Abstract:
Provided is a wide angle optical imaging system composed of four lenses, the wide angle optical imaging system allowing various types of aberrations including chromatic aberration of magnification to be sufficiently reduced. The wide angle optical imaging system includes the following arranged from the object side to the image plane side: a first lens that is a negative meniscus lens having a convex surface on the object side; a second lens that is negative; a third lens that is positive; an aperture stop; and a fourth lens that is positive, wherein the following expressions are satisfied, where v2, v3, and v4 represent Abbe numbers of materials that form the second to fourth lenses with respect to a d-line, respectively, f2 and f3 represent focal distances of the second and third lenses, respectively, and f represents a focal distance of the whole optical system: v2&gt;35 (1) v3&lt;45 (2) v4&gt;35 (3) v2−v3≧10 (4) v4−v3≧10 (5) −2.3≦f2/f≦−1.5 (6) 3.0≦f3/f≦4.0 (7)

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a wide-range optical imaging system including four lenses. 
       BACKGROUND ART 
       [0002]    Wide-range optical imaging systems are used in a wide application area such as surveillance cameras and vehicle-mounted cameras. Conventionally, most wide-range optical imaging systems having an F-number of 2.8 or less and a pixel account around three hundred thousand include five or six lenses. However, wide-range optical imaging systems including five or six lenses are not capable of responding to needs for further reducing the total weight and costs. A wide-range optical imaging system including four lenses has also been developed. Refer to JP2006259704A, for example. However, in the wide-range optical imaging system described in JP2006259704A, various types of aberrations including chromatic aberration of magnification cannot be reduced to a sufficient degree. 
       PATENT DOCUMENT 
       [0003]    Patent document 1: JP2006259704A 
         [0004]    Accordingly, there is a need for a wide-range optical imaging system including four lenses, which allows various types of aberrations including chromatic aberration of magnification to be sufficiently reduced. 
       SUMMARY OF INVENTION 
       [0005]    A wide-range optical imaging system according to the present invention includes a first lens, a second lens, a third lens, an aperture stop, and a fourth lens, arranged from the object side to the image plane side, the first lens being a negative meniscus lens having a convex surface on the object side, the second lens being negative, the third lens being positive and the fourth lens being positive. When Abbe numbers for a d-line of the second to the fourth lenses are represented respectively by v 2 , v 3  and v 4 , the expressions 
         [0000]        v 2&gt;35  (1)
 
         [0000]        v 3&lt;45  (2)
 
         [0000]        v 4&gt;35  (3)
 
         [0000]        v 2− v 3≧10  (4)
 
         [0000]        v 4− v 3≧10  (5)
 
         [0000]    are satisfied, and when a focal length of the second lens is represented as f2, a focal length of the third lens is represented as f3, and a focal length of the whole optical system is represented as f, the expressions 
         [0000]      −2.3≦ f 2/ f≦− 1.5  (6)
 
         [0000]      3.0≦ f 3/ f≦ 4.0  (7)
 
         [0000]    are satisfied. 
         [0006]    When an arrangement of the four lenses and the aperture stop, an Abbe number and a focal length of each of the lenses, and a focal length of the whole optical system are determined as described above, an optical system that allows various types of aberrations including chromatic aberration of magnification to be sufficiently reduced and that can be easily manufactured, can be obtained. 
         [0007]    In a wide-range optical imaging system according to a first embodiment of the present invention, the expressions 
         [0000]        v 2≧50  (8)
 
         [0000]        v 3≦30  (9)
 
         [0000]        v 4≧50  (10)
 
         [0000]        v 2− v 3≧20  (11)
 
         [0000]        v 4− v 3≧20  (12)
 
         [0000]    are further satisfied. 
         [0008]    According to the present embodiment, chromatic aberration of magnification and longitudinal chromatic aberration can be further reduced. 
         [0009]    A wide-range optical imaging system according to a second embodiment of the present invention is the above-described wide-range optical imaging system according to the present invention in which when a focal length of the fourth lens is represented as f4, the expression 
         [0000]      1.72≦ f 4/ f≦ 2.45  (13)
 
