Abstract:
Positive first and second lenses each having a convex surface directed onto the object side, a negative third lens having a concave surface directed onto an image side, a negative fourth lens having a concave surface directed onto the object side, and positive fifth and sixth lenses each having a convex surface directed onto the image side are successively disposed from the object side, and predetermined conditional expressions are satisfied, thus yielding an image readout imaging lens suitable for reading out color originals. Successively from the object side, positive first and second lenses L1 and L2 each having a convex surface directed onto the object side, a negative third lens L3 having a concave surface directed onto an image side, a negative fourth lens L4 having a concave surface directed onto the object side, and positive fifth and sixth lenses L5 and L6 each having a convex surface directed onto the image side are disposed, and the following conditional expressions (1) to (6) are satisfied: 
     
       Nda+0.015 νda&gt;2.58                                      (1) 
     
     
       Ndb+0.015 νdb&gt;2.58                                      (2) 
     
     
       0.59f&lt;fa&lt;1.08f                                             (3) 
     
     
       0.53f&lt;fb&lt;1.60f                                             (4) 
     
     
       0.46&lt;fa/fb&lt;1.23                                            (5) 
     
     
       -0.56f&lt;f4&lt;-0.31f                                           (6)

Description:
RELATED APPLICATIONS 
     This application claims the priority of Japanese Patent Application No. 9-70402 filed on Mar. 7, 1997, which is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an image readout lens having a small chromatic aberration and an image readout apparatus; and, in particular, to an image readout apparatus such as facsimile or image scanner, and an image readout imaging lens used in its optical system. 
     2. Description of the Prior Art 
     As the image readout lens used in facsimile, image scanner, and the like, various types have conventionally been known. For example, those disclosed in Japanese Patent Publication No. 5-68686, and Japanese Unexamined Patent Publication Nos. 5-113535, 5-210048, 6-109971, and 6-342120, and the like have been known. 
     Each of these lenses, however, has an amount of chromatic aberration which is too large to be used for reading out a very fine color image, and thus is not always satisfactory in terms of performance. 
     SUMMARY OF THE INVENTION 
     In view of such circumstances, it is an object of the present invention to provide an image readout lens and image readout apparatus in which chromatic aberration is favorably corrected so as to allow a very fine color original to be read out. 
     The image readout lens having a small chromatic aberration in accordance with the present invention comprises, successively from an object side, positive first and second lenses each having a convex surface directed onto the object side, a negative third lens having a concave surface directed onto an image side, a negative fourth lens having a concave surface directed onto the object side, and positive fifth and sixth lenses each having a convex surface directed onto the image side, 
     wherein a material forming at least one of the first and second lenses satisfies the following conditional expression (1); a material forming at least one of the fifth and sixth lenses satisfies the following conditional expression (2); of the lenses satisfying the conditional expression (1), the lens having a shorter focal length satisfies the following conditional expression (3); and, of the lenses satisfying the conditional expression (2), the lens having a shorter focal length satisfies the following conditional expression (4): 
     
         Nda+0.015 νda&gt;2.58                                      (1) 
    
     
         Ndb+0.015 νdb&gt;2.58                                      (2) 
    
     
         0.59f&lt;fa&lt;1.08f                                             (3) 
    
     
         0.53f&lt;fb&lt;1.60f                                             (4) 
    
     wherein 
     f is a focal length of the whole system; 
     fa is a focal length of the first or second lens (the lens having a shorter focal length when both lenses satisfy conditional expression (1)) using a material satisfying conditional expression (1); 
     fb is a focal length of the fifth or sixth lens (the lens having a shorter focal length when both lenses satisfy conditional expression (2)) using a material satisfying conditional expression (2); 
     Nda is a refractive index of a lens material; 
     Ndb is a refractive index of a lens material; 
     νda is an Abbe number of a lens material; and 
     νdb is an Abbe number of a lens material. 
     Preferably, in this configuration, the following conditional expressions (5) and (6): 
     
         0.46&lt;fa/fb&lt;1.23                                            (5) 
    
