lens system of Example 4 satisfies the aforesaid condition (a). 
     FIGS. 5 a  and  5   b  are schematic views illustrative of one lens arrangement of Example 5. The overall power profile and zooming movements in Example 5 are the same as in Example 1. 
     A first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof, and a double-convex lens. The two lenses are cemented together. A second lens group G 2  is made up of, in order from an object side thereof, a double-concave lens, a positive lens, and a double-concave lens, with an aspherical surface being used for an image-side surface of the positive lens. A third lens group G 3  is made up of, in order from an object side thereof, a double-convex lens, a positive meniscus lens convex on an object side thereof, and a negative meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface of the double-convex lens. A fourth lens group G 4  is made up of one positive meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface thereof. Also, the zoom lens system of Example 5 satisfies the aforesaid condition (a). 
     FIGS. 6 a  and  6   b  are schematic views illustrative of one lens arrangement of Example 6. The overall power profile and zooming movements in Example 6 are the same as in Example 1. 
     A first lens group G 1  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof, and a positive meniscus lens convex on an object side thereof. The two lens are cemented together. A second lens group G 2  is made up of, in order from an object side thereof, a negative meniscus lens convex on an object side thereof, a double-concave lens, and a positive meniscus lens convex on an object side thereof. A third lens group G 3  is made up of, in order from an object side thereof, two double-convex lenses, and a negative meniscus lens convex on an object side thereof, with an aspherical surface being used for an object-side surface of the double-convex lens located nearest to the object side. A fourth lens group G 4  is made up of one double-convex lens. Also, the zoom lens system of Example 6 satisfies the aforesaid condition (a). 
     FIGS. 7 to  16  are schematics illustrative of specific lens arrangements of the zoom lens systems of Examples 7 to 16 at the wide-angle ends thereof. 
     Example 7 is directed to a zoom lens system having a focal length of 5.50 to 15.75 and a field angle of 66.42° to 24°. As illustrated in FIG. 7, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a double-convex lens, and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a double-convex lens. At the rear of the second lens group G 2  there is located a stop S. A third lens group G 3  is made up of two double-convex lenses, and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one positive meniscus lens convex on an object side thereof. An aspherical surface is used for a surface in the third lens group G 3  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as shown by arrows. 
     Example 8 is directed to a zoom lens system having a focal length of 5.52 to 15.91 and a field angle of 67.04° to 23.72°. As shown in FIG. 8, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, a double-concave lens, and a positive meniscus lens convex on an object side thereof. At the rear of the second lens group G 2  there is located a stop S. A third lens group G 3  is made up of two double-convex lenses, and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. An aspherical surface is used for the surface in the third lens group G 3  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide. 
     Example 9 is directed to a zoom lens system having a focal length of 5.50 to 15.81 and a field angle of 66.82° to 23.88°. As can be seen from FIG. 9, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a double-convex lens. A second lens group G 2  is made up of a double-concave lens and a positive lens, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, a positive meniscus lens convex on an object side thereof, and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one positive meniscus lens convex on an object side thereof. Three aspherical surfaces are used, one for the surface in the second lens group G 2  that is located nearest to the image plane side, one for the surface in the third lens group G 3  that is located nearest to the object side, and one for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     Example 10 is directed to a zoom lens system having a focal length of 5.50 to 15.87 and a field angle of 64.93° to 24.87°. As depicted in FIG. 10, a first lens group G 1  is made up of one positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group that is located nearest to the object side, and one for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     Example 11 is directed to a zoom lens system having a focal length of 5.50 to 15.86 and a field angle of 68.30° to 24.54°. As illustrated in FIG. 11, a first lens group G 1  is made up of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. Three aspherical surfaces are used, one for the surface in the second lens group G 2  that is located nearest to the image plane side, one for the surface in the third lens group G 3  that is located nearest to the object side, and one for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     As can be seen from FIG. 17, it is to be noted that, in Example 11, the peripheries of object side-directed convex surfaces of both an object-side positive lens L 31  and a doublet L 32  in the third lens group G 3  are held by a holder frame  1  while they are abutting at their peripheries or some points on the holder frame  1 . 
     Example 12 is directed to a zoom lens system having a focal length of 6.608 to 19.098 and a field angle of 67.32° to 25.95°. As shown in FIG. 12, a first lens group G 1  is made up of one plano-convex lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to an object side thereof and one for the surface in the fourth lens group G 4  that is located to an object side thereof. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     Example 13 is directed to a zoom lens system having a focal length of 6.613 to 18.999 and a field angle of 67.68° to 26.08°. As depicted in FIG. 13, a first lens group G 1  is made up of one plane-convex lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of a double-convex lens, and a negative meniscus lens convex on an image side thereof. An aspherical surface is used for the surface in the third lens group G 3  that is located nearest to an object side thereof. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     Example 14 is directed to a zoom lens system having a focal length of 6.548 to 19 and a field angle of 67.80° to 26.08°. As illustrated in FIG. 14, a first lens group G 1  is made up of a negative meniscus lens convex on an object side thereof, and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to an object side thereof, and one for the surface in the fourth lens group G 4  that is located nearest to an object side thereof. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with the space between them becoming wide, as indicated by arrows. 
     Example 15 is directed to a zoom lens system having a focal length of 6.562 to 19 and a field angle of 67.69° to 26.08°. As shown in FIG. 15, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to an object side thereof, and one for the surface in the fourth lens group G 4  that is located nearest to an object side thereof. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from an object side to an image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side with a space between them becoming wide, as indicated by arrows. 
     Example 16 is directed to a zoom lens system having a focal length of 6.46 to 19 and a field angle of 68.52° to 26.08°. As shown in FIG. 16, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof, and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to an object side thereof, and one for the surface in the fourth lens group G 4  that is located nearest to an object side thereof. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Next, Examples 17 to 26 of the zoom lens system according to the present invention are given. 
     FIGS. 17 to  26  are sectional schematics illustrative of lens arrangements in Examples 17 to 26 of the zoom lens system according to the invention at their wide-angle ends. Numerical data regarding each example will be enumerated. In each of FIGS. 17 to  26 , a plane-parallel plate is disposed between the fourth lens group G 4  and the image plane. For this plane-parallel plate use may be made of an image pickup element cover glass, or a filter such as an IR cut filter or a low-pass filter. It is here noted that the plane-parallel plate is not referred to in the numerical data to be given later. 
     Example 17 is directed to a zoom lens system having a focal length of 3.643 to 10.410 mm and a field angle of 66.42° to 240°. As shown in FIG. 17, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a double-convex lens, and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, and a doublet consisting of a double-concave lens and a double-convex lens, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of two double-convex lenses and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one positive meniscus lens convex on an object side thereof. One aspherical surface is used for the surface in the third lens group G 3  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 18 is directed to a zoom lens system having a focal length of 2.924 to 8.425 mm and a field angle of 67.04° to 23.72°. As shown in FIG. 18, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof, a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of two double-convex lenses and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. One aspherical surface is used for the surface in the third lens group G 3  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 19 is directed to a zoom lens system having a focal length of 3.238 to 9.300 mm and a field angle of 66.82° to 23.88°. As shown in FIG. 19, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a double-convex lens. A second lens group G 2  is made up of a double-concave lens and a positive lens, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens, a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one positive meniscus lens convex on an object side thereof. One aspherical surface is used for the surface in the third lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 20 is directed to a zoom lens system having a focal length of 3.144 to 9.070 mm and a field angle of 64.93° to 24.87°. As shown in FIG. 20, a first lens group G 1  is made up of one positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens, and a fourth lens group G 4  is made up of one double-convex lens. One aspherical surface is used for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 21 is directed to a zoom lens system having a focal length of 3.578 to 10.193 mm and a field angle of 68.30° to 24.54°. As shown in FIG. 21, a first lens group G 1  is made up of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. Three aspherical surfaces are used, one for the surface in the second lens group G 2  that is located nearest to the object side, one for the surface in the third lens group G 3  that is located nearest to the object side, and one for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     As can be seen from FIG. 27, it is to be noted that, in Example 21, the peripheries of object side-directed convex surfaces of both an object-side positive lens L 31  and a doublet L 32  in the third lens group G 3  are held by a holder frame  1  while they are abutting at their peripheries or some points on the holder frame  1 , thereby reducing decentration errors likely to have influences on performance. 
     Example 22 is directed to a zoom lens system having a focal length of 2.478 to 7.162 mm and a field angle of 67.32° to 25.95°. As shown in FIG. 22, a first lens group G 1  is made up of one plano-convex lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to the object side and another for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 23 is directed to a zoom lens system having a focal length of 2.976 to 8.549 mm and a field angle of 67.68° to 26.08°. As shown in FIG. 23, a first lens group G 1  is made up of one plano-convex lens. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a positive meniscus lens convex on an object side thereof and a negative meniscus lens convex on an object side thereof, and a fourth lens group G 4  is made up of a double-convex lens a negative meniscus lens convex on image plane side thereof. One aspherical surface is used for the surface in the thrid lens group G 3  that is located nearest to the object side and another for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 24 is directed to a zoom lens system having a focal length of 4.093 to 11.875 mm and a field angle of 67.80° to 26.08°. As shown in FIG. 24, a first lens group G 1  is made up of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to the object side and another for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 25 is directed to a zoom lens system having a focal length of 3.281 to 9.500 mm and a field angle of 67.69° to 26.08°. As shown in FIG. 25, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to the object side and another for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Example 26 is directed to a zoom lens system having a focal length of 3.634 to 10.687 mm and a field angle of 68.52° to 26.08°. As shown in FIG. 26, a first lens group G 1  is made up of a doublet consisting of a negative meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof and a positive meniscus lens convex on an object side thereof. A second lens group G 2  is made up of a negative meniscus lens convex on an object side thereof and a doublet consisting of a double-concave lens and a positive meniscus lens convex on an object side thereof, and at the rear thereof there is located a stop S. A third lens group G 3  is made up of a double-convex lens and a doublet consisting of a double-convex lens and a double-concave lens, and a fourth lens group G 4  is made up of one double-convex lens. Two aspherical surfaces are used, one for the surface in the third lens group G 3  that is located nearest to the object side and another for the surface in the fourth lens group G 4  that is located nearest to the object side. For zooming from the wide-angle end to the telephoto end of the system, while the first lens group G 1  and the stop S remain fixed, the second lens group G 2  moves from the object side to the image plane side of the system, and the third and fourth lens groups G 3  and G 4  move together from the image plane side to the object side, with the space between them becoming wide, as indicated by arrows. 
     Enumerated below are numerical data in each example. Symbols used hereinafter but not hereinbefore have the following meanings. 
     f . . . Focal length of the system. 
     F NO  . . . F-number. 
     ω . . . Half field angle. 
     r 1 , r 2 , . . . Radius of curvature of each lens surface. 
     d 1 , d 2 , . . . space between adjacent lens surfaces. 
     n d1 , n d2 , . . . Refractive index of each lens at d-line. 
     ν d1 , ν d2 , . . . Abbe&#39;s number of each lens at d-line. 
     Here let x stand for an optical axis assuming the direction of propagation of light is positive and y indicate a direction perpendicular to the optical axis. Then, aspherical shape is given by 
     
       
           x =( y   2   /r )/[1+{1-( K+ 1)( y/r ) 2 } 1/2   ]+A   4   y   4   +A   6   y   6   +A   8   y   8   +A   10   y   10   +A   12   y   12   
       
     
     where r is a paraxial radius of curvature, K is a conical coefficient, and A 4 , A 6 , A 8 , A 10 , and A 12  are fourth, sixth, eighth, tenth, and twelfth aspherical coefficients, respectively. 
     EXAMPLE 1 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.50˜9.52˜15.94 
               
               
                 F NO  = 2.79˜3.39˜4.22 
               
               
                 2ω = 63.5˜39.3˜24.1 
               
             
          
           
               
                 r 1  = 
                    17.3312 
                 d 1  = 
                 1.200 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                    14.2714 
                 d 2  = 
                 0.550 
               
               
                 r 3  = 
                    19.0981 
                 d 3  = 
                 2.566 
                 n d2  = 
                 1.69680 
                 ν d2  = 
                 55.53 
               
               
                 r 4  = 
                 −211.9146 
                 d 4  = 
                 (Variable) 
               
               
                 r 5  = 
                  −99.9978 
                 d 5  = 
                 0.840 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 6  = 
                    4.9137 
                 d 6  = 
                 1.765 
               
               
                 r 7  = 
                    16.3236 
                 d 7  = 
                 1.760 
                 n d4  = 
                 1.80518 
                 ν d4  = 
                 25.42 
               
               
                 r 8  = 
                    99.9991 
                 d 8  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 9  = 
                 ∞ (Stop) 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                    4.9282 
                 d 10  = 
                 2.900 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 11  = 
                  −21.5942 
                 d 11  = 
                 0.316 
               
               
                 r 12  = 
                    8.1812 
                 d 12  = 
                 0.700 
                 n d6  = 
                 1.84666 
                 ν d6  = 
                 23.78 
               
               
                 r 13  = 
                    3.9286 
                 d 13  = 
                 (Variable) 
               
               
                 r 14  = 
                    12.8501 
                 d 14  = 
                 2.100 
                 n d7  = 
                 1.69680 
                 ν d7  = 
                 55.53 
               