         [0000]    is satisfied. 
         [0010]    In the wide-range optical imaging system according to the present embodiment, Expressions (6), (7) and (13) are simultaneously satisfied, and thereby chromatic aberration of magnification and longitudinal chromatic aberration are well balanced. When the value is lower than the lower limit of Expression (13), the manufacture and assembly of the fourth lens become difficult. When the value is greater than the upper limit of Expression (13), correction of various types of aberrations becomes difficult. 
         [0011]    In a wide-range optical imaging system according to a third embodiment of the present invention, the image plane side surface of the second lens is concave, the object side surface of the third lens is convex, and the both surfaces of the fourth lens are convex. 
         [0012]    According to the present embodiment, various types of aberrations can be efficiently corrected. 
         [0013]    A wide-range optical imaging system according to a fourth embodiment of the present invention is the wide-range optical imaging system according to the third embodiment in which the edge of the object side surface of the second lens is configured to be warped toward the object side. 
         [0014]    In the present embodiment, the configuration functions to bring the direction of a ray bundle with a greater angle of view close to the direction of the optical axis, and therefore the configuration has an advantage in its suitability for widening the angle of view. 
         [0015]    Wide-range optical imaging systems according to the fifth and sixth embodiments of the present invention are the wide-range optical imaging systems of the third and fourth embodiments, respectively, in which the image plane side surface of the second lens and the object side surface of the third lens are configured such that among rays in a ray bundle that forms an image at the maximum image height, the further from the optical axis a position of a ray, the greater the traveling distance of the ray between the two surfaces around the edges of the two surfaces becomes. 
         [0016]    The wide-range optical imaging systems according to the fifth and sixth embodiments have an advantage in its suitability for correcting comatic aberration of ray bundles that form an image around the maximum image height. 
         [0017]    A wide-range optical imaging system according to a seventh embodiment of the present invention is the wide-range optical imaging system according to the sixth embodiment in which when a coordinate representing a position in the direction of the optical axis of a point on a lens surface with reference to the intersection point of the lens surface and the optical axis is represented as z, a sign of z is set to be positive on the image plane side, a distance between the point on the lens surface and the optical axis is represented as r, and the lens surface is represented as 
         [0000]        z=f ( r ), 
         [0000]    where f(x) represents a function of x, a sign of the second derivative of the above-described function around the optical axis of the image plane side surface of the second lens differs from a sign of the second derivative of the above-described function at the periphery of a circle having a diameter of 0.9 of the effective diameter of the image plane side surface of the second lens. 
         [0018]    The wide-range optical imaging system according to the present embodiment has an advantage in its suitability for correcting comatic aberration of ray bundles that form an image around the maximum image height. 
         [0019]    In a wide-range optical imaging system according to an eighth embodiment of the present invention, the expressions 
         [0000]      −2.3≦ f 2/ f≦− 1.9  (14)
 
         [0000]      3.0≦ f 3/ f≦ 3.5  (15)
 