     
         -0.56f&lt;f4&lt;-0.31f                                           (6) 
    
     wherein 
     f4 is a focal length of the fourth lens 
     are satisfied. 
     Further, each lens is preferably constituted by a material which contains neither lead nor arsenic. 
     The image readout apparatus in accordance with the present invention comprises the above-mentioned image readout lens. 
     As mentioned above, in accordance with the present invention, successively from the object side, positive first and second lenses each having a convex surface directed onto the object side, a negative third lens having a concave surface directed onto the image side, a negative fourth lens having a concave surface directed onto the object side, and positive fifth and sixth lenses each having a convex surface directed onto the image side are disposed; wherein a material forming at least one of the first and second lenses satisfies conditional expression (1); a material forming at least one of the fifth and sixth lenses satisfies conditional expression (2); of the lenses satisfying the conditional expression (1), the lens having a shorter focal length satisfies conditional expression (3); and, of the lenses satisfying the conditional expression (2), the lens having a shorter focal length satisfies conditional expression (4); whereby axial chromatic aberration and chromatic aberrations upon magnification can be corrected favorably. Accordingly, when this lens is incorporated in an image readout apparatus so as to be used for reading out images, very fine color images can be read out favorably. 
     In this case, the above-mentioned conditional expressions (1) to (4) are satisfied due to the following reasons. 
     Namely, below the lower limit of conditional expression (1), it mainly becomes impossible to favorably correct axial chromatic aberration, thus making it difficult to form the respective color images of blue, green, and red on the same plane. 
     Below the lower limit of conditional expression (2), axial chromatic aberration cannot be corrected favorably, whereby the respective images of blue, green, and red colors cannot be formed on the same plane. Also, chromatic aberration upon magnification cannot be corrected favorably, thereby making it difficult for the respective color images of blue, green, and red to have sizes accurately coinciding with each other. 
     Below the lower limit of conditional expression (3), spherical aberration and image curvature increase so much that it becomes difficult to obtain a favorable image. Above the upper limit thereof, axial chromatic aberration cannot be corrected favorably, thus making it difficult to form the respective color images of blue, green, and red on the same plane. 
     Below the lower limit of conditional expression (4), chromatic aberration upon magnification is corrected in excess. Above the upper limit thereof, chromatic aberration upon magnification is corrected insufficiently. In these cases, it becomes difficult for the respective color images of blue, green, and red to have sizes accurately coinciding with each other. 
     The above-mentioned conditional expressions (5) and (6) are preferably satisfied due to the following reasons. 
     Below the lower limit of conditional expression (5), chromatic aberration upon magnification is corrected in excess. Above the upper limit thereof, chromatic aberration upon magnification is corrected insufficiently. In these cases, it becomes difficult for the respective color images of blue, green, and red to have sizes accurately coinciding with each other. 
     Below the lower limit of conditional expression (6), spherical aberration is corrected insufficiently. Above the upper limit thereof, it is corrected in excess. In either cases, favorable imaging performances may not be obtained. 
     In the configuration mentioned above, when each of the lenses is constituted by a material which contains neither lead nor arsenic (so-called eco-glass species), the image readout lens can have a lighter weight, and even when the lens is discarded, its adverse effect on the environment can be minimized. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a perspective view showing an image readout apparatus equipped with an image readout lens in accordance with an embodiment of the present invention; 
     FIG. 2 is a lens configurational view showing the above-mentioned image readout lens; 
     FIGS. 3 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 1 of the present invention; 
     FIGS. 4 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 2 of the present invention; 
     FIGS. 5 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 3 of the present invention; 
     FIGS. 6 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 4 of the present invention; 
     FIGS. 7 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 5 of the present invention; 
     FIGS. 8 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 6 of the present invention; and 
     FIGS. 9 (A), (B) and (C) are aberration charts showing various kinds of aberration in the image readout lens in accordance with Example 7 of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following, embodiments of the present invention will be explained. 
     FIG. 1 is a perspective view showing an image readout apparatus equipped with an image readout lens in accordance with an embodiment of the present invention. 
     As depicted, in this image readout apparatus 10, a color original 2 placed on a surface of a glass plate 3 is irradiated with light in a band-like form by means of a linear or linearly-arranged light source (fluorescent light, halogen lamp, LED, and the like) 12 and a reflector 13 along directions of arrow A (shorter side direction), and its reflected luminous flux is converged by an image readout imaging lens 14 so as to form an image on image sensors (CCDs) 16 arranged in one to several rows, whereby the information of the color original 2 in the directions of arrow A (on the shorter side) is read out. 
     Further, the original 2 is relatively moved in the direction of arrow B with respect to the image readout imaging lens 14, so that the information of the original 2 is read out. 
     In order for this image readout apparatus 10 to read out a very fine color image, the imaging lens 14 is required to favorably correct chromatic aberration. In order to enable this feature, the imaging lens 14 has a lens configuration shown in FIG. 2. 
     Namely, the imaging lens comprises, successively from the object side, positive first and second lenses each having a convex surface directed onto the object side, a negative third lens having a concave surface directed onto the image side, a negative fourth lens having a concave surface directed onto the object side, and positive fifth and sixth lenses each having a convex surface directed onto the image side; wherein a material forming at least one of the first and second lenses satisfies the following conditional expression (1); a material forming at least one of the fifth and sixth lenses satisfies the following conditional expression (2); of the lenses satisfying the conditional expression (1), the lens having a shorter focal length satisfies the following conditional expression (3); and, of the lenses satisfying the conditional expression (2), the lens having a shorter focal length satisfies the following conditional expression (4); and wherein the following conditional expressions (5) and (6) are further satisfied: 
     