               
                 r 15  = 
                  −35.2750 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.50 
                 9.52 
                 15.94 
               
               
                   
                 d 4   
                 0.989 
                 4.786 
                 8.395 
               
               
                   
                 d 8   
                 8.706 
                 4.910 
                 1.300 
               
               
                   
                 d 9   
                 5.958 
                 2.921 
                 0.936 
               
               
                   
                 d 13   
                 2.295 
                 4.273 
                 4.368 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 8th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −6.0228 × 10 −4   
               
               
                   
                 A 6  = 
                 −8.2596 × 10 −6   
               
               
                   
                 A 8  = 
                 −2.9515 × 10 −8   
               
               
                   
                 A 10  = 
                 −3.1439 × 10 −8   
               
             
          
           
               
                   
                 10th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −9.2750 × 10 −4   
               
               
                   
                 A 6  = 
                 −4.4012 × 10 −6   
               
               
                   
                 A 8  = 
                 −3.1389 × 10 −7   
               
               
                   
                 A 10  = 
                 −2.1537 × 10 −8   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.678 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 2 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.33˜9.23˜15.45 
               
               
                 F NO  = 2.79˜3.11˜3.56 
               
               
                 2ω = 65.1˜40.5˜24.8 
               
             
          
           
               
                 r 1  = 
                   17.5585 
                 d 1  = 
                 1.200 
                 n d1 =   
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                   12.7200 
                 d 2  = 
                 1.068 
               
               
                 r 3  = 
                   16.3917 
                 d 3  = 
                 3.679 
                 n d2  = 
                 1.69680 
                 ν d2  = 
                 55.53 
               
               
                 r 4  = 
                 −84.4913 
                 d 4  = 
                 (Variable) 
               
               
                 r 5  = 
                 −48.2980 
                 d 5  = 
                 0.840 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 6  = 
                    5.3611 
                 d 6  = 
                 1.827 
               
               
                 r 7  = 
                   19.9998 
                 d 7  = 
                 0.600 
                 n d4  = 
                 1.48749 
                 ν d4  = 
                 70.21 
               
               
                 r 8  = 
                    8.1444 
                 d 8  = 
                 1.800 
                 n d5  = 
                 1.84666 
                 ν d5  = 
                 23.78 
               
               
                 r 9  = 
                   18.3790 
                 d 9  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                    5.9522 
                 d 11  = 
                 2.300 
                 n d6  = 
                 1.58913 
                 ν d6  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                 −23.5594 
                 d 12  = 
                 0.150 
               
               
                 r 13  = 
                    8.1391 
                 d 13  = 
                 1.500 
                 n d7  = 
                 1.60311 
                 ν d7  = 
                 60.64 
               
               
                 r 14  = 
                   19.5373 
                 d 14  = 
                 0.100 
               
               
                 r 15  = 
                   12.8481 
                 d 15  = 
                 0.700 
                 n d8  = 
                 1.84666 
                 ν d8  = 
                 23.78 
               
               
                 r 16  = 
                    4.0598 
                 d 16  = 
                 (Variable) 
               
               
                 r 17  = 
                    9.9038 
                 d 17  = 
                 2.100 
                 n d9  = 
                 1.69680 
                 ν d9  = 
                 55.53 
               
               
                 r 18  = 
                 −33.9009 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.33 
                 9.23 
                 15.45 
               
               
                   
                 d 4   
                 0.903 
                 5.403 
                 8.750 
               
               
                   
                 d 9   
                 9.247 
                 4.746 
                 1.400 
               
               
                   
                 d 10   
                 3.751 
                 2.293 
                 0.936 
               
               
                   
                 d 16   
                 3.894 
                 3.917 
                 3.510 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −3.8188 × 10 −4   
               
               
                   
                 A 6  = 
                 −5.4534 × 10 −6   
               
               
                   
                 A 8  = 
                 −5.0916 × 10 −7   
               
               
                   
                 A 10  = 
                   1.5222 × 10 −8   
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −7.0868 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.5182 × 10 −5   
               
               
                   
                 A 8  = 
                 −3.9567 × 10 −6   
               
               
                   
                 A 10  = 
                   1.7645 × 10 −7   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.359 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 3 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.50˜9.53˜15.81 
               
               
                 F NO  = 2.79˜3.35˜4.33 
               
               
                 2ω = 63.4˜39.3˜24.3 
               
             
          
           
               
                 r 1  = 
                    19.0896 
                 d 1  = 
                 1.200 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                    14.7521 
                 d 2  = 
                 3.097 
                 n d2  = 
                 1.60311 
                 ν d2  = 
                 60.64 
               
               
                 r 3  = 
                 −7692.3867 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                  −76.4386 
                 d 4  = 
                 0.840 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 5  = 
                     4.8598 
                 d 5  = 
                 1.811 
               
               
                 r 6  = 
                    18.2814 
                 d 6  = 
                 1.760 
                 n d4  = 
                 1.80518 
                 ν d4  = 
                 25.42 
               
               
                 r 7  = 
                 ∞ 
                 d 7  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 8  = 
                 ∞ (Stop) 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                     7.3400 
                 d 9  = 
                 2.642 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                  −22.1205 
                 d 10  = 
                 0.150 
               
               
                 r 11  = 
                     8.0241 
                 d 11  = 
                 1.973 
                 n d6  = 
                 1.72916 
                 ν d6  = 
                 54.68 
               
               
                 r 12  = 
                    52.4926 
                 d 12  = 
                 0.150 
               
               
                 r 13  = 
                    14.0423 
                 d 13  = 
                 0.700 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 14  = 
                     4.0797 
                 d 14  = 
                 (Variable) 
               
               
                 r 15  = 
                    10.1820 
                 d 15  = 
                 1.745 
                 n d8  = 
                 1.58913 
                 ν d8  = 
                 61.14 
               
               
                   
                 (Aspheric) 
               
               
                 r 16  = 
                   1133.0330 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.50 
                 9.53 
                 15.81 
               
               
                   
                 d 3   
                 1.157 
                 5.471 
                 8.096 
               
               
                   
                 d 7   
                 8.238 
                 3.924 
                 1.300 
               
               
                   
                 d 8   
                 5.647 
                 3.626 
                 0.936 
               
               
                   
                 d 14   
                 2.073 
                 3.422 
                 4.464 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 7th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −5.8146 × 10 −4   
               
               
                   
                 A 6  = 
                 −3.5256 × 10 −7   
               
               
                   
                 A 8  = 
                 −1.1100 × 10 −6   
               
               
                   
                 A 10  = 
                   9.7216 × 10 −9   
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −5.1506 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.2707 × 10 −6   
               
               
                   
                 A 8  = 
                   2.5686 × 10 −7   
               
               
                   
                 A 10  = 
                 −1.0482 × 10 −8   
               
             
          
           
               
                   
                 15th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −2.2630 × 10 −4   
               
               
                   
                 A 6  = 
                   1.7763 × 10 −5   
               
               
                   
                 A 8  = 
                 −1.5096 × 10 −6   
               
               
                   
                 A 10  = 
                   9.3766 × 10 −8   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.679 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 4 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.50˜9.53˜15.95 
               
               
                 F NO  = 2.79˜3.14˜3.97 
               
               
                 2ω = 63.4˜39.3˜24.1 
               
             
          
           
               
                 r 1  = 
                    19.3574 
                 d 1  = 
                 1.200 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                    14.9375 
                 d 2  = 
                 0.349 
               
               
                 r 3  = 
                    17.7409 
                 d 3  = 
                 2.752 
                 n d2  = 
                 1.69680 
                 ν d2  = 
                 55.53 
               
               
                 r 4  = 
                 −175.9537 
                 d 4  = 
                 (Variable) 
               
               
                 r 5  = 
                  −99.9969 
                 d 5  = 
                 0.840 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 6  = 
                    4.6050 
                 d 6  = 
                 1.733 
               
               
                 r 7  = 
                    14.5468 
                 d 7  = 
                 1.760 
                 n d4  = 
                 1.80518 
                 ν d4  = 
                 25.42 
               
               
                 r 8  = 
                    60.0003 
                 d 8  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 9  = 
                 ∞ (Stop) 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                    6.3631 
                 d 10  = 
                 2.300 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 11  = 
                  −29.3771 
                 d 11  = 
                 0.150 
               
               
                 r 12  = 
                    12.3021 
                 d 12  = 
                 1.270 
                 n d6  = 
                 1.60311 
                 ν d6  = 
                 60.64 
               
               
                 r 13  = 
                    69.7876 
                 d 13  = 
                 0.650 
               
               
                 r 14  = 
                    11.6182 
                 d 14  = 
                 0.700 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 15  = 
                    4.4105 
                 d 15  = 
                 (Variable) 
               
               
                 r 16  = 
                    15.0443 
                 d 16  = 
                 2.100 
                 n d8  = 
                 1.69680 
                 ν d8  = 
                 55.53 
               
               
                 r 17  = 
                  −22.9162 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.50 
                 9.53 
                 15.95 
               
               
                   
                 d 4   
                 1.089 
                 5.514 
                 8.193 
               
               
                   
                 d 8   
                 8.404 
                 3.979 
                 1.300 
               
               
                   
                 d 9   
                 5.452 
                 3.557 
                 0.936 
               
               
                   
                 d 15   
                 2.363 
                 2.908 
                 3.253 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 8th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −6.0060 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.5355 × 10 −5   
               
               
                   
                 A 8  = 
                   1.4947 × 10 −6   
               
               
                   
                 A 10  = 
                   1.2788 × 10 −7   
               
             
          
           
               
                   
                 10th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −6.2370 × 10 −4   
               
               
                   
                 A 6  = 
                 −6.8746 × 10 −7   
               
               
                   
                 A 8  = 
                   1.5135 × 10 −7   
               
               
                   
                 A 10  = 
                 −1.2164 × 10 −8   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.636 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 5 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.34˜9.26˜15.34 
               
               
                 F NO  = 2.79˜3.36˜4.48 
               
               
                 2ω = 64.9˜40.3˜25.0 
               
             
          
           
               
                 r 1  = 
                    19.0276 
                 d 1  = 
                 1.200 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                    13.5393 
                 d 2  = 
                 3.589 
                 n d2  = 
                 1.60311 
                 ν d2  = 
                 60.64 
               
               
                 r 3  = 
                 −422.2925 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                 −644.1560 
                 d 4  = 
                 0.840 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 5  = 
                    4.6769 
                 d 5  = 
                 1.796 
               
               
                 r 6  = 
                    12.4221 
                 d 6  = 
                 1.760 
                 n d4  = 
                 1.80518 
                 ν d4  = 
                 25.42 
               
               
                 r 7  = 
                 ∞ 
                 d 7  = 
                 0.300 
               
               
                   
                 (Aspheric) 
               
               
                 r 8  = 
                  −19.3978 
                 d 8  = 
                 0.800 
                 n d5  = 
                 1.51633 
                 ν d5  = 
                 64.14 
               
               
                 r 9  = 
                   112.3274 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                    7.4109 
                 d 11  = 
                 2.727 
                 n d6  = 
                 1.58913 
                 ν d6  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                  −19.0346 
                 d 12  = 
                 0.150 
               
               
                 r 13  = 
                    8.1629 
                 d 13  = 
                 2.046 
                 n d7  = 
                 1.72916 
                 ν d7  = 
                 54.68 
               
               
                 r 14  = 
                   103.6201 
                 d 14  = 
                 0.150 
               
               
                 r 15  = 
                    14.0489 
                 d 15  = 
                 0.700 
                 n d8  = 
                 1.84666 
                 ν d8  = 
                 23.78 
               
               
                 r 16  = 
                    3.9993 
                 d 16  = 
                 (Variable) 
               
               
                 r 17  = 
                    10.7947 
                 d 17  = 
                 1.676 
                 n d9  = 
                 1.58913 
                 ν d9  = 
                 61.14 
               
               
                   
                 (Aspheric) 
               
               
                 r 18  = 
                   244.0022 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.34 
                 9.26 
                 15.34 
               
               
                   
                 d 3   
                 0.983 
                 4.951 
                 6.943 
               
               
                   
                 d 9   
                 7.260 
                 3.292 
                 1.300 
               
               
                   
                 d 10   
                 5.781 
                 3.776 
                 0.936 
               
               
                   
                 d 16   
                 2.140 
                 3.006 
                 3.335 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 7th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −5.8146 × 10 −4   
               
               
                   
                 A 6  = 
                 −3.5256 × 10 −7   
               
               
                   
                 A 8  = 
                 −1.1100 × 10 −6   
               
               
                   
                 A 10  = 
                   9.7216 × 10 −9   
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −6.0173 × 10 −4   
               
               
                   
                 A 6  = 
                 −3.9633 × 10 −8   
               
               
                   
                 A 8  = 
                   5.1710 × 10 −7   
               
               
                   
                 A 10  = 
                 −1.9276 × 10 −8   
               
             
          
           
               
                   
                 17th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −9.0648 × 10 −5   
               
               
                   
                 A 6  = 
                   1.6145 × 10 −5   
               
               
                   
                 A 8  = 
                 −1.1806 × 10 −6   
               
               
                   
                 A 10  = 
                   1.0627 × 10 −7   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.813 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 6 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 5.52˜9.54˜15.91 
               