         [0000]    are further satisfied. 
         [0020]    In a wide-range optical imaging system according to a ninth embodiment of the present invention, the maximum angle of view (in full angle) is 170 degrees or more. 
         [0021]    In a wide-range optical imaging system according to a tenth embodiment of the present invention, the maximum angle of view (in full angle) is 180 degrees or more. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0022]      FIG. 1  shows an arrangement of a wide-range optical imaging system according to Example 1; 
           [0023]      FIGS. 2A to 2D  show aberrations of the wide-range optical imaging system according to Example 1; 
           [0024]      FIG. 3  shows an arrangement of a wide-range optical imaging system according to Example 2; 
           [0025]      FIGS. 4A to 4D  show aberrations of the wide-range optical imaging system according to Example 2; 
           [0026]      FIG. 5  shows an arrangement of a wide-range optical imaging system according to Example 3; 
           [0027]      FIGS. 6A to 6D  show aberrations of the wide-range optical imaging system according to Example 3; 
           [0028]      FIG. 7  shows an arrangement of a wide-range optical imaging system according to Example 4; 
           [0029]      FIGS. 8A to 8D  show aberrations of the wide-range optical imaging system according to Example 4; 
           [0030]      FIG. 9  shows an arrangement of a wide-range optical imaging system according to Example 5; 
           [0031]      FIGS. 10A to 10D  show aberrations of the wide-range optical imaging system according to Example 5; 
           [0032]      FIG. 11  shows an arrangement of a wide-range optical imaging system according to Example 6; 
           [0033]      FIGS. 12A to 12D  show aberrations of the wide-range optical imaging system according to Example 6; 
           [0034]      FIG. 13  shows an arrangement of a wide-range optical imaging system according to Example 7; 
           [0035]      FIGS. 14A to 14D  show aberrations of the wide-range optical imaging system according to Example 7; 
           [0036]      FIG. 15  shows an arrangement of a wide-range optical imaging system according to Example 8; 
           [0037]      FIGS. 16A to 16D  show aberrations of the wide-range optical imaging system according to Example 8; 
           [0038]      FIG. 17  shows an arrangement of a wide-range optical imaging system according to Example 9; 
           [0039]      FIGS. 18A to 18D  show aberrations of the wide-range optical imaging system according to Example 9; 
           [0040]      FIG. 19  shows an arrangement of a wide-range optical imaging system according to Example 10; 
           [0041]      FIGS. 20A to 20D  show aberrations of the wide-range optical imaging system according to Example 10; 
           [0042]      FIG. 21  shows an arrangement of a wide-range optical imaging system according to Example 11; 
           [0043]      FIGS. 22A to 22D  show aberrations of the wide-range optical imaging system according to Example 11; and 
           [0044]      FIG. 23  illustrates the ray bundle which travels between the image plane side surface of the second lens and the object side surface of the third lens and forms an image at the maximum image height. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0045]      FIG. 1  shows an arrangement of a wide-range optical imaging system according to an embodiment of the present invention. The wide-range optical imaging system according to the present embodiment includes, from the object side to the image plane side, a first lens  101 , a second lens  102 , a third lens  103 , an aperture stop  105 , and a fourth lens  104 . Light which has passed through the first lens  101 , the second lens  102 , the third lens  103 , the aperture stop  105 , and the fourth lens  104  passes through a glass plate  106  and reaches an image plane  107 . 
         [0046]    Features of the wide-range optical imaging system according to the present embodiment will be described below. In the following description, “i” represents an integer from 1 to 5, “fi” represents a focal length of the i-th lens, and “vi” represents an Abbe number of the material of the i-th lens at d line (wavelength of 587.6 nm). 
       Types of the Four Lenses 
       [0047]    The wide-range optical imaging system according to the present embodiment includes, from the object side to the image plane side, the first lens  101  which is a negative meniscus lens having a convex surface on the object side, the second lens  102  which is negative, the third lens  103  which is positive, the aperture stop  105 , and the fourth lens  104  which is positive. The lens which is positive means a lens which has a positive power on the optical axis while the lens which is negative means a lens which has a negative power on the optical axis. Further, the convex surface means a lens surface which is convex to the air side around the vertex which is at the intersection point of the optical axis and the lens surface. 
         [0048]    For wide-range optical imaging systems including four lenses, such an arrangement as described above in which a negative lens, a negative lens, a positive lens and a positive lens are arranged and an aperture stop is located between the third and fourth lenses is suited for reducing geometric aberrations except for distortion, chromatic aberration of magnification, and longitudinal chromatic aberration while balancing them. 
         [0049]    Chromatic aberration of magnification is caused by dispersion of refractive index (an Abbes number) of a material of a lens. In the following combinations of two lenses, chromatic aberrations of magnifications described above are cancelled with each other. 
         [0050]    1) A positive lens on the object side with reference to the aperture stop and a negative lens on the object side with reference to the aperture stop 
         [0051]    2) A positive lens on the object side with reference to the aperture stop and a positive lens on the image plane side with reference to the aperture stop 
         [0052]    3) A negative lens on the image plane side with reference to the aperture stop and a positive lens on the image plane side with reference to the aperture stop 
         [0053]    4) A negative lens on the object side with reference to the aperture stop and a negative lens on the image plane side with reference to the aperture stop Further, since the whole optical imaging system has a positive power without fail, the composite focal length of the lenses of the former group (the first to the third lenses) is negative and its absolute value is greater than that of a focal length of the fourth lens or the composite focal length is positive. Under the above-described situation, an Abbe number of the material of the second lens which is included in the former group of lenses and has a relatively short focal length should preferably be greater than an Abbe number of the material of the third lens which is included in the former group of lenses. Further, an Abbe number of the material of the fourth lens should preferably be greater than an Abbe number of the material of the third lens. Thus, when Abbe numbers for d-line of the second to the fourth lenses are represented respectively by v 2 , v 3  and v 4 , it is preferable that the following expressions are satisfied. 
         [0000]        v 2&gt;35  (1)
 