         Nda+0.015 νda&gt;2.58                                      (1) 
    
     
         Ndb+0.015 νdb&gt;2.58                                      (2) 
    
     
         0.59f&lt;fa&lt;1.08f                                             (3) 
    
     
         0.53f&lt;fb&lt;1.60f                                             (4) 
    
     
         0.46&lt;fa/fb&lt;1.23                                            (5) 
    
     
         -0.56f&lt;f4&lt;-0.31f                                           (6) 
    
     wherein 
     f is a focal length of the whole system; 
     fa is a focal length of the first or second lens (the lens having a shorter focal length when both lenses satisfy conditional expression (1)) using a material satisfying conditional expression (1); 
     fb is a focal length of the fifth or sixth lens (the lens having a shorter focal length when both lenses satisfy conditional expression (2)) using a material satisfying conditional expression (2); 
     Nda is a refractive index of a lens material; 
     Ndb is a refractive index of a lens material; 
     νda is an Abbe number of a lens material; 
     νdb is an Abbe number of a lens material; and 
     f4 is a focal length of the fourth lens. 
     In the following, Examples 1 to 7 of the image readout imaging lens in accordance with the present invention will be explained. 
     The image readout imaging lens in accordance with each example is standardized at a focal length of 100 mm. In order to be actually used in an image readout apparatus, each imaging lens is proportionally reduced or enlarged so as to match the size of an original to be read out, and it is used with a focal length determined for each original size. Each of these imaging lenses is optimal for reading out an original having a shorter side of A3 size or the like. In this case, their focal length will be proportionally reduced in practice. 
     EXAMPLE 1 
     Table 1 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, center thickness of each lens and air gap between adjacent lenses (hereinafter collectively referred to as axial surface spacing) d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 1, numbers successively increase from the object side. 
     Also, Table 2 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 2 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 66.7 mm, it can be optimized for reading out the shorter side of A3-sized originals. 
     FIG. 3 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 5.85 mm and a glass plate having a thickness of 1.05 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     EXAMPLE 2 
     Table 3 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 3, numbers successively increase from the object side. 
     Also, Table 4 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 4 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 76.5 mm, it can be optimized for reading out the shorter side of A3-sized originals. 
     FIG. 4 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 5.85 mm and a glass plate having a thickness of 1.05 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     EXAMPLE 3 
     Table 5 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 5, numbers successively increase from the object side. 
     Also, Table 6 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 6 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 97.8 mm, it can be optimized for reading out the shorter side of A3-sized originals. 
     FIG. 5 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 2.86 mm and a glass plate having a thickness of 0.82 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     In this example, each lens is constituted by a material which contains neither lead nor arsenic (so-called eco-glass species), whereby the image readout imaging lens can have a lighter weight, and even when the lens is discarded, its adverse effect on the environment can be minimized. 
     EXAMPLE 4 
     Table 7 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 7, numbers successively increase from the object side. 
     Also, Table 8 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 8 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 97.8 mm, it can be optimized for reading out the shorter side of A3-sized originals. 
     FIG. 6 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 2.86 mm and a glass plate having a thickness of 0.82 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     EXAMPLE 5 
     Table 9 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 9, numbers successively increase from the object side. 
     Also, Table 10 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 4 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 72.1 mm, it can be optimized for reading out the shorter side of A3-sized originals. 
     FIG. 7 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 5.41 mm and a glass plate having a thickness of 0.97 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     EXAMPLE 6 
     Table 11 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 11, numbers successively increase from the object side. 
     Also, Table 12 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 12 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 75.0 mm, it can be optimized for reading out the shorter side of A6-sized originals. 
     FIG. 8 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 3.73 mm and a glass plate having a thickness of 0.93 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     EXAMPLE 7 
     Table 13 (follows) shows radius of curvature r (mm) of each lens surface in the image readout lens, axial surface spacing d (mm), refractive index Nd and Abbe number νd of each lens at d-line, and material (product name) constituting each lens in accordance with this example. In Table 13, numbers successively increase from the object side. 
     Also, Table 14 (follows) shows specific values of Nda+0.015 νda, Ndb+0.015 νdb, fa, fb, fa/fb, and f4 in the above-mentioned conditional expressions (1) to (6). Further, the lower part of Table 14 shows F number (FNo), focal length f of the whole system, magnification (β), and half angle of view (ω). 
     When the image readout lens in accordance with this example is actually used in an image readout apparatus, it is made to match the size of the original to be read out. When its focal length is proportionally reduced to 80.0 mm, it can be optimized for reading out the shorter side of Japanese B0-sized originals. 
     FIG. 9 is an aberration chart showing various kinds of aberration in the image readout imaging lens in accordance with this example. This aberration chart illustrates a case where the focal length is 100 mm, and a glass plate having a thickness of 5.00 mm and a glass plate having a thickness of 1.00 mm are respectively included on the object side and image surface side in its optical path. 
     As can be seen from this chart, an image readout lens having a favorable imaging performance extending to the periphery of its visual field can be obtained in accordance with this example. 
     As explained in the foregoing, in accordance with the present invention, various kinds of aberration such as chromatic aberration can be made favorable. When this imaging lens is incorporated in an image readout apparatus so as to be used for reading out images, very fine color images can be read out. 
     