               
                 F NO  = 2.78˜3.39˜4.22 
               
               
                 2ω = 63.2˜39.2˜24.1 
               
             
          
           
               
                 r 1  = 
                  18.1384 
                 d 1  = 
                 1.200 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                  12.8515 
                 d 2  = 
                 5.173 
                 n d2  = 
                 1.60311 
                 ν d2  = 
                 60.64 
               
               
                 r 3  = 
                 229.0224 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                  41.3044 
                 d 4  = 
                 0.783 
                 n d3  = 
                 1.65160 
                 ν d3  = 
                 58.55 
               
               
                 r 5  = 
                  5.1749 
                 d 5  = 
                 3.535 
               
               
                 r 6  = 
                 −33.2963 
                 d 6  = 
                 0.700 
                 n d4  = 
                 1.56384 
                 ν d4  = 
                 60.67 
               
               
                 r 7  = 
                  20.7633 
                 d 7  = 
                 0.000 
               
               
                 r 8  = 
                  8.2198 
                 d 8  = 
                 1.760 
                 n d5  = 
                 1.80518 
                 ν d5  = 
                 25.42 
               
               
                 r 9  = 
                  13.1948 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                  12.3402 
                 d 11  = 
                 3.698 
                 n d6  = 
                 1.67790 
                 ν d6  = 
                 55.34 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                 −11.8524 
                 d 12  = 
                 0.858 
               
               
                 r 13  = 
                  11.4834 
                 d 13  = 
                 2.355 
                 n d7  = 
                 1.60311 
                 ν d7  = 
                 60.64 
               
               
                 r 14  = 
                 −18.6404 
                 d 14  = 
                 0.130 
               
               
                 r 15  = 
                  48.4996 
                 d 15  = 
                 0.700 
                 n d8  = 
                 1.84666 
                 ν d8  = 
                 23.78 
               
               
                 r 16  = 
                  5.5496 
                 d 16  = 
                 (Variable) 
               
               
                 r 17  = 
                  14.2502 
                 d 17  = 
                 1.722 
                 n d9  = 
                 1.58913 
                 ν d9  = 
                 61.14 
               
               
                 r 18  = 
                 −86.9086 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.52 
                 9.54 
                 15.91 
               
               
                   
                 d 3   
                 0.684 
                 4.781 
                 7.816 
               
               
                   
                 d 9   
                 8.425 
                 4.327 
                 1.300 
               
               
                   
                 d 10   
                 5.375 
                 3.214 
                 0.936 
               
               
                   
                 d 16   
                 1.927 
                 3.500 
                 3.547 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −7.1086 × 10 −4   
               
               
                   
                 A 6  = 
                   2.9893 × 10 −5   
               
               
                   
                 A 8  = 
                 −3.3152 × 10 −6   
               
               
                   
                 A 10  = 
                   1.3762 × 10 −7   
               
             
          
           
               
                   
                 | L 3  | / | L 2  | = 0.622 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 7 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 5.505˜9.536˜15.745 
               
               
                 F NO  = 2.792˜3.216˜4.113 
               
             
          
           
               
                 r 1  = 
                   186.5411 
                 d 1  = 
                 1.2000 
                 n d1  = 
                 1.84666 
                 μ d1  = 
                 23.78 
               
               
                 r 2  = 
                    39.3312 
                 d 2  = 
                 3.9807 
                 n d2  = 
                 1.48749 
                 ν d2  = 
                 70.23 
               
               
                 r 3  = 
                  −56.8902 
                 d 3  = 
                 0.1800 
               
               
                 r 4  = 
                    14.7260 
                 d 4  = 
                 3.2694 
                 n d3  = 
                 1.69680 
                 ν d3  = 
                 55.53 
               
               
                 r 5  = 
                    62.1210 
                 d 5  = 
                 (Variable) 
               
               
                 r 6  = 
                    74.5065 
                 d 6  = 
                 0.8400 
                 n d4  = 
                 1.77250 
                 ν d4  = 
                 49.60 
               
               
                 r 7  = 
                    5.5423 
                 d 7  = 
                 2.9761 
               
               
                 r 8  = 
                  −9.7293 
                 d 8  = 
                 0.8400 
                 n d5  = 
                 1.48749 
                 ν d5  = 
                 70.21 
               
               
                 r 9  = 
                    11.8229 
                 d 9  = 
                 1.8000 
                 n d6  = 
                 1.84666 
                 ν d6  = 
                 23.78 
               
               
                 r 10  = 
                 −139.7255 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                 ∞ (Stop) 
                 d 11  = 
                 (Variable) 
               
               
                 r 12  = 
                    11.6742 
                 d 12  = 
                 1.9422 
                 n d7  = 
                 1.58913 
                 ν d7  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 13  = 
                  −23.0900 
                 d 13  = 
                 0.1500 
               
               
                 r 14  = 
                    8.6783 
                 d 14  = 
                 2.6167 
                 n d8  = 
                 1.72916 
                 ν d8  = 
                 54.68 
               
               
                 r 15  = 
                  −12.4135 
                 d 15  = 
                 0.3000 
               
               
                 r 16  = 
                    26.9742 
                 d 16  = 
                 0.7000 
                 n d9  = 
                 1.84666 
                 ν d9  = 
                 23.78 
               
               
                 r 17  = 
                    4.2272 
                 d 17  = 
                 (Variable) 
               
               
                 r 18  = 
                    9.6808 
                 d 18  = 
                 1.6130 
                 n d10  = 
                 1.72916 
                 ν d10  = 
                 54.68 
               
               
                 r 19  = 
                    32.9326 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.505 
                 9.536 
                 15.745 
               
               
                   
                 d 5   
                 0.9695 
                 4.4520 
                 6.3793 
               
               
                   
                 d 10   
                 6.7009 
                 3.2199 
                 1.3000 
               
               
                   
                 d 11   
                 4.8930 
                 3.4069 
                 0.9360 
               
               
                   
                 d 17   
                 2.4323 
                 3.4685 
                 5.3700 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 12th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −9.0556 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.5457 × 10 −5   
               
               
                   
                 A 8  = 
                   1.4387 × 10 −6   
               
               
                   
                 A 10  = 
                 −9.7103 × 10 −8   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                 0.714 
               
               
                   
                 F 3 /F 4  = 
                 0.539 
               
               
                   
                 | β 2τ  | = 
                 0.897 
               
               
                   
                 | L 3 /L 2  | = 
                 0.73 
               
               
                   
                 (F 3.4W )/IH = 
                 2.44 
               
               
                   
                 F 1 /IH = 
                 6.97 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 8 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 5.524˜9.537˜15.914 
               
               
                 F NO  = 2.784˜3.389˜4.215 
               
             
          
           
               
                 r 1  = 
                  18.1384 
                 d 1  = 
                   1.2000 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                  12.8515 
                 d 2  = 
                   5.1730 
                 n d2  = 
                 1.60311 
                 ν d2  = 
                 60.64 
               
               
                 r 3  = 
                 229.0224 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                  41.3044 
                 d 4  = 
                   0.7827 
                 n d3  = 
                 1.65160 
                 ν d3  = 
                 58.55 
               
               
                 r 5  = 
                  5.1749 
                 d 5  = 
                   3.5350 
               
               
                 r 6  = 
                 −33.2963 
                 d 6  = 
                   0.7000 
                 n d4  = 
                 1.56384 
                 ν d4  = 
                 60.67 
               
               
                 r 7  = 
                  20.7633 
                 d 7  = 
                 −0.0132 
               
               
                 r 8  = 
                  8.2198 
                 d 8  = 
                   1.7596 
                 n d5  = 
                 1.80518 
                 ν d5  = 
                 25.42 
               
               
                 r 9  = 
                  13.1948 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                  12.3402 
                 d 11  = 
                   3.6983 
                 n d6  = 
                 1.67790 
                 ν d6  = 
                 55.34 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                 −11.8524 
                 d 12  = 
                   0.8580 
               
               
                 r 13  = 
                  11.4834 
                 d 13  = 
                   2.3550 
                 n d7  = 
                 1.60311 
                 ν d7  = 
                 60.64 
               
               
                 r 14  = 
                 −18.6404 
                 d 14  = 
                   0.1297 
               
               
                 r 15  = 
                  48.4996 
                 d 15  = 
                   0.7000 
                 n d8  = 
                 1.84666 
                 ν d8  = 
                 23.78 
               
               
                 r 16  = 
                  5.5496 
                 d 16  = 
                 (Variable) 
               
               
                 r 17  = 
                  14.2502 
                 d 17  = 
                   1.7219 
                 n d9  = 
                 1.58913 
                 ν d9  = 
                 61.14 
               
               
                 r 18  = 
                 −86.9086 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.524 
                 9.537 
                 15.914 
               
               
                   
                 d 3   
                 0.6836 
                 4.7810 
                 7.8162 
               
               
                   
                 d 9   
                 8.4251 
                 4.3267 
                 1.3000 
               
               
                   
                 d 10   
                 5.3747 
                 3.2145 
                 0.9360 
               
               
                   
                 d 16   
                 1.9272 
                 3.5002 
                 3.5470 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4 =   
                 −7.1086 × 10 −4   
               
               
                   
                 A 6 =   
                   2.9893 × 10 −6   
               
               
                   
                 A 8 =   
                 −3.3152 × 10 −6   
               
               
                   
                 A 10 =   
                   1.3762 × 10 −7   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.837 
               
               
                   
                 F 3 /F 4  = 
                  0.475 
               
               
                   
                 | β 2τ  | = 
                  0.501 
               
               
                   
                 | L 3 /L 2  | = 
                  0.62 
               
               
                   
                 (F 3.4W )/IH = 
                  2.58 
               
               
                   
                 F 1 /IH = 
                 10.99 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 9 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 5.505˜9.528˜15.810 
               
               
                 F NO  = 2.786˜3.348˜4.330 
               
             
          
           
               
                 r 1  = 
                    19.0896 
                 d 1  = 
                 1.2000 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                    14.7521 
                 d 2  = 
                 3.0968 
                 n d2  = 
                 1.60311 
                 ν d2  = 
                 60.64 
               
               
                 r 3  = 
                 −7692.3867 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                  −76.4386 
                 d 4  = 
                 0.8400 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 5  = 
                     4.8598 
                 d 5  = 
                 1.8112 
               
               
                 r 6  = 
                    18.2814 
                 d 6  = 
                 1.7596 
                 n d4  = 
                 1.80518 
                 ν d4  = 
                 25.42 
               
               
                 r 7  = 
                 ∞ 
                 d 7  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 8  = 
                 ∞ (Stop) 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                     7.3400 
                 d 9  = 
                 2.6421 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.18 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                  −22.1205 
                 d 10  = 
                 0.1500 
               
               
                 r 11  = 
                     8.0241 
                 d 11  = 
                 1.9734 
                 n d6  = 
                 1.72916 
                 ν d6  = 
                 54.68 
               
               
                 r 12  = 
                    52.4926 
                 d 12  = 
                 0.1500 
               
               
                 r 13  = 
                    14.0423 
                 d 13  = 
                 0.7000 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 14  = 
                     4.0797 
                 d 14  = 
                 (Variable) 
               
               
                 r 15  = 
                    10.1820 
                 d 15  = 
                 1.7446 
                 n d8  = 
                 1.58913 
                 ν d8  = 
                 61.14 
               
               
                   
                 (Aspheric) 
               
               
                 r 16  = 
                   1133.0330 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.505 
                 9.528 
                 15.810 
               
               
                   
                 d 3   
                 1.1566 
                 5.4711 
                 8.0959 
               
               
                   
                 d 7   
                 8.2383 
                 3.9238 
                 1.3000 
               
               
                   
                 d 8   
                 5.6465 
                 3.6256 
                 0.9360 
               
               
                   
                 d 14   
                 2.0735 
                 3.4220 
                 4.4638 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 7th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −5.8146 × 10 −4   
               
               
                   
                 A 6  = 
                 −3.5256 × 10 −7   
               
               
                   
                 A 8  = 
                 −1.1100 × 10 −6   
               
               
                   
                 A 10  = 
                   9.7216 × 10 −9   
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −5.1506 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.2707 × 10 −6   
               
               
                   
                 A 8  = 
                   2.5686 × 10 −7   
               
               
                   
                 A 10  = 
                 −1.0482 × 10 −8   
               
             
          
           
               
                   
                 15th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −2.2630 × 10 −4   
               
               
                   
                 A 6  = 
                   1.7763 × 10 −5   
               
               
                   
                 A 8  = 
                 −1.5096 × 10 −6   
               
               
                   
                 A 10  = 
                   9.3766 × 10 −8   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.866 
               
               
                   
                 F 3 /F 4  = 
                  0.591 
               
               
                   
                 | β 2τ  | = 
                  0.575 
               
               
                   
                 | L 3 /L 2  | = 
                  0.68 
               
               
                   
                 (F 3.4W )/IH = 
                  2.52 
               
               
                   
                 F 1 /IH = 
                 10.06 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 10 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 5.502˜9.509˜15.873 
               
               
                 F NO  = 2.777˜3.341˜4.352 
               
             
          
           
               
                 r 1  = 
                  16.5657 
                 d 1  = 
                 3.6105 
                 n d1  = 
                 1.48749 
                 ν d1  = 
                 70.23 
               
               
                 r 2  = 
                 570.4842 
                 d 2  = 
                 (Variable) 
               