         [0000]        v 3&lt;45  (2)
 
         [0000]        v 4&gt;35(3) 
         [0000]        v 2− v 3≧10  (4)
 
         [0000]        v 4− v 3≧10  (5)
 
         [0000]    Further, it is more preferable that the following expressions are satisfied. 
         [0000]        v 2≧50  (8)
 
         [0000]        v 3≦30  (9)
 
         [0000]        v 4≧50  (10)
 
         [0000]        v 2− v 3≧20  (11)
 
         [0000]        v 4− v 3≧20  (12)
 
         [0054]    All of Examples 1 to 11 satisfy the conditions concerning Abbe numbers expressed by Expressions (1) to (5) and those expressed by Expressions (8) to (12). 
         [0055]    More specifically, the four lenses of Examples 1 to 11 are made of any of the following materials. However, the materials of the four lenses are not restricted to the following materials. 
         [0056]    S-LAH65V: n=1.80400, v=46.57 (Ohara inc.) 
         [0057]    S-NBH55: n=1.79999, v=29.84 (Ohara inc.) 
         [0058]    ZEONEX 480R: n=1.52512, v=56.28 (Zeon) 
         [0059]    PANLITE SP1516: n=1.61411, v=25.32 (Teijin) 
         [0000]    “n” represents refractive index while “v” represents Abbe number. 
         [0060]    Further, it is preferable that the image plane side surface of the second lens is concave, the object side surface of the third lens is convex, and the both surfaces of the fourth lens are convex. All of Examples 1 to 11 satisfy the above-described conditions. 
         [0061]    The edge of the object side surface of the second lens should preferably be warped toward the object side. All of Examples 1 to 11 satisfy the above-described condition. 
         [0062]    Further, the image plane side surface of the second lens and the object side surface of the third lens should preferably be configured such that among rays in a ray bundle which forms an image at the maximum image height, the further from the optical axis a position of a ray, the greater the traveling distance of the ray between the two surfaces around the edges of the two surfaces becomes. 
         [0063]      FIG. 23  illustrates the ray bundle which travels between the image plane side surface of the second lens and the object side surface of the third lens and forms an image at the maximum image height. 
         [0064]    When a coordinate of a position in the direction of the optical axis of a point on a lens surface with reference to the intersection point of the lens surface and the optical axis is represented by z, a sign of z is set to be positive on the image plane side, a distance between the point on the lens surface and the optical axis is represented as r, and the lens surface is represented as 
         [0000]        z=f ( r ), 
         [0000]    where f(x) represents a function of x, a sign of the second derivative of the above-described function around the optical axis of the image plane side surface of the second lens should preferably differ from a sign of the second derivative of the above-described function at the periphery of a circle having a diameter of 0.9 of the effective diameter of the image plane side surface of the second lens. Examples 1 to 6 and Example 11 satisfy the above-described condition. 
       Ratio of a Focal Length of the Second Lens to a Focal Length of the Whole Optical System and Ratio of a Focal Length of the Third Lens to the Focal Length of the Whole Optical System 
       [0065]    Since aberrations of each lens around the maximum image height are significantly affected by aspheric terms of each lens, aberrations of the wide-range optical imaging system cannot be controlled by the focal length alone which is determined by the curvature at the center of the lens. However, when aberrations become greater at least in an area of image height in which an influence of the curvature at the center of a lens is predominant, an image quality in the area becomes worse, and in the outer area, aberrations become too great to be corrected by the aspheric surface. Accordingly, control of the curvature at the center of the lens (control of the focal length) is important. 
         [0066]    Further, when types of the four lenses are selected as described above, the second lens and the third lens tend to become closer and the power of the second lens and the power of the third lens tend to become greater, and difficulties arise in the manufacture. If a focal length of the second lens and a focal length of the third lens are determined such that the following expressions are satisfied when the focal length of the second lens is represented as f2, the focal length of the third lens is represented as f3, and the focal length of the whole optical system is represented as f, aberrations can be corrected to a sufficient extent and at the same time the manufacture will become easier. 
         [0000]      −2.3≦ f 2/ f≦− 1.5  (6)
 