                       TABLE 1______________________________________                              ProductSurface  r       d       N.sub.d                        ν.sub.d                              name of material______________________________________1      65.421  6.45    1.77250                        49.6  LASF-n7                                     (Sumita)2      189.426 0.303      26.820  8.45    1.59240                        68.3  GFK-68 (Sumita)4      50.424  0.005      50.424  2.88    1.71735                        29.5  SF-1   (Sumita)6      23.667  32.177      -19.288 2.97    1.62005                        36.3  F-2    (Sumita)8      -53.096 0.009      -53.096 7.95    1.77250                        49.6  LASF-N7                                     (Sumita)10     -29.012 0.3211     765.562 8.06    1.59240                        68.3  GFK-68 (Sumita)12     -74.281______________________________________ 
    
     
                       TABLE 2______________________________________N.sub.da + 0.015ν.sub.da =              2.62N.sub.db + 0.015ν.sub.db =              2.62f.sub.a =          0.854ff.sub.b =          1.147ff.sub.a /f.sub.b = 0.744f.sub.4 =          -0.506fF/3.5   f = 100      β = -0.1571                          ω = 17°______________________________________ 
    
     
                       TABLE 3______________________________________                              ProductSurface  r       d       N.sub.d                        ν.sub.d                              name of material______________________________________1      67.486  5.75    1.77250                        49.6  LASF-n7                                     (Sumita)2      200.941 0.383      28.042  10.40   1.59240                        68.3  GFK-68 (Sumita)4      49.850  0.005      49.850  2.29    1.71735                        29.5  SF-1   (Sumita)6      23.518  31.777      -19.349 2.31    1.62005                        36.3  F-2    (Sumita)8      -56.824 0.009      -56.824 7.36    1.77250                        49.6  LASF-N7                                     (Sumita)10     -27.861 1.8311     ∞ 6.90    1.59240                        68.3  GFK-68 (Sumita)12     -67.341______________________________________ 
    
     
                       TABLE 4______________________________________N.sub.da + 0.015ν.sub.da =              2.62N.sub.db + 0.015ν.sub.db =              2.62f.sub.a =          0.919ff.sub.b =          1.137ff.sub.a /f.sub.b = 0.808f.sub.4 =          -0.485fF/3.5   f = 100      β = -0.189                          ω = 17.3°______________________________________ 
    
     
                       TABLE 5______________________________________                              ProductSurface r        d       N.sub.d                        ν.sub.d                              name of material______________________________________1     27.505   3.47    1.77250                        49.6  S-LAH66                                     (Ohara)2     49.059   0.153     19.445   4.06    1.49700                        81.6  S-FPL51                                     (Ohara)4     37.802   0.005     37.802   1.59    1.59551                        39.2  S-TIM8 (Ohara)6     14.418   24.617     -26.762  1.59    1.56732                        42.8  E-FL6  (Ohara)8     1035.382 0.009     1035.382 2.62    1.49700                        81.6  S-FPL51                                     (Ohara)10    -77.640  0.1511    -149.361 4.41    1.77250                        49.6  S-LAH66                                     (Ohara)12    -31.858______________________________________ 
    
     
                       TABLE 6______________________________________N.sub.da + 0.015ν.sub.da =              2.72N.sub.db + 0.015ν.sub.db =              2.72f.sub.a =          0.751ff.sub.b =          1.454ff.sub.a /f.sub.b = 0.516f.sub.4 =          -0.460fF/6.3   f = 100      β = -0.252                          ω = 17.3°______________________________________ 
    