               
                 r 3  = 
                  33.8910 
                 d 3  = 
                 0.8356 
                 n d2  = 
                 1.84666 
                 ν d2  = 
                 23.78 
               
               
                 r 4  = 
                  5.4863 
                 d 4  = 
                 2.6452 
               
               
                 r 5  = 
                 −13.8594 
                 d 5  = 
                 0.8000 
                 n d3  = 
                 1.48749 
                 ν d3  = 
                 70.23 
               
               
                 r 6  = 
                  7.7346 
                 d 6  = 
                 2.6020 
                 n d4  = 
                 1.84666 
                 ν d4  = 
                 23.78 
               
               
                 r 7  = 
                 423.2622 
                 d 7  = 
                 (Variable) 
               
               
                 r 8  = 
                 ∞ (Stop) 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                  8.6181 
                 d 9  = 
                 3.3470 
                 n d5  = 
                 1.56384 
                 ν d5  = 
                 60.67 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                 −16.8991 
                 d 10  = 
                 0.1208 
               
               
                 r 11  = 
                  7.7569 
                 d 11  = 
                 2.8653 
                 n d6  = 
                 1.77250 
                 ν d6  = 
                 49.60 
               
               
                 r 12  = 
                 258.5476 
                 d 12  = 
                 0.7000 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 13  = 
                  4.5291 
                 d 13  = 
                 (Variable) 
               
               
                 r 14  = 
                  9.7155 
                 d 14  = 
                 2.4486 
                 n d8  = 
                 1.56384 
                 ν d8  = 
                 60.67 
               
               
                   
                 (Aspheric) 
               
               
                 r 15  = 
                 −47.1886 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.502 
                 9.509 
                 15.873 
               
               
                   
                 d 2   
                 0.9830 
                 5.3731 
                 8.0323 
               
               
                   
                 d 7   
                 8.3593 
                 3.9739 
                 1.3000 
               
               
                   
                 d 8   
                 6.5283 
                 4.2008 
                 0.9360 
               
               
                   
                 d 13   
                 2.2562 
                 3.7723 
                 5.1579 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −3.1865 × 10 −4   
               
               
                   
                 A 6  = 
                   2.3167 × 10 −7   
               
               
                   
                 A 8  = 
                   1.3223 × 10 −8   
               
               
                   
                 A 10  = 
                 −1.9200 × 10 −10   
               
             
          
           
               
                   
                 14th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4 =   
                 −1.1041 × 10 −4   
               
               
                   
                 A 6 =   
                 −2.7188 × 10 −6   
               
               
                   
                 A 8 =   
                   3.7776 × 10 −7   
               
               
                   
                 A 10 =   
                   0 
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                 0.779 
               
               
                   
                 F 3 /F 4  = 
                 0.794 
               
               
                   
                 | β 2τ  | = 
                 0.586 
               
               
                   
                 | L 3 /L 2  | = 
                 0.792 
               
               
                   
                 (F 3.4W )/IH = 
                 2.71 
               
               
                   
                 F 1 /IH = 
                 9.98 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 11 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 5.504˜9.432˜15.856 
               
               
                 F NO  = 1.990˜2.270˜2.711 
               
             
          
           
               
                 r 1  = 
                  18.2001 
                 d 1  = 
                 1.1730 
                 n d1  = 
                 1.80518 
                 ν d1  = 
                 25.42 
               
               
                 r 2  = 
                  13.0296 
                 d 2  = 
                 0.3357 
               
               
                 r 3  = 
                  13.9728 
                 d 3  = 
                 4.8470 
                 n d2  = 
                 1.69680 
                 ν d2  = 
                 55.53 
               
               
                 r 4  = 
                 3102.7527 
                 d 4  = 
                 (Variable) 
               
               
                 r 5  = 
                  424.6070 
                 d 5  = 
                 0.8000 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 6  = 
                   5.6105 
                 d 6  = 
                 2.9586 
               
               
                 r 7  = 
                 −105.0017 
                 d 7  = 
                 0.8000 
                 n d4  = 
                 1.48749 
                 ν d4  = 
                 70.23 
               
               
                 r 8  = 
                  10.6618 
                 d 8  = 
                 2.3225 
                 n d5  = 
                 1.72250 
                 ν d5  = 
                 29.20 
               
               
                 r 9  = 
                  74.1193 
                 d 9  = 
                 (Variable) 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                   9.2181 
                 d 11  = 
                 2.9948 
                 n d6  = 
                 1.66910 
                 ν d6  = 
                 55.40 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                  −30.4447 
                 d 12  = 
                 0.1424 
               
               
                 r 13  = 
                   7.5345 
                 d 13  = 
                 2.5546 
                 n d7  = 
                 1.67790 
                 ν d7  = 
                 55.34 
               
               
                 r 14  = 
                  80.3022 
                 d 14  = 
                 0.7000 
                 n d8  = 
                 1.84666 
                 ν d8  = 
                 23.78 
               
               
                 r 15  = 
                   4.9693 
                 d 15  = 
                 (Variable) 
               
               
                 r 16  = 
                   9.4973 
                 d 16  = 
                 2.8365 
                 n d9  = 
                 1.66910 
                 ν d9  = 
                 55.40 
               
               
                   
                 (Aspheric) 
               
               
                 r 17  = 
                  −38.4689 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 5.504 
                 9.432 
                 15.856 
               
               
                   
                 d 4   
                 0.7566 
                 5.0506 
                 8.1970 
               
               
                   
                 d 9   
                 8.7125 
                 4.4098 
                 1.3000 
               
               
                   
                 d 10   
                 4.9718 
                 3.2094 
                 0.9360 
               
               
                   
                 d 15   
                 2.2537 
                 3.0666 
                 3.9604 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −2.6558 × 10 −4   
               
               
                   
                 A 6  = 
                   4.2392 × 10 −6   
               
               
                   
                 A 8  = 
                 −5.4464 × 10 −7   
               
               
                   
                 A 10  = 
                   1.2756 × 10 −8   
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                 −0.2184 
               
               
                   
                 A 4  = 
                 −1.8121 × 10 −4   
               
               
                   
                 A 6  = 
                 −1.3295 × 10 −6   
               
               
                   
                 A 8  = 
                   1.4549 × 10 −7   
               
               
                   
                 A 10  = 
                 −4.6461 × 10 −9   
               
             
          
           
               
                   
                 16th surface 
               
             
          
           
               
                   
                 K = 
                   0 
               
               
                   
                 A 4  = 
                 −2.5114 × 10 −4   
               
               
                   
                 A 6  = 
                   3.1103 × 10 −6   
               
               
                   
                 A 8  = 
                 −1.1345 × 10 −8   
               
               
                   
                 A 10  = 
                   0 
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                 0.628 
               
               
                   
                 F 3 /F 4  = 
                 1.088 
               
               
                   
                 | β 2τ  | = 
                 0.760 
               
               
                   
                 | L 3 /L 2  | = 
                 0.54 
               
               
                   
                 (F 3.4W )/IH = 
                 2.67 
               
               
                   
                 F 1 /IH = 
                 8.73 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 12 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 6.608˜11.270˜19.098 
               
               
                 F NO  = 2.03˜2.36˜2.91 
               
             
          
           
               
                 r 1  = 
                   36.688 
                 d 1  = 
                 4.14 
                 n d1  = 
                 1.48749 
                 ν d1  = 
                 70.23 
               
               
                 r 2  = 
                 ∞ 
                 d 2  = 
                 (Variable) 
               
               
                 r 3  = 
                   21.750 
                 d 3  = 
                 1.25 
                 n d2  = 
                 1.84666 
                 ν d2  = 
                 23.78 
               
               
                 r 4  = 
                    8.054 
                 d 4  = 
                 5.45 
               
               
                 r 5  = 
                 −27.511 
                 d 5  = 
                 1.00 
                 n d3  = 
                 1.48749 
                 ν d3  = 
                 70.23 
               
               
                 r 6  = 
                   10.412 
                 d 6  = 
                 4.50 
                 n d4  = 
                 1.84666 
                 ν d4  = 
                 23.78 
               
               
                 r 7  = 
                   40.550 
                 d 7  = 
                 (Variable) 
               
               
                 r 8  = 
                 ∞ (Stop) 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                   17.583 
                 d 9  = 
                 3.42 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                 −35.670 
                 d 10  = 
                 0.20 
               
               
                 r 11  = 
                    9.390 
                 d 11  = 
                 4.35 
                 n d6  = 
                 1.77250 
                 ν d6  = 
                 49.60 
               
               
                 r 12  = 
                   87.943 
                 d 12  = 
                 0.90 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 13  = 
                    6.609 
                 d 13  = 
                 (Variable) 
               
               
                 r 14  = 
                   13.553 
                 d 14  = 
                 3.28 
                 n d8  = 
                 1.58913 
                 ν d8  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 15  = 
                 −30.808 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 6.608 
                 11.270 
                 19.098 
               
               
                   
                 d 2   
                 1.00 
                 9.66 
                 15.80 
               
               
                   
                 d 7   
                 16.20 
                 7.55 
                 1.50 
               
               
                   
                 d 8   
                 8.66 
                 5.46 
                 1.50 
               
               
                   
                 d 13   
                 3.46 
                 5.00 
                 5.71 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4 =   
                 −4.66054 × 10 −5   
               
               
                   
                 A 6 =   
                 −1.33346 × 10 −6   
               
               
                   
                 A 8 =   
                   6.88261 × 10 −8   
               
               
                   
                 A 10 =   
                 −1.18171 × 10 −9   
               
               
                   
                 A 12 =   
                   1.21868 × 10 −12   
               
             
          
           
               
                   
                 14th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4 =   
                 −9.93375 × 10 −5   
               
               
                   
                 A 6 =   
                 −9.76311 × 10 −7   
               
               
                   
                 A 8 =   
                   3.21037 × 10 −7   
               
               
                   
                 A 10 =   
                 −1.95172 × 10 −8   
               
               
                   
                 A 12 =   
                   3.74139 × 10 −10   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.77 
               
               
                   
                 F 3 /F 4  = 
                  1.12 
               
               
                   
                 | β 2τ  | = 
                  0.35 
               
               
                   
                 | L 3 /L 2  | = 
                  0.48 
               
               
                   
                 (F 3.4W )/IH = 
                  3.06 
               
               
                   
                 F 1 /IH = 
                 17.10 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 13 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 6.613˜11.256˜18.999 
               
               
                 F NO  = 2.64˜3.01˜3.85 
               
             
          
           
               
                 r 1  = 
                   27.567 
                 d 1  = 
                 4.40 
                 n d1  = 
                 1.48749 
                 ν d1  = 
                 70.23 
               
               
                 r 2  = 
                 ∞ 
                 d 2  = 
                 (Variable) 
               
               
                 r 3  = 
                   34.610 
                 d 3  = 
                 1.00 
                 n d2  = 
                 1.84666 
                 ν d2  = 
                 23.78 
               
               
                 r 4  = 
                    7.611 
                 d 4  = 
                 4.17 
               
               
                 r 5  = 
                 −26.015 
                 d 5  = 
                 0.95 
                 n d3  = 
                 1.48749 
                 ν d3  = 
                 70.23 
               
               
                 r 6  = 
                    9.781 
                 d 6  = 
                 3.36 
                 n d4  = 
                 1.84666 
                 ν d4  = 
                 23.78 
               
               
                 r 7  = 
                   77.491 
                 d 7  = 
                 (Variable) 
               
               
                 r 8  = 
                 ∞ (Stop) 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                    9.059 
                 d 9  = 
                 3.46 
                 n d5  = 
                 1.58913 
                 ν d5  = 
                 61.28 
               
               
                   
                 (Aspheric) 
               
               
                 r 10  = 
                 −28.867 
                 d 10  = 
                 0.20 
               
               
                 r 11  = 
                   13.765 
                 d 11  = 
                 3.12 
                 n d6  = 
                 1.77250 
                 ν d6  = 
                 49.60 
               
               
                 r 12  = 
                   81.243 
                 d 12  = 
                 0.90 
                 n d7  = 
                 1.84666 
                 ν d7  = 
                 23.78 
               
               
                 r 13  = 
                    6.376 
                 d 13  = 
                 (Variable) 
               
               
                 r 14  = 
                   16.883 
                 d 14  = 
                 2.54 
                 n d8  = 
                 1.80400 
                 ν d8  = 
                 46.57 
               
               
                 r 15  = 
                 −22.639 
                 d 15  = 
                 0.90 
               
               
                 r 16  = 
                 −13.830 
                 d 16  = 
                 1.00 
                 n d9  = 
                 1.84666 
                 ν d9  = 
                 23.78 
               
               
                 r 17  = 
                 −20.854 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 6.613 
                 11.256 
                 18.999 
               
               
                   
                 d 2   
                 1.00 
                 8.49 
                 13.22 
               
               
                   
                 d 7   
                 13.73 
                 6.24 
                 1.50 
               
               
                   
                 d 8   
                 8.03 
                 5.46 
                 1.30 
               
               
                   
                 d 13   
                 2.38 
                 3.71 
                 5.53 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 9th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −2.44569 × 10 −4   
               
               
                   
                 A 6  = 
                   1.63587 × 10 −6   
               
               
                   
                 A 8  = 
                 −2.54100 × 10 −7   
               
               
                   