         [0000]      3.0≦ f 3/ f≦ 4.0  (7)
 
         [0067]    When the value is lower than the lower limit of Expression (6), correction of chromatic aberration of magnification becomes difficult. When the value is greater than the upper limit of Expression (6), the curvature of the lens becomes greater and therefore the manufacture becomes more difficult. 
         [0068]    When the value is lower than the lower limit of Expression (7), the curvature of the lens becomes greater and therefore the manufacture becomes more difficult. When the value is greater than the upper limit of Expression (7), correction of chromatic aberration of magnification becomes difficult. 
         [0069]    Further, it is more preferable that the following expressions are satisfied. 
         [0000]        v 2≧50  (8)
 
         [0000]        v 3≦30  (9)
 
         [0000]        v 4≧50  (10)
 
         [0000]        v 2− v 3≧20  (11)
 
         [0000]        v 4− v 3≧20  (12)
 
         [0000]      −2.3≦ f 2/ f≦− 1.9  (14)
 
         [0000]      3.0≦ f 3/ f≦ 3.5  (15)
 
       Ratio of the Focal Length of the Fourth Lens to the Focal Length of the Whole Optical System 
       [0070]    The following expression should preferably be satisfied when the focal length of the fourth lens is represented as f4 and the focal length of the whole optical system is represented as f, 
         [0000]      1.72≦ f 4/ f≦ 2.45  (13)
 
         [0071]    If Expressions (6), (7) and (13) are simultaneously satisfied, a balance between chromatic aberration of magnification and longitudinal chromatic aberration is achieved to a satisfactory extent. When the value is lower than the lower limit of Expression (13), the manufacture and assembly of the fourth lens becomes more difficult. When the value is greater than the upper limit of Expression (13), correction of various types of aberrations becomes difficult. 
       Focal Length of Each Lens and Focal Length of the Whole Optical System Concerning Wide-Range Optical Imaging Systems According to Examples 
       [0072]    Table 1 shows the focal length of each lens and the focal length of the whole optical system of each of wide-range optical imaging systems according to Examples 1 to 11. In each Example, an absolute value of the focal length of the second lens which is negative is smaller than an absolute value of the focal length of the third lens which is positive. Further, in each Example, an absolute value of the focal length of the fourth lens which is positive is smaller than an absolute value of the focal length of the third lens which is positive. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 f1 
                 f2 
                 f3 
                 f4 
                 f 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Example 1 
                 −6.623 
                 −2.260 
                 2.962 
                 2.305 
                 0.985 
               
               
                   
                 Example 2 
                 −12.277 
                 −2.197 
                 3.349 
                 2.038 
                 0.956 
               
               
                   
                 Example 3 
                 −16.719 
                 −2.400 
                 4.174 
                 2.099 
                 1.044 
               
               
                   
                 Example 4 
                 −12.854 
                 −1.980 
                 3.128 
                 2.073 
                 1.042 
               
               
                   
                 Example 5 
                 −24.197 
                 −2.143 
                 3.938 
                 2.191 
                 1.125 
               
               
                   
                 Example 6 
                 −31.497 
                 −2.356 
                 4.908 
                 2.270 
                 1.229 
               
               
                   
                 Example 7 
                 −37.231 
                 −1.892 
                 3.702 
                 2.315 
                 1.234 
               
               
                   
                 Example 8 
                 −45.900 
                 −2.174 
                 4.938 
                 2.440 
                 1.418 
               
               
                   