     
                       TABLE 7______________________________________                              ProductSurface r        d       N.sub.d                        ν.sub.d                              name of material______________________________________1     28.451   3.63    1.77250                        49.6  LASF-n7                                     (Ohara)2     52.838   0.153     20.715   4.15    1.49700                        81.6  S-FPL51                                     (Ohara)4     42.794   0.005     42.794   1.83    1.59551                        39.2  F-8    (Ohara)6     15.044   23.667     -25.833  1.60    1.56732                        42.8  LF-6   (Ohara)8     948.840  0.009     948.840  3.07    1.49700                        81.6  S-FPL51                                     (Ohara)10    -64.177  0.1511    -132.829 4.39    1.77250                        49.6  LASF-n7                                     (Ohara)12    -31.898______________________________________ 
    
     
                       TABLE 8______________________________________N.sub.da + 0.015ν.sub.da =              2.72N.sub.db + 0.015ν.sub.db =              2.72f.sub.a =          0.760ff.sub.b =          1.211ff.sub.a /f.sub.b = 0.628f.sub.4 =          -0.443fF/6.3   f = 100      β = -0.252                          ω = 17.3°______________________________________ 
    
     
                       TABLE 9______________________________________                              ProductSurface  r       d       N.sub.d                        ν.sub.d                              name of material______________________________________1      69.319  5.96    1.78800                        47.4  LASF-n16                                     (Sumita)2      205.002 0.283      27.678  10.20   1.59240                        68.3  GFK-68 (Sumita)4      50.033  0.005      50.033  2.37    1.71736                        29.5  SF-1   (Sumita)6      23.363  31.437      -19.495 2.38    1.62004                        36.3  F-2    (Sumita)8      -56.477 0.009      -56.477 7.57    1.77250                        49.6  LASF-n7                                     (Sumita)10     -28.464 1.8211     ∞ 7.35    1.59240                        68.3  GFK-68 (Sumita)12     -65.279______________________________________ 
    
     
                       TABLE 10______________________________________N.sub.da + 0.015ν.sub.da =              2.62N.sub.db + 0.015ν.sub.db =              2.62f.sub.a =          0.894ff.sub.b =          1.102ff.sub.a /f.sub.b = 0.811f.sub.4 =          -0.492fF/4.0   f = 1000     β = -0.189                          ω = 18.3°______________________________________ 
    
     
                       TABLE 11______________________________________                              ProductSurface r        d       N.sub.d                        ν.sub.d                              name of material______________________________________1     31.583   9.67    1.49700                        81.6  S-FPL51                                     (Ohara)2     650.085  0.393     29.227   5.47    1.62041                        60.3  SK-16  (Sumita)4     73.789   1.075     194.591  2.40    1.61340                        43.8  KZFS-4 (Sumita)6     20.106   22.537     -19.387  2.33    1.61340                        43.8  KZFS-4 (Sumita)8     -201.906 0.009     -201.906 8.21    1.59240                        68.3  GFK-68 (Sumita)10    -30.354  0.3911    -331.071 6.85    1.63854                        55.5  SK-18  (Sumita)12    -44.946______________________________________ 
    
     
                       TABLE 12______________________________________N.sub.da + 0.015ν.sub.da =              2.72N.sub.db + 0.015ν.sub.db =              2.62f.sub.a =          0.664ff.sub.b =          0.593ff.sub.a /f.sub.b = 1.121f.sub.4 =          -0.351fF/3.5   f = 100      β = -0.3775                          ω = 11.2°______________________________________ 
    
     
                       TABLE 13______________________________________                              ProductSurface r        d       N.sub.d                        ν.sub.d                              name of material______________________________________1     32.042   4.05    1.77250                        49.6  LASF-N7                                     (Sumita)2     59.749   0.203     21.520   4.58    1.49700                        81.6  S-FPL51                                     (Ohara)4     35.847   0.005     35.847   1.87    1.62005                        36.3  F-2    (Sumita)6     16.115   20.747     -27.919  1.75    1.56732                        42.8  LF-6   (Sumita)8     413.357  0.009     413.357  3.15    1.49700                        81.6  S-FPL51                                     (Ohara)10    -79.592  0.1911    -212.312 4.84    1.77250                        49.6  LASF-N (Sumita)12    -34.368______________________________________ 
    
     
                       TABLE 14______________________________________N.sub.da + 0.015ν.sub.da =              2.72N.sub.db + 0.015ν.sub.db =              2.72f.sub.a =          0.979ff.sub.b =          1.346ff.sub.a /f.sub.b = 0.728f.sub.4 =          -0.460fF/8.0   f = 100      β = -0.075                          ω = 23.3°______________________________________