                 A 10  = 
                   1.25155 × 10 −8   
               
               
                   
                 A 12  = 
                 −2.30862 × 10 −10   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.76 
               
               
                   
                 F 3 /F 4  = 
                  1.09 
               
               
                   
                 | β 2τ  | = 
                  0.50 
               
               
                   
                 | L 3 /L 2  | = 
                  0.55 
               
               
                   
                 (F 3.4W )/IH = 
                  2.79 
               
               
                   
                 F 1 /IH = 
                 12.85 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 14 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 6.548˜11.266˜19.000 
               
               
                 F NO  = 2.02˜2.33˜2.80 
               
             
          
           
               
                 r 1  = 
                  28.972 
                 d 1  = 
                 1.50 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                  19.691 
                 d 2  = 
                 0.22 
               
               
                 r 3  = 
                  20.405 
                 d 3  = 
                 4.96 
                 n d2  = 
                 1.77250 
                 ν d2  = 
                 49.60 
               
               
                 r 4  = 
                 196.549 
                 d 4  = 
                 (Variable) 
               
               
                 r 5  = 
                  42.098 
                 d 5  = 
                 1.00 
                 n d3  = 
                 1.77250 
                 ν d3  = 
                 49.60 
               
               
                 r 6  = 
                  7.090 
                 d 6  = 
                 4.71 
               
               
                 r 7  = 
                 −42.112 
                 d 7  = 
                 0.95 
                 n d4  = 
                 1.57250 
                 ν d4  = 
                 57.74 
               
               
                 r 8  = 
                  7.798 
                 d 8  = 
                 3.63 
                 n d5  = 
                 1.80100 
                 ν d5  = 
                 34.97 
               
               
                 r 9  = 
                  51.433 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                 ∞ (Stop) 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                  13.438 
                 d 11  = 
                 2.85 
                 n d6  = 
                 1.58913 
                 ν d6  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 12  = 
                 −33.468 
                 d 12  = 
                 0.20 
               
               
                 r 13  = 
                  16.565 
                 d 13  = 
                 5.00 
                 n d7  = 
                 1.77250 
                 ν d7  = 
                 49.60 
               
               
                 r 14  = 
                  −9.106 
                 d 14  = 
                 0.90 
                 n d8  = 
                 1.68893 
                 ν d8  = 
                 31.07 
               
               
                 r 15  = 
                  7.645 
                 d 15  = 
                 (Variab1e) 
               
               
                 r 16  = 
                  13.914 
                 d 16  = 
                 5.00 
                 n d9  = 
                 1.58913 
                 ν d9  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 17  = 
                 −26.414 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 6.548 
                 11.266 
                 19.000 
               
               
                   
                 d 4   
                 1.00 
                 7.40 
                 12.09 
               
               
                   
                 d 9   
                 12.59 
                 6.19 
                 1.50 
               
               
                   
                 d 10   
                 7.10 
                 4.41 
                 1.35 
               
               
                   
                 d 15   
                 2.01 
                 3.28 
                 3.97 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 11th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −1.15802 × 10 −4   
               
               
                   
                 A 6  = 
                 −2.30929 × 10 −6   
               
               
                   
                 A 8  = 
                   9.29778 × 10 −8   
               
               
                   
                 A 10  = 
                 −1.70572 × 10 −9   
               
             
          
           
               
                   
                 16th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −1.50902 × 10 −4   
               
               
                   
                 A 6  = 
                   7.59738 × 10 −6   
               
               
                   
                 A 8  = 
                 −4.34345 × 10 −7   
               
               
                   
                 A 10  = 
                   9.20410 × 10 −9   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.64 
               
               
                   
                 F 3 /F 4  = 
                  1.07 
               
               
                   
                 | β 2τ  | = 
                  0.56 
               
               
                   
                 | L 3 /L 2  | = 
                  0.52 
               
               
                   
                 (F 3.4W )/IH = 
                  2.81 
               
               
                   
                 F 1 /IH = 
                 10.96 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 15 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 6.562˜11.266˜19.000 
               
               
                 F NO  = 2.03˜2.41˜2.98 
               
             
          
           
               
                 r 1  = 
                  27.565 
                 d 1  = 
                 1.80 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                  22.250 
                 d 2  = 
                 5.28 
                 n d2  = 
                 1.69680 
                 ν d2  = 
                 55.53 
               
               
                 r 3  = 
                 146.290 
                 d 3  = 
                 (Variable) 
               
               
                 r 4  = 
                  33.155 
                 d 4  = 
                 1.20 
                 n d3  = 
                 1.84666 
                 ν d3  = 
                 23.78 
               
               
                 r 5  = 
                  7.643 
                 d 5  = 
                 5.94 
               
               
                 r 6  = 
                 −32.864 
                 d 6  = 
                 0.95 
                 n d4  = 
                 1.58913 
                 ν d4  = 
                 61.14 
               
               
                 r 7  = 
                  9.442 
                 d 7  = 
                 5.00 
                 n d5  = 
                 1.84666 
                 ν d5  = 
                 23.78 
               
               
                 r 8  = 
                  72.713 
                 d 8  = 
                 (Variable) 
               
               
                 r 9  = 
                 ∞ (Stop) 
                 d 9  = 
                 (Variable) 
               
               
                 r 10  = 
                  13.995 
                 d 10  = 
                 4.65 
                 n d6  = 
                 1.58913 
                 ν d6  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 11  = 
                 −26.315 
                 d 11  = 
                 0.20 
               
               
                 r 12  = 
                  11.896 
                 d 12  = 
                 5.00 
                 n d7  = 
                 1.77250 
                 ν d7  = 
                 49.60 
               
               
                 r 13  = 
                 −19.763 
                 d 13  = 
                 0.90 
                 n d8  = 
                 1.80518 
                 ν d8  = 
                 25.42 
               
               
                 r 14  = 
                  7.049 
                 d 14  = 
                 (Variable) 
               
               
                 r 15  = 
                  12.657 
                 d 15  = 
                 5.00 
                 n d9  = 
                 1.58913 
                 ν d9  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 16  = 
                 −36.523 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 6.562 
                 11.266 
                 19.000 
               
               
                   
                 d 3   
                 1.00 
                 7.09 
                 11.56 
               
               
                   
                 d 8   
                 12.07 
                 5.98 
                 1.50 
               
               
                   
                 d 9   
                 7.83 
                 4.88 
                 1.35 
               
               
                   
                 d 14   
                 1.29 
                 3.19 
                 4.54 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 10th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −8.42531 × 10 −5   
               
               
                   
                 A 6  = 
                 −1.06102 × 10 −6   
               
               
                   
                 A 8  = 
                   4.82414 × 10 −8   
               
               
                   
                 A 10  = 
                 −7.21004 × 10 −10   
               
             
          
           
               
                   
                 15th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4 =   
                 −1.53723 × 10 −4   
               
               
                   
                 A 6 =   
                   8.03934 × 10 −6   
               
               
                   
                 A 8 =   
                 −4.64104 × 10 −7   
               
               
                   
                 A 10 =   
                   9.96594 × 10 −9   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.72 
               
               
                   
                 F 3 /F 4  = 
                  0.96 
               
               
                   
                 | β 2τ  | = 
                  0.55 
               
               
                   
                 | L 3 /L 2  | = 
                  0.61 
               
               
                   
                 (F 3.4W )/IH = 
                  2.73 
               
               
                   
                 F 1 /IH = 
                 11.41 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 16 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
             
               
             
               
               
             
               
               
               
             
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
               
             
             
               
                 f = 6.460˜11.267˜19.000 
               
               
                 F NO  = 2.03˜2.36˜2.86 
               
             
          
           
               
                 r 1  = 
                  45.399 
                 d 1  = 
                 1.50 
                 n d1  = 
                 1.84666 
                 ν d1  = 
                 23.78 
               
               
                 r 2  = 
                  30.450 
                 d 2  = 
                 3.42 
                 n d2  = 
                 1.77250 
                 ν d2  = 
                 49.60 
               
               
                 r 3  = 
                  73.068 
                 d 3  = 
                 0.20 
               
               
                 r 4  = 
                  30.537 
                 d 4  = 
                 4.00 
                 n d3  = 
                 1.60311 
                 ν d3  = 
                 60.64 
               
               
                 r 5  = 
                 114.998 
                 d 5  = 
                 (Variable) 
               
               
                 r 6  = 
                  37.983 
                 d 6  = 
                 1.00 
                 n d4  = 
                 1.80610 
                 ν d4  = 
                 40.92 
               
               
                 r 7  = 
                  7.134 
                 d 7  = 
                 4.94 
               
               
                 r 8  = 
                 −34.697 
                 d 8  = 
                 0.95 
                 n d5  = 
                 1.59551 
                 ν d5  = 
                 39.24 
               
               
                 r 9  = 
                  7.910 
                 d 9  = 
                 3.74 
                 n d6  = 
                 1.80518 
                 ν d6  = 
                 25.42 
               
               
                 r 10  = 
                  61.919 
                 d 10  = 
                 (Variable) 
               
               
                 r 11  = 
                 ∞ (Stop) 
                 d 11  = 
                 (Variable) 
               
               
                 r 12  = 
                  20.148 
                 d 12  = 
                 3.82 
                 n d7  = 
                 1.58913 
                 ν d7  = 
                 61.30 
               
               
                   
                 (Aspheric) 
               
               
                 r 13  = 
                 −27.415 
                 d 13  = 
                 0.20 
               
               
                 r 14  = 
                  11.775 
                 d 14  = 
                 5.00 
                 n d8  = 
                 1.77250 
                 ν d8  = 
                 49.60 
               
               
                 r 15  = 
                 −16.598 
                 d 15  = 
                 0.90 
                 n d9  = 
                 1.74077 
                 ν d9  = 
                 27.79 
               
               
                 r 16  = 
                  7.678 
                 d 16  = 
                 (Variable) 
               
               
                 r 17  = 
                  14.447 
                 d 17  = 
                 5.00 
                 n d10  = 
                 1.58913 
                 ν d10  = 
                 61.30 
               
               
                 r 18  = 
                 −24.089 
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 6.460 
                 11.267 
                 19.000 
               
               
                   
                 d 5   
                 1.00 
                 7.29 
                 11.76 
               
               
                   
                 d 10   
                 12.25 
                 5.96 
                 1.50 
               
               
                   
                 d 11   
                 7.87 
                 4.72 
                 1.35 
               
               
                   
                 d 16   
                 2.96 
                 4.38 
                 4.80 
               
             
          
           
               
                 Aspherical Coefficients 
               
             
          
           
               
                   
                 12th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −4.84618 × 10 −5   
               
               
                   
                 A 6  = 
                 −1.50477 × 10 −6   
               
               
                   
                 A 8  = 
                   6.27337 × 10 −8   
               
               
                   
                 A 10  = 
                 −9.73311 × 10 −10   
               
             
          
           
               
                   
                 17th surface 
               
             
          
           
               
                   
                 K = 
                   0.000 
               
               
                   
                 A 4  = 
                 −1.24232 × 10 −4   
               
               
                   
                 A 6  = 
                   4.55032 × 10 −6   
               
               
                   
                 A 8  = 
                 −2.09257 × 10 −7   
               
               
                   
                 A 10  = 
                   3.76691 × 10 −9   
               
             
          
           
               
                   
                 | F 2 /F 3  | = 
                  0.59 
               
               
                   
                 F 3 /F 4  = 
                  1.08 
               
               
                   
                 | β 2τ  | = 
                  0.55 
               
               
                   
                 | L 3 /L 2  | = 
                  0.61 
               
               
                   
                 (F 3.4W )/IH = 
                  2.96 
               
               
                   
                 F 1 /IH = 
                 11.19 
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 17 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.643˜6.310˜10.420 
               
               
                 F NO  = 2.79˜3.22˜4.11 
               
               
                 f B  = 3.43˜3.73˜4.11  
               
               
                   
               
             
          
           
               
                 r 1  = 123.446 
                 d 1  = 0.79 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 26.028 
                 d 2  = 2.63 
                 n d2  = 1.48749 
                 ν d2  = 70.23 
               
               
                 r 3  = −37.648 
                 d 3  = 0.12 
               
               
                 r 4  = 9.745 
                 d 4  = 2.16 
                 n d3  = 1.69680 
                 ν d3  = 55.53 
               
               
                 r 5  = 41.109 
                 d 5  = (Variable) 
               
               
                 r 6  = 49.306 
                 d 6  = 0.56 
                 n d4  = 1.77250 
                 ν d4  = 49.60 
               
               
                 r 7  = 3.668 
                 d 7  = 1.97 
               
               
                 r 8  = −6.439 
                 d 8  = 0.56 
                 n d5  = 1.48749 
                 ν d5  = 70.21 
               
               
                 r 9  = 7.824 
                 d 9  = 1.19 
                 n d6  = 1.84666 
                 ν d6  = 23.78 
               
               
                 r 10  = −92.465 
                 d 10  = (Variable) 
               
               
                 r 11  = ∞ (Stop) 
                 d 11  = (Variable) 
               
               
                 r 12  = 7.726 (Aspheric) 
                 d 12  = 1.29 
                 n d7  = 1.58913 
                 ν d7  = 61.18 
               