                 Example 9 
                 −47.753 
                 −2.179 
                 5.567 
                 2.440 
                 1.407 
               
               
                   
                 Example 10 
                 −13.477 
                 −1.928 
                 3.501 
                 2.021 
                 1.010 
               
               
                   
                 Example 11 
                 −6.508 
                 −2.184 
                 2.930 
                 2.363 
                 0.970 
               
               
                   
                   
               
             
          
         
       
     
         [0073]    Table 2 shows a ratio of the focal length of the second lens to the focal length of the whole optical system, a ratio of the focal length of the third lens to the focal length of the whole optical system, and a ratio of the focal length of the fourth lens to the focal length of the whole optical system. In all the examples, Expression (6), Expression (7) and Expression (13) are satisfied. Further, in Examples 1, 4, 5, 10 and 11, Expression (14) and Expression (15) are satisfied. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 f2/f 
                 f3/f 
                 f4/f 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Example 1 
                 −2.294 
                 3.006 
                 2.339 
               
               
                   
                 Example 2 
                 −2.298 
                 3.502 
                 2.131 
               
               
                   
                 Example 3 
                 −2.299 
                 3.999 
                 2.011 
               
               
                   
                 Example 4 
                 −1.900 
                 3.001 
                 1.989 
               
               
                   
                 Example 5 
                 −1.904 
                 3.499 
                 1.947 
               
               
                   
                 Example 6 
                 −1.917 
                 3.994 
                 1.847 
               
               
                   
                 Example 7 
                 −1.533 
                 3.001 
                 1.876 
               
               
                   
                 Example 8 
                 −1.533 
                 3.483 
                 1.721 
               
               
                   
                 Example 9 
                 −1.549 
                 3.957 
                 1.734 
               
               
                   
                 Example 10 
                 −1.909 
                 3.466 
                 2.001 
               
               
                   
                 Example 11 
                 −2.253 
                 3.022 
                 2.437 
               
               
                   
                   
               
             
          
         
       
     
       Equation Representing Lens Surfaces of Examples 
       [0074]    Surfaces of each lens in Examples can be expressed by the following equation. 
         [0000]    
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         
                           r 
                           2 
                         
                         / 
                         R 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                                
                               
                                 
                                   ( 
                                   
                                     r 
                                     / 
                                     R 
                                   
                                   ) 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           
                             i 
                             = 
                             4 
                           
                           , 
                           
                             i 
                              
                             
                                 
                             
                              
                             even 
                           
                         
                         12 
                       
                        
                       
                         
                           A 
                           i 
                         
                          
                         
                           r 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   A 
                   ) 
                 
               
             
           
         
       
     
         [0000]    z represents a coordinate of a position in the direction of the optical axis of a point on a lens surface with reference to the intersection point of the lens surface and the optical axis. A sign of z is set to be positive on the image plane side. r represents a distance between the point on the lens surface and the optical axis. R represents the radius of curvature at the vertex of a lens surface. k represents a conic constant. Ai represents a coefficient of a polynomial. 
       Example 1 
       [0075]      FIG. 1  shows an arrangement of a wide-range optical imaging system according to Example 1. The wide-range optical imaging system according to Example 1 includes, from the object side to the image plane side, a first lens  101 , a second lens  102 , a third lens  103 , an aperture stop  105 , and a fourth lens  104 . Light which has passed through the first lens  101 , the second lens  102 , the third lens  103 , the aperture stop  105 , and the fourth lens  104  passes through a glass plate  106  and reaches an image plane  107 . 
         [0076]      FIGS. 2A to 2D  show aberrations of the wide-range optical imaging system according to Example 1. In the following drawings including  FIGS. 2A to 2D , aberrations for F-line (wavelength of 486.1 nm), d-line (wavelength of 587.6 nm) and C-line (wavelength of 656.3 nm) are shown.  FIG. 2A  shows astigmatism. In  FIG. 2A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 2A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 2B  shows distortion. In  FIG. 2B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 2C  shows spherical aberration. In  FIG. 2C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.1759 millimeters.  FIG. 2D  shows chromatic aberration of magnification. In  FIG. 2D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0077]    Table 3 shows lens data of the wide-range optical imaging system according to Example 1. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  101 , the second lens  102  and the third lens  103 , respectively. Surface number 7 represents the aperture stop  105 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  104 , respectively. Surface number 10 represents the object side surface of the glass plate  106 , and surface number 11 represents the image plane side surface of the glass plate  106 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  101 , and the value of d (2.98304) in the row of surface number 2 represents distance between the first lens  101  and the second lens  102 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 3 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 14.30900 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 3.76000 
                 2.98304 
               