               
                 r 13  = −15.280 
                 d 13  = 0.10 
               
               
                 r 14  = 5.743 
                 d 14  = 1.73 
                 n d8  = 1.72916 
                 ν d8  = 54.68 
               
               
                 r 15  = −8.215 
                 d 15  = 0.20 
               
               
                 r 16  = 17.851 
                 d 16  = 0.46 
                 n d9  = 1.84666 
                 ν d9  = 23.78 
               
               
                 r 17  = 2.797 
                 d 17  = (Variable) 
               
               
                 r 18  = 6.406 
                 d 18  = 1.07 
                 n d10  = 1.72916 
                 ν d10  = 54.68 
               
               
                 r 19  = 21.794  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.643 
                 6.310 
                 10.420 
               
               
                   
                   
               
               
                   
                 d 5   
                 0.64 
                 2.95 
                 4.22 
               
               
                   
                 d 10   
                 4.43 
                 2.13 
                 0.86 
               
               
                   
                 d 11   
                 3.24 
                 2.25 
                 0.62 
               
               
                   
                 d 17   
                 1.61 
                 2.30 
                 3.55  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                 12th surface 
               
               
                   
                   
               
               
                   
                 K = −0.218 
               
               
                   
                 A 4  = −3.12469 × 10 −3   
               
               
                   
                 A 6  = −2.00580 × 10 −4   
               
               
                   
                 A 8  = 2.58848 × 10 −5   
               
               
                   
                 A 10  = −3.98934 × 10 −6   
               
               
                   
                 |F 2 /F 3 | = 0.714 
               
               
                   
                 F 3 /F 4  = 0.539 
               
               
                   
                 |β 2T | = 0.897 
               
               
                   
                 |L 3 /L 2 | = 0.73 
               
               
                   
                 (F 3,4W )/IH = 2.44 
               
               
                   
                 F 1 /IH = 6.97 
               
               
                   
                 IH = 2.25  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 18 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 2.924˜5.049˜8.425 
               
               
                 F NO  = 2.78˜3.39˜4.22 
               
               
                 f B  = 2.69˜3.00˜4.18  
               
               
                   
               
             
          
           
               
                 r 1  = 9.603 
                 d 1  = 0.64 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 6.804 
                 d 2  = 2.74 
                 n d2  = 1.60311 
                 ν d2  = 60.64 
               
               
                 r 3  = 121.247 
                 d 3  = (Variable) 
               
               
                 r 4  = 21.867 
                 d 4  = 0.41 
                 n d3  = 1.65160 
                 ν d3  = 58.55 
               
               
                 r 5  = 2.740 
                 d 5  = 1.87 
               
               
                 r 6  = −17.627 
                 d 6  = 0.37 
                 n d4  = 1.56384 
                 ν d4  = 60.67 
               
               
                 r 7  = 10.992 
                 d 7  = −0.01 
               
               
                 r 8  = 4.352 
                 d 8  = 0.93 
                 n d5  = 1.80518 
                 ν d5  = 25.42 
               
               
                 r 9  = 6.985 
                 d 9  = (Variable) 
               
               
                 r 10  = ∞ (Stop) 
                 d 10  = (Variable) 
               
               
                 r 11  = 6.533 (Aspheric) 
                 d 11  = 1.96 
                 n d6  = 1.67790 
                 ν d6  = 55.34 
               
               
                 r 12  = −6.275 
                 d 12  = 0.45 
               
               
                 r 13  = 6.079 
                 d 13  = 1.25 
                 n d7  = 1.60311 
                 ν d7  = 60.64 
               
               
                 r 14  = −9.868 
                 d 14  = 0.07 
               
               
                 r 15  = 25.676 
                 d 15  = 0.37 
                 n d8  = 1.84666 
                 ν d8  = 23.78 
               
               
                 r 16  = 2.938 
                 d 16  = (Variable) 
               
               
                 r 17  = 7.544 
                 d 17  = 0.91 
                 n d9  = 1.58913 
                 ν d9  = 61.14 
               
               
                 r 18  = −46.010  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 2.924 
                 5.049 
                 8.425 
               
               
                   
                   
               
               
                   
                 d 3   
                 0.36 
                 2.53 
                 4.14 
               
               
                   
                 d 9   
                 4.46 
                 2.29 
                 0.69 
               
               
                   
                 d 10   
                 2.85 
                 1.70 
                 0.50 
               
               
                   
                 d 16   
                 1.02 
                 1.85 
                 1.88  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                 11th surface 
               
               
                   
                   
               
               
                   
                 K = −0.218 
               
               
                   
                 A 4  = −4.79076 × 10 −3   
               
               
                   
                 A 6  = 7.18792 × 10 −4   
               
               
                   
                 A 8  = −2.84416 × 10 −4   
               
               
                   
                 A 10  = 4.21243 × 10 −5   
               
               
                   
                 |F 2 /F 3 | = 0.837 
               
               
                   
                 F 3 /F 4  = 0.475 
               
               
                   
                 |β 2T | = 0.501 
               
               
                   
                 |L 3 /L 2 | = 0.62 
               
               
                   
                 (F 3,4W )/IH = 2.58 
               
               
                   
                 F 1 /IH = 10.99 
               
               
                   
                 IH = 1.8  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 19 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.238˜5.605˜9.300 
               
               
                 F NO  = 2.79˜3.35˜4.33 
               
               
                 f B  = 3.05˜3.45˜4.42  
               
               
                   
               
             
          
           
               
                 r 1  = 11.229 
                 d 1  = 0.71 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 8.678 
                 d 2  = 1.82 
                 n d2  = 1.60311 
                 ν d2  = 60.64 
               
               
                 r 3  = −4524.933 
                 d 3  = (Variable) 
               
               
                 r 4  = −44.964 
                 d 4  = 0.49 
                 n d3  = 1.77250 
                 ν d3  = 49.60 
               
               
                 r 5  = 2.859 
                 d 5  = 1.07 
               
               
                 r 6  = 10.754 
                 d 6  = 1.04 
                 n d4  = 1.80518 
                 ν d4  = 25.42 
               
               
                 r 7  = ∞ (Aspheric) 
                 d 7  = (Variable) 
               
               
                 r 8  = ∞ (Stop) 
                 d 8  = (Variable) 
               
               
                 r 9  = 4.318 (Aspheric) 
                 d 9  = 1.55 
                 n d5  = 1.58913 
                 ν d5  = 61.18 
               
               
                 r 10  = −13.012 
                 d 10  = 0.09 
               
               
                 r 11  = 4.720 
                 d 11  = 1.16 
                 n d6  = 1.72916 
                 ν d6  = 54.68 
               
               
                 r 12  = 30.878 
                 d 12  = 0.09 
               
               
                 r 13  = 8.260 
                 d 13  = 0.41 
                 n d7  = 1.84666 
                 ν d7  = 23.78 
               
               
                 r 14  = 2.400 
                 d 14  = (Variable) 
               
               
                 r 15  = 5.989 (Aspheric) 
                 d 15  = 1.03 
                 n d8  = 1.58913 
                 ν d8  = 61.14 
               
               
                 r 16  = 666.490  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.238 
                 5.605 
                 9.300 
               
               
                   
                   
               
               
                   
                 d 3   
                 0.68 
                 3.22 
                 4.76 
               
               
                   
                 d 7   
                 4.85 
                 2.31 
                 0.76 
               
               
                   
                 d 8   
                 3.32 
                 2.13 
                 0.55 
               
               
                   
                 d 14   
                 1.22 
                 2.01 
                 2.63  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                 7th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −2.85671 × 10 −3   
               
               
                   
                 A 6  = −5.00585 × 10 −6   
               
               
                   
                 A 8  = −4.55482 × 10 −5   
               
               
                   
                 A 10  = 1.15287 × 10 −6   
               
               
                   
                 9th surface 
               
               
                   
                 K = −0.218 
               
               
                   
                 A 4  = −2.53050 × 10 −3   
               
               
                   
                 A 6  = −3.22409 × 10 −5   
               
               
                   
                 A 8  = 1.05400 × 10 −5   
               
               
                   
                 A 10  = −1.24302 × 10 −6   
               
               
                   
                 15th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −1.11182 × 10 −3   
               
               
                   
                 A 6  = 2.52212 × 10 −4   
               
               
                   
                 A 8  = −6.19443 × 10 −5   
               
               
                   
                 A 10  = 1.11195 × 10 −5   
               
               
                   
                 |F 2 /F 3 | = 0.866 
               
               
                   
                 F 3 /F 4  = 0.591 
               
               
                   
                 |β 2T | = 0.575 
               
               
                   
                 |L 3 /L 2 | = 0.68 
               
               
                   
                 (F 3,4W )/IH = 2.52 
               
               
                   
                 F 1 /IH = 10.06 
               
               
                   
                 IH = 2.0  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 20 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.144˜5.518˜9.070 
               
               
                 F NO  = 2.78˜3.34˜4.35 
               
               
                 f B  = 2.85˜3.29˜4.40  
               
               
                   
               
             
          
           
               
                 r 1  = 9.466 
                 d 1  = 2.06 
                 n d1  = 1.48749 
                 ν d1  = 70.23 
               
               
                 r 2  = 325.991 
                 d 2  = (Variable) 
               
               
                 r 2  = 19.366 
                 d 3  = 0.48 
                 n d2  = 1.84666 
                 ν d2  = 23.78 
               
               
                 r 4  = 3.135 
                 d 4  = 1.51 
               
               
                 r 5  = −7.920 
                 d 5  = 0.46 
                 n d3  = 1.48749 
                 ν d3  = 70.23 
               
               
                 r 6  = 4.420 
                 d 6  = 1.49 
                 n d4  = 1.84666 
                 ν d4  = 23.78 
               
               
                 r 7  = 241.864 
                 d 7  = (Variable) 
               
               
                 r 8  = ∞ (Stop) 
                 d 8  = (Variable) 
               
               
                 r 9  = 4.925 (Aspheric) 
                 d 9  = 1.91 
                 n d5  = 1.56384 
                 ν d5  = 60.67 
               
               
                 r 10  = −9.657 
                 d 10  = 0.07 
               
               
                 r 11  = 4.433 
                 d 11  = 1.64 
                 n d6  = 1.77250 
                 ν d6  = 49.60 
               
               
                 r 12  = 147.741 
                 d 12  = 0.40 
                 n d7  = 1.84666 
                 ν d7  = 23.78 
               
               
                 r 13  = 2.588 
                 d 13  = (Variable) 
               
               
                 r 14  = 5.552 (Aspheric) 
                 d 14  = 1.40 
                 n d8  = 1.56384 
                 ν d8  = 60.67 
               
               
                 r 15  = −26.965  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.144 
                 5.518 
                 9.070 
               
               
                   
                   
               
               
                   
                 d 2   
                 0.56 
                 3.27 
                 4.59 
               
               
                   
                 d 7   
                 4.78 
                 2.27 
                 0.74 
               
               
                   
                 d 8   
                 3.73 
                 2.40 
                 0.53 
               
               
                   
                 d 13   
                 1.29 
                 2.16 
                 2.95  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                 9th surface 
               
               
                   
                 K = −0.218 
               
               
                   
                 A 4  = −1.70776 × 10 −3   
               
               
                   
                 A 6  = 3.80242 × 10 −6   
               
               
                   
                 A 8  = 6.65158 × 10 −7   
               
               
                   
                 A 10  = −2.95559 × 10 −8   
               
               
                   
                 14th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −5.91729 × 10 −4   
               
               
                   
                 A 6  = −4.46239 × 10 −5   
               
               
                   
                 A 8  = 1.89881 × 10 −5   
               
               
                   
                 A 10  = 0 
               
               
                   
                 |F 2 /F 3 | = 0.779 
               
               
                   
                 F 3 /F 4  = 0.794 
               
               
                   
                 |β 2T | = 0.586 
               
               
                   
                 |L 3 /L 2 | = 0.792 
               
               
                   
                 (F 3,4W )/IH = 2.71 
               
               
                   
                 F 1 /IH = 9.98 
               
               
                   
                 IH = 2.0  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 21 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.538˜6.063˜10.193 
               
               
                 F NO  = 1.99˜2.27˜2.71 
               
               
                 f B  = 3.52˜4.13˜5.01  
               
               
                   
               
             
          
           
               
                 r 1  = 11.700 
                 d 1  = 0.75 
                 n d1  = 1.80518 
                 ν d1  = 25.42 
               
               
                 r 2  = 8.376 
                 d 2  = 0.22 
               
               
                 r 3  = 8.983 
                 d 3  = 3.12 
                 n d2  = 1.69680 
                 ν d2  = 55.53 
               
               
                 r 4  = 1994.627 
                 d 4  = (Variable) 
               
               
                 r 5  = 272.962 
                 d 5  = 0.51 
                 n d3  = 1.77250 
                 ν d3  = 49.60 
               
               
                 r 6  = 3.607 
                 d 6  = 1.90 
               
               
                 r 7  = −67.501 
                 d 7  = 0.51 
                 n d4  = 1.48749 
                 ν d4  = 70.23 
               
               
                 r 8  = 6.854 
                 d 8  = 1.49 
                 n d5  = 1.72250 
                 ν d5  = 29.20 
               
               
                 r 9  = 47.648 (Aspheric) 
                 d 9  = (Variable) 
               
               
                 r 10  = ∞ (Stop) 
                 d 10  = (Variable) 
               
               
                 r 11  = 5.926 (Aspheric) 
                 d 11  = 1.93 
                 n d6  = 1.66910 
                 ν d6  = 55.40 
               
               
                 r 12  = −19.572 
                 d 12  = 0.09 
               
               
                 r 13  = 4.844 
                 d 13  = 1.64 
                 n d7  = 1.67790 
                 ν d7  = 55.34 
               
               
                 r 14  = 51.623 
                 d 14  = 0.45 
                 n d8  = 1.84666 
                 ν d8  = 23.78 
               
               
                 r 15  = 3.195 
                 d 15  = (Variable) 
               
               
                 r 16  = 6.105 (Aspheric) 
                 d 16  = 1.82 
                 n d9  = 1.66910 
                 ν d9  = 55.40 
               
               
                 r 17  = −24.730  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.538 
                 6.063 
                 10.193 
               
               
                   
                   
               
               
                   
                 d 4   
                 0.49 
                 3.25 
                 5.27 
               
               
                   
                 d 9   
                 5.60 
                 2.83 
                 0.84 
               
               
                   
                 d 10   
                 3.20 
                 2.06 
                 0.60 
               
               
                   
                 d 15   
                 1.45 
                 1.97 
                 2.55  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                  9th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −9.99655 × 10 −4   
               
               
                   
                 A 6  = 3.86110 × 10 −5   
               
               
                   
                 A 8  = −1.20035 × 10 −5   
               
               
                   
                 A 10  = 6.80269 × 10 −7   
               
               
                   
                 11th surface 
               
               
                   
                 K = −0.218 
               
               
                   
                 A 4  = −6.82101 × 10 −4   
               
               
                   
                 A 6  = −1.21088 × 10 −5   
               
               
                   
                 A 8  = 3.20658 × 10 −6   
               
               
                   
                 A 10  = −2.47777 × 10 −7   
               
               
                   
                 16th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −9.45299 × 10 −4   
               
               
                   
                 A 6  = 2.83288 × 10 −5   
               
               
                   
                 A 8  = −2.50040 × 10 −7   
               
               
                   
                 A 10  = 0 
               
               
                   
                 |F 2 /F 3 | = 0.628 
               
               
                   
                 F 3 /F 4  = 1.088 
               
               
                   
                 |β 2T | = 0.760 
               
               
                   
                 |L 3 /L 2 | = 0.54 
               
               
                   
                 (F 3,4W )/IH = 2.67 
               
               
                   
                 F 1 /IH = 8.73 
               
               
                   
                 IH = 2.25  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 22 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 2.478˜4.226˜7.162 
               
               
                 F NO  = 2.03˜2.36˜2.91 
               
               
                 f B  = 2.83˜3.44˜4.66  
               
               
                   
               
             
          
           
               
                 r 1  = 13.758 
                 d 1  = 1.55 
                 n d1  = 1.48749 
                 ν d1  = 70.23 
               
               
                 r 2  = ∞ 
                 d 2  = (Variable) 
               
               
                 r 3  = 8.156 
                 d 3  = 0.47 
                 n d2  = 1.84666 
                 ν d2  = 23.78 
               
               
                 r 4  = 3.020 
                 d 4  = 2.04 
               
               
                 r 5  = −10.317 
                 d 5  = 0.38 
                 n d3  = 1.48749 
                 ν d3  = 70.23 
               
               
                 r 6  = 3.905 
                 d 6  = 1.69 
                 n d4  = 1.84666 
                 ν d4  = 23.78 
               
               
                 r 7  = 15.206 
                 d 7  = (Variable) 
               
               
                 r 8  = ∞ (Stop) 
                 d 8  = (Variable) 
               
               
                 r 9  = 6.594 (Aspheric) 
                 d 9  = 1.28 
                 n d5  = 1.58913 
                 ν d5  = 61.30 
               
               
                 r 10  = −13.376 
                 d 10  = 0.08 
               
               
                 r 11  = 3.521 
                 d 11  = 1.63 
                 n d6  = 1.77250 
                 ν d6  = 49.60 
               
               
                 r 12  = 32.979 
                 d 12  = 0.34 
                 n d7  = 1.84666 
                 ν d7  = 23.78 
               
               
                 r 13  = 2.478 
                 d 13  = (Variable) 
               
               
                 r 14  = 5.082 (Aspheric) 
                 d 14  = 1.23 
                 n d8  = 1.58913 
                 ν d8  = 61.30 
               
               
                 r 15  = −11.553  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 2.478 
                 4.226 
                 7.162 
               
               
                   
                   
               
               
                   
                 d 2   
                 0.38 
                 3.62 
                 5.92 
               
               
                   
                 d 7   
                 6.07 
                 2.83 
                 0.56 
               
               
                   
                 d 8   
                 3.25 
                 2.05 
                 0.56 
               
               
                   
                 d 13   
                 1.30 
                 1.88 
                 2.14  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                  9th surface 
               
               
                   
                 K =  0.000 
               
               
                   
                 A 4  = −8.83776 × 10 −4   
               
               
                   
                 A 6  = −1.79814 × 10 −4   
               
               
                   
                 A 8  = 6.59986 × 10 −5   
               
               
                   
                 A 10  = −8.05802 × 10 −6   
               
               
                   
                 A 12  = 5.90942 × 10 −8   
               
               
                   
                 14th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −1.88373 × 10 −3   
               
               
                   
                 A 6  = −1.31653 × 10 −4   
               
               
                   
                 A 8  = 3.07847 × 10 −4   
               
               
                   
                 A 10  = −1.33087 × 10 −4   
               
               
                   
                 A 12  = 1.81422 × 10 −5   
               
               
                   
                 |F 2 /F 3 | = 0.77 
               
               
                   
                 F 3 /F 4  = 1.12 
               
               
                   
                 |β 2T | = 0.35 
               
               
                   
                 |L 3 /L 2 | = 0.48 
               
               
                   
                 (F 3,4W )/IH = 3.06 
               
               
                   
                 F 1 /IH = 17.10 
               
               
                   
                 IH = 1.5  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 23 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 2.976˜5.065˜8.549 
               
               
                 F NO  = 2.64˜3.01˜3.85 
               
               
                 f B  = 2.91˜3.47˜4.54  
               
               
                   
               
             
          
           
               
                 r 1  = 12.405 
                 d 1  = 1.98 
                 n d1  = 1.48749 
                 ν d1  = 70.23 
               
               
                 r 2  = ∞ 
                 d 2  = (Variable) 
               
               
                 r 3  = 15.574 
                 d 3  = 0.45 
                 n d2  = 1.84666 
                 ν d2  = 23.78 
               
               
                 r 4  = 3.425 
                 d 4  = 1.88 
               
               
                 r 5  = −11.707 
                 d 5  = 0.43 
                 n d3  = 1.48749 
                 ν d3  = 70.23 
               
               
                 r 6  = 4.402 
                 d 6  = 1.51 
                 n d4  = 1.84666 
                 ν d4  = 23.78 
               
               
                 r 7  = 34.871 
                 d 7  = (Variable) 
               
               
                 r 8  = ∞ (Stop) 
                 d 8  = (Variable) 
               
               
                 r 9  = 4.077 (Aspheric) 
                 d 9  = 1.55 
                 n d5  = 1.58913 
                 ν d5  = 61.28 
               
               
                 r 10  = −12.990 
                 d 10  = 0.09 
               
               
                 r 11  = 6.194 
                 d 11  = 1.40 
                 n d6  = 1.77250 
                 ν d6  = 49.60 
               
               
                 r 12  = 36.559 
                 d 12  = 0.41 
                 n d7  = 1.84666 
                 ν d7  = 23.78 
               
               
                 r 13  = 2.869 
                 d 13  = (Variable) 
               
               
                 r 14  = 7.598 
                 d 14  = 1.14 
                 n d8  = 1.80400 
                 ν d8  = 46.57 
               
               
                 r 15  = −10.188 
                 d 15  = 0.41 
               
               
                 r 16  = −6.224 
                 d 16  = 0.45 
                 n d9  = 1.84666 
                 ν d9  = 23.78 
               
               
                 r 17  = −9.384  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 2.976 
                 5.065 
                 8.549 
               
               
                   
                   
               
               
                   
                 d 2   
                 0.45 
                 3.82 
                 5.95 
               
               
                   
                 d 7   
                 6.18 
                 2.81 
                 0.68 
               
               
                   
                 d 8   
                 3.61 
                 2.46 
                 0.59 
               
               
                   
                 d 13   
                 1.07 
                 1.67 
                 2.49  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                 9th surface 
               
               
                   
                   
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −2.68388 × 10 −3   
               
               
                   
                 A 6  = 8.86517 × 10 −5   
               
               
                   
                 A 8  = −6.80012 × 10 −5   
               
               
                   
                 A 10  = 1.65400 × 10 −5   
               
               
                   
                 A 12  = −1.50666 × 10 −6   
               
               
                   
                 |F 2 /F 3 | = 0.76 
               
               
                   
                 F 3 /F 4  = 1.09 
               
               
                   
                 |β 2T | = 0.50 
               
               
                   
                 |L 3 /L 2 | = 0.55 
               
               
                   
                 (F 3,4W )/IH = 2.79 
               
               
                   
                 F 1 /IH = 12.85 
               
               
                   
                 IH = 1.8  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 24 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 4.093˜7.041˜11.875 
               
               
                 F NO  = 2.02˜2.33˜2.80 
               
               
                 f B  = 4.53˜5.42˜6.90  
               
               
                   
               
             
          
           
               
                 r 1  = 18.108 
                 d 1  = 0.94 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 12.307 
                 d 2  = 0.14 
               
               
                 r 3  = 12.753 
                 d 3  = 3.10 
                 n d2  = 1.77250 
                 ν d2  = 49.60 
               
               
                 r 4  = 122.843 
                 d 4  = (Variable) 
               
               
                 r 5  = 26.311 
                 d 5  = 0.63 
                 n d3  = 1.77250 
                 ν d3  = 49.60 
               
               
                 r 6  = 4.431 
                 d 6  = 2.94 
               
               
                 r 7  = −26.320 
                 d 7  = 0.59 
                 n d4  = 1.57250 
                 ν d4  = 57.74 
               
               
                 r 8  = 4.874 
                 d 8  = 2.27 
                 n d5  = 1.80100 
                 ν d5  = 34.97 
               
               
                 r 9  = 32.145 
                 d 9  = (Variable) 
               
               
                 r 10  = ∞ (Stop) 
                 d 10  = (Variable) 
               
               
                 r 11  = 8.399 (Aspheric) 
                 d 11  = 1.78 
                 n d6  = 1.58913 
                 ν d6  = 61.30 
               
               
                 r 12  = −20.918 
                 d 12  = 0.13 
               
               
                 r 13  = 10.353 
                 d 13  = 3.13 
                 n d7  = 1.77250 
                 ν d7  = 49.60 
               
               
                 r 14  = −5.691 
                 d 14  = 0.56 
                 n d8  = 1.68893 
                 ν d8  = 31.07 
               
               
                 r 15  = 4.778 
                 d 15  = (Variable) 
               
               
                 r 16  = 8.696 (Aspheric) 
                 d 16  = 3.13 
                 n d9  = 1.58913 
                 ν d9  = 61.30 
               
               
                 r 17  = −16.508  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 4.093 
                 7.041 
                 11.875 
               
               
                   
                   
               
               
                   
                 d 4   
                 0.63 
                 4.63 
                 7.56 
               
               
                   
                 d 9   
                 7.87 
                 3.87 
                 0.94 
               
               
                   
                 d 10   
                 4.43 
                 2.75 
                 0.84 
               
               
                   
                 d 15   
                 1.26 
                 2.05 
                 2.48  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                 11th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −4.74324 × 10 −4   
               
               
                   
                 A 6  = −2.42146 × 10 −5   
               
               
                   
                 A 8  = 2.49585 × 10 −6   
               
               
                   
                 A 10  = −1.17216 × 10 −7   
               
               
                   
                 16th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −6.18094 × 10 −4   
               
               
                   
                 A 6  = 7.96643 × 10 −5   
               
               
                   
                 A 8  = −1.16593 × 10 −5   
               
               
                   
                 A 10  = 6.32501 × 10 −7   
               
               
                   
                 |F 2 /F 3 | = 0.64 
               
               
                   
                 F 3 /F 4  = 1.07 
               
               
                   
                 |β 2T | = 0.56 
               
               
                   
                 |L 3 /L 2 | = 0.52 
               
               
                   
                 (F 3,4W )/IH = 2.81 
               
               
                   
                 F 1 /IH = 10.96 
               
               
                   
                 IH = 2.5  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 25 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.281˜5.633˜9.500 
               
               
                 F NO  = 2.03˜2.41˜2.98 
               
               
                 f B  = 2.98˜3.50˜4.60  
               
               
                   
               
             
          
           
               
                 r 1  = 13.782 
                 d 1  = 0.90 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 11.125 
                 d 2  = 2.64 
                 n d2  = 1.69680 
                 ν d2  = 55.53 
               
               
                 r 3  = 73.145 
                 d 3  = (Variable) 
               
               
                 r 4  = 16.578 
                 d 4  = 0.60 
                 n d3  = 1.84666 
                 ν d3  = 23.78 
               