               
                 3 
                 −13.91776 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.32965 
                 0.30848 
               
               
                 5 
                 2.08119 
                 2.69443 
                 1.61411 
                 25.32 
               
               
                 6 
                 −7.31663 
                 0.85448 
               
               
                 7 
                 ∞ 
                 0.87937 
               
               
                 8 
                 4.10996 
                 2.10864 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.41234 
                 1.41210 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0078]    Table 4 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 1. Since the both surfaces of the first lens  101  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  -5.10116E+01 
                 −2.33742E−03  
                 2.40285E−04 
                 −9.32063E−06 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −7.29698E−01 
                 5.40020E−03 
                 −1.83818E−03  
                 −1.72344E−03 
                 5.56873E−05 
                 6.01837E−06 
               
               
                 5 
                 −3.78734E−01 
                 3.99271E−02 
                 −4.55267E−03  
                 −5.33569E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                 −2.67688E+02 
                 9.31244E−03 
                 9.05869E−04 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −3.74056E+00 
                 6.59283E−03 
                 2.01226E−04 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −1.42444E+00 
                 2.20175E−02 
                 2.48032E−03 
                 −3.09279E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 2 
       [0079]      FIG. 3  shows an arrangement of a wide-range optical imaging system according to Example 2. The wide-range optical imaging system according to Example 2 includes, from the object side to the image plane side, a first lens  201 , a second lens  202 , a third lens  203 , an aperture stop  205 , and a fourth lens  204 . Light which has passed through the first lens  201 , the second lens  202 , the third lens  203 , the aperture stop  205 , and the fourth lens  204  passes through a glass plate  206  and reaches an image plane  207 . 
         [0080]      FIGS. 4A to 4D  show aberrations of the wide-range optical imaging system according to Example 2.  FIG. 4A  shows astigmatism. In  FIG. 4A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 4A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 4B  shows distortion. In  FIG. 4B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 4C  shows spherical aberration. In  FIG. 4C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.1708 millimeters.  FIG. 4D  shows chromatic aberration of magnification. In  FIG. 4D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0081]    Table 5 shows lens data of the wide-range optical imaging system according to Example 2. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  201 , the second lens  202  and the third lens  203 , respectively. Surface number 7 represents the aperture stop  205 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  204 , respectively. Surface number 10 represents the object side surface of the glass plate  206 , and surface number 11 represents the image plane side surface of the glass plate  206 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  201 , and the value of d (3.17972) in the row of surface number 2 represents distance between the first lens  201  and the second lens  202 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 5 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 16.75588 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 6.04641 
                 3.17972 
               
               
                 3 
                 20.38928 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.07351 
                 0.93491 
               
               
                 5 
                 1.98129 
                 4.00003 
                 1.61411 
                 25.32 
               
               
                 6 
                 12.55009 
                 0.53850 
               
               
                 7 
                 ∞ 
                 0.36557 
               
               
                 8 
                 5.06355 
                 2.18712 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.15501 
                 1.38990 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0082]    Table 6 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 2. Since the both surfaces of the first lens  201  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.37145E−03  
                  6.68848E−05 
                 −7.05904E−07 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −8.99384E−01 
                 4.32445E−03 
                 −5.20968E−04 
                 −1.08167E−03 
                 1.07817E−04 
                 −3.08204E−06  
               