               
                 r 5  = 3.821 
                 d 5  = 2.97 
               
               
                 r 6  = −16.432 
                 d 6  = 0.47 
                 n d4  = 1.58913 
                 ν d4  = 61.14 
               
               
                 r 7  = 4.721 
                 d 7  = 2.50 
                 n d5  = 1.84666 
                 ν d5  = 23.78 
               
               
                 r 8  = 36.357 
                 d 8  = (Variable) 
               
               
                 r 9  = ∞ (Stop) 
                 d 9  = (Variable) 
               
               
                 r 10  = 6.997 (Aspheric) 
                 d 10  = 2.32 
                 n d6  = 1.58913 
                 ν d6  = 61.30 
               
               
                 r 11  = −13.157 
                 d 11  = 0.10 
               
               
                 r 12  = 5.948 
                 d 12  = 2.50 
                 n d7  = 1.77250 
                 ν d7  = 49.60 
               
               
                 r 13  = −9.882 
                 d 13  = 0.45 
                 n d8  = 1.80518 
                 ν d8  = 25.42 
               
               
                 r 14  = 3.525 
                 d 14  = (Variable) 
               
               
                 r 15  = 6.328 (Aspheric) 
                 d 15  = 2.50 
                 n d9  = 1.58913 
                 ν d9  = 61.30 
               
               
                 r 16  = −18.262  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.281 
                 5.633 
                 9.500 
               
               
                   
                   
               
               
                   
                 d 3   
                 0.50 
                 3.55 
                 5.78 
               
               
                   
                 d 8   
                 6.03 
                 2.99 
                 0.75 
               
               
                   
                 d 9   
                 3.91 
                 2.44 
                 0.68 
               
               
                   
                 d 14   
                 0.64 
                 1.59 
                 2.27  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                  10th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −6.74025 × 10 −4   
               
               
                   
                 A 6  = −3.39527 × 10 −5   
               
               
                   
                 A 8  = 6.17490 × 10 −6   
               
               
                   
                 A 10  = −3.69154 × 10 −7   
               
               
                   
                 15th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −1.22978 × 10 −3   
               
               
                   
                 A 6  = 2.57259 × 10 −4   
               
               
                   
                 A 8  = −5.94053 × 10 −5   
               
               
                   
                 A 10  = 5.10256 × 10 −6   
               
               
                   
                 |F 2 /F 3 | = 0.72 
               
               
                   
                 F 3 /F 4  = 0.96 
               
               
                   
                 |β 2T | = 0.55 
               
               
                   
                 |L 3 /L 2 | = 0.61 
               
               
                   
                 (F 3,4W )/IH = 2.73 
               
               
                   
                 F 1 /IH = 11.41 
               
               
                   
                 IH = 2.0  
               
               
                   
                   
               
             
          
         
       
     
     EXAMPLE 26 
     
       
         
               
             
               
               
               
               
             
               
             
               
               
               
               
               
             
               
               
             
           
               
                   
               
             
             
               
                 f = 3.634˜6.338˜10.687 
               
               
                 F NO  = 2.03˜2.36˜2.86 
               
               
                 f B  = 4.06˜5.03˜6.69  
               
               
                   
               
             
          
           
               
                 r 1  = 25.537 
                 d 1  = 0.84 
                 n d1  = 1.84666 
                 ν d1  = 23.78 
               
               
                 r 2  = 17.128 
                 d 2  = 1.92 
                 n d2  = 1.77250 
                 ν d2  = 49.60 
               
               
                 r 3  = 41.101 
                 d 3  = 0.11 
               
               
                 r 4  = 17.177 
                 d 4  = 2.25 
                 n d3  = 1.60311 
                 ν d3  = 60.64 
               
               
                 r 5  = 64.686 
                 d 5  = (Variable) 
               
               
                 r 6  = 21.366 
                 d 6  = 0.56 
                 n d4  = 1.80610 
                 ν d4  = 40.92 
               
               
                 r 7  = 4.013 
                 d 7  = 2.78 
               
               
                 r 8  = −19.517 
                 d 8  = 0.53 
                 n d5  = 1.59551 
                 ν d5  = 39.24 
               
               
                 r 9  = 4.450 
                 d 9  = 2.10 
                 n d6  = 1.80518 
                 ν d6  = 25.42 
               
               
                 r 10  = 34.830 
                 d 10  = (Variable) 
               
               
                 r 11  = ∞ (Stop) 
                 d 11  = (Variable) 
               
               
                 r 12  = 11.333 
                 d 12  = 2.15 
                 n d7  = 1.58913 
                 ν d7  = 61.30 
               
               
                 (Aspheric) 
               
               
                 r 13  = −15.421 
                 d 13  = 0.11 
               
               
                 r 14  = 6.624 
                 d 14  = 2.81 
                 n d8  = 1.77250 
                 ν d8  = 49.60 
               
               
                 r 15  = −9.336 
                 d 15  = 0.51 
                 n d9  = 1.74077 
                 ν d9  = 27.79 
               
               
                 r 16  = 4.319 
                 d 16  = (Variable) 
               
               
                 r 17  = 8.127 (Aspheric) 
                 d 17  = 2.81 
                 n d10  = 1.58913 
                 ν d10  = 61.30 
               
               
                 r 18  = −13.550  
               
               
                   
               
             
          
           
               
                 Zooming Spaces 
               
             
          
           
               
                   
                 f 
                 3.634 
                 6.338 
                 10.687 
               
               
                   
                   
               
               
                   
                 d 5   
                 0.56 
                 4.10 
                 6.61 
               
               
                   
                 d 10   
                 6.89 
                 3.35 
                 0.84 
               
               
                   
                 d 11   
                 4.43 
                 2.65 
                 0.76 
               
               
                   
                 d 16   
                 1.66 
                 2.46 
                 2.70  
               
               
                   
                   
               
             
          
           
               
                   
                 Aspherical Coefficients 
               
               
                   
                   
               
               
                   
                 12th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −2.72290 × 10 −4   
               
               
                   
                 A 6  = −2.67214 × 10 −5   
               
               
                   
                 A 8  = 3.52082 × 10 −6   
               
               
                   
                 A 10  = −1.72643 × 10 −7   
               
               
                   
                 17th surface 
               
               
                   
                 K = 0.000 
               
               
                   
                 A 4  = −6.98015 × 10 −4   
               
               
                   
                 A 6  = 8.08033 × 10 −5   
               
               
                   
                 A 8  = −1.17442 × 10 −5   
               
               
                   
                 A 10  = 6.68163 × 10 −7   
               
               
                   
                 |F 2 /F 3 | = 0.59 
               
               
                   
                 F 3 /F 4  = 1.08 
               
               
                   
                 |β 2T | = 0.55 
               
               
                   
                 |L 3 /L 2 | = 0.61 
               
               
                   
                 (F 3,4W )/IH = 2.96 
               
               
                   
                 F 1 /IH = 11.19 
               
               
                   
                 IH = 2.25  
               
               
                   
                   
               
             
          
         
       
     
     Aberration curve diagrams for Example 1 are shown in FIGS. 28 a - 28   d ,  29   a - 29   d  and  30   a - 30   d  wherein FIGS. 28 a - 28   d  show aberrations at the wide-angle end thereof, FIGS. 29 a - 29   d  show aberrations at an intermediate focal length thereof, and FIGS. 30 a - 30   d  show aberrations at the telephoto end thereof. Aberration diagrams for Example 17 of the zoom lens system according to the invention when focused on an object at infinity are attached hereto as FIGS. 31 a - 31   e  (at the wide-angle end) and FIGS. 32 a - 32   e  (at the telephoto end) wherein FIGS. 31 a  and  32   a  show spherical aberration, FIGS. 31 b  and  32   b  show astigmatism, FIGS. 31 c  and  32   c  show distortion, FIGS. 31 d  and  32   d  show chromatic aberration of magnification, and FIGS. 31 e  and  32   e  show coma, with ω standing for a half field angle. 
     The zoom lens of the invention as explained above may be used with various phototaking systems using an electronic image pickup device such as a CCD or CMOS sensor, as specifically explained below. 
     An electronic camera with the zoom lens of the invention incorporated in the form of an objective optical system is shown in FIGS. 33 to  35 . FIG. 33 is a front perspective view illustrating the appearance of an electronic camera  200 , FIG. 34 is a rear perspective view of the same, and FIG. 35 is a sectional schematic illustrating one embodiment of the electronic camera  200 . As shown in FIGS. 33 to  35 , the electronic camera  200  comprises a phototaking optical system  202  having a phototaking optical path  201 , a finder optical system  204  having a finder optical path  203 , a shutter  205 , a flash  206  and a liquid crystal display monitor  207 . Upon the shutter  205  located on the camera  200  pushed, phototaking occurs through an objective  12  comprising the zoom lens of the invention (not shown) located in the form of a phototaking objective optical system. A subject image formed through the phototaking objective optical system is formed on an image pickup element chip  62  such as a CCD via an IR (infrared) cut filter  80 . 
     An object image received at the image pickup element chip  62  is displayed as an electronic image on the liquid crystal display monitor  207  located on the back side of the camera via a processor means  208  electrically connected to a terminal  66 . This processor  208  also controls a recorder means  209  in which the object image phototaken by the image pickup element chip  62  is recorded in the form of electronic information. The recorder  209  may be either a memory located in the processor  208  or a device electrically connected to the processor  208 , with which information is electronically written in a magnetic recording medium such as a floppy disk or smart medium. 
     The finder optical system  204  having the finder optical path  203  further comprises a finder objective optical subsystem  210 , a Porro prism  211  for erecting an object image formed through the finder objective optical subsystem  201 , and an eyepiece  212  for guiding the object image to an observer&#39;s eyeball E. The Porro prism  211  is divided into front and rear portions, between which there is a plane with the object image formed thereon, on which plane there is provided a field frame  213 . The Porro prism  211  comprises four reflecting surfaces for erecting the object image formed through the finder objective optical subsystem  210  into an erect image. 
     To achieve compactness and low cost, it is acceptable to remove the finder optical system  204  form the camera  200 . In this case, the observer may phototake images while viewing the liquid crystal display monitor  207 . 
     In FIGS. 36 to  38 , a personal computer is shown as one example of the information processor with the zoom lens of the invention incorporated in the form of an objective optical system. FIG. 36 is a front perspective view of an uncovered personal computer  300 , FIG. 37 is a sectional view of a phototaking system  303  in the personal computer  300 , and FIG. 38 is a side view of one state shown in FIG.  36 . As shown in FIGS. 36 to  38 , the personal computer  300  comprises a keyboard  301  for allowing an operator to enter information from outside, an information processing and recording means (not shown), a monitor  302  for presenting information to the observer and a phototaking system  303  for phototaking the image of the observer itself or surrounding images. For the monitor  302 , use may be made of a transmission type liquid crystal display device which is illuminated from the back side with a backlight (not shown), a reflection type liquid crystal display device for displaying images by reflecting light coming from the front, or a CRT display device. While the phototaking system  303  is shown as being built in the right-upper portion of the monitor  302 , it is understood that the system  303  may be located around the monitor  302  or somewhere around the keyboard  301 . 
     The phototaking system  303  comprises an objective  12  located on a phototaking optical path  304 , which is made up of the zoom lens of the invention (not shown), and an image pickup element chip  62  for receiving an image. These are built in the personal computer  300 . 
     An object image received at the image pickup element chip  62  is entered into the processing means in the personal computer  300  via a terminal  66 , so that the object image can be displayed as an electronic image on the monitor  302 . As an example, a phototaken image  305  of the operator is shown in FIG.  36 . This image  305  may be displayed on a remote personal computer via the processing means and by way of internet or a telephone. 
     In FIG. 39, an easy-to-carry portable telephone is shown as one example of the information processor with the zoom lens of the invention incorporated in the form of a phototaking system. FIG.  39 ( a ) is a front view of a portable telephone  400 , FIG.  39 ( b ) is a side view of the same, and FIG.  39 ( c ) is a sectional view of a phototaking system  405 . As shown in FIGS.  39 ( a ) to  39 ( c ), the portable telephone  400  comprises a microphone  401  for entering operator&#39;s voice in the form of information, a speaker  402  for outputting the voice of a person at the other end of the line, an input dial  403  with which an operator enters information, a monitor  404  for displaying the image of the operator per se or the person at the other end and information such as telephone numbers, etc., a phototaking system  405 , an antenna  406  for the transmission and reception of communication radio waves, and means for processing images, communication information, input signals, etc. (not shown). The monitor  404  shown in a liquid crystal display device. It is not always required to locate these parts as illustrated. The phototaking system  405  comprises an objective  12  located on a phototaking optical path  407 , which is made up of the zoom lens of the invention (not shown), and an image pickup element chip  62  for receiving an object image. These are all built in the portable telephone  400 . 
     The object image received at the image pickup element chip  62  is entered into processing means (not shown) via a terminal  66 , so that it can be displayed as an electronic image on the monitor  404  and/or a monitor for the person at the other end of the line. The processing means further includes a signal processing function capable of transmitting an image to the person at the other end of the line by converting the information regarding the object image received at the image pickup element chip  62  to transmittable signals. 
     As can be understood from the foregoing explanation, the present invention can provide a compact yet low-cost zoom lens system which is particularly suited for use with small portable information terminal equipment.