               
                 5 
                 −4.63562E−01 
                 9.89755E−03 
                  8.49346E−05 
                 −2.14724E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 4.24028E−02 
                  1.20781E−02 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −1.55413E+02 
                 3.26018E−02 
                 −2.21010E−02 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −6.10821E−01 
                 4.88710E−02 
                 −1.29661E−03 
                  2.81440E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 3 
       [0083]      FIG. 5  shows an arrangement of a wide-range optical imaging system according to Example 3. The wide-range optical imaging system according to Example 3 includes, from the object side to the image plane side, a first lens  301 , a second lens  302 , a third lens  303 , an aperture stop  305 , and a fourth lens  304 . Light which has passed through the first lens  301 , the second lens  302 , the third lens  303 , the aperture stop  305 , and the fourth lens  304  passes through a glass plate  306  and reaches an image plane  307 . 
         [0084]      FIGS. 6A to 6D  show aberrations of the wide-range optical imaging system according to Example 3.  FIG. 6A  shows astigmatism. In  FIG. 6A , distance (in millimeters) from the image surface to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 6A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 6B  shows distortion. In  FIG. 6B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 6C  shows spherical aberration. In  FIG. 6C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.1864 millimeters.  FIG. 6D  shows chromatic aberration of magnification. In  FIG. 6D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0085]    Table 7 shows lens data of the wide-range optical imaging system according to Example 3. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  301 , the second lens  302  and the third lens  303 , respectively. Surface number 7 represents the aperture stop  305 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  304 , respectively. Surface number 10 represents the object side surface of the glass plate  306 , and surface number 11 represents the image plane side surface of the glass plate  306 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  301 , and the value of d (2.34677) in the row of surface number 2 represents distance between the first lens  301  and the second lens  302 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 7 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 19.62909 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 7.79721 
                 2.34677 
               
               
                 3 
                 12.53754 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.11358 
                 1.29204 
               
               
                 5 
                 2.34739 
                 3.99993 
                 1.61411 
                 25.32 
               
               
                 6 
                 9.79945 
                 0.53876 
               
               
                 7 
                 ∞ 
                 0.39578 
               
               
                 8 
                 4.79310 
                 2.12255 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.21291 
                 1.46755 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0086]    Table 8 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 3. Since the both surfaces of the first lens  301  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.97406E−03  
                 7.09798E−05 
                 −6.63820E−07 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −8.87458E−01 
                 1.13754E−02 
                 −2.30953E−04  
                 −1.20153E−03 
                 1.13226E−04 
                 −3.46288E−06  
               
               
                 5 
                 −4.46515E−01 
                 1.35420E−02 
                 1.73996E−04 
                 −8.86447E−05 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 4.43072E−02 
                 9.81984E−03 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −5.80087E+01 
                 1.83295E−02 
                 −4.23490E−03  
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −9.05465E−01 
                 2.14000E−02 
                 3.11502E−04 
                  3.80733E−05 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 4 
       [0087]      FIG. 7  shows an arrangement of a wide-range optical imaging system according to Example 4. The wide-range optical imaging system according to Example 4 includes, from the object side to the image plane side, a first lens  401 , a second lens  402 , a third lens  403 , an aperture stop  405 , and a fourth lens  404 . Light which has passed through the first lens  401 , the second lens  402 , the third lens  403 , the aperture stop  405 , and the fourth lens  404  passes through a glass plate  406  and reaches an image plane  407 . 
         [0088]      FIGS. 8A to 8D  show aberrations of the wide-range optical imaging system according to Example 4.  FIG. 8A  shows astigmatism. In  FIG. 8A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 8A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 8B  shows distortion. In  FIG. 8B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 8C  shows spherical aberration. In  FIG. 8C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.1861 millimeters.  FIG. 8D  shows chromatic aberration of magnification. In  FIG. 8D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0089]    Table 9 shows lens data of the wide-range optical imaging system according to Example 4. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  401 , the second lens  402  and the third lens  403 , respectively. Surface number 7 represents the aperture stop  405 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  404 , respectively. Surface number 10 represents the object side surface of the glass plate  406 , and surface number 11 represents the image plane side surface of the glass plate  406 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  401 , and the value of d (2.50237) in the row of surface number 2 represents distance between the first lens  401  and the second lens  402 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 9 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 9 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 15.91688 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 6.09058 
                 2.50237 
               
               
                 3 
                 160.21972 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.03064 
                 0.66806 
               
               
                 5 
                 1.88037 
                 3.31803 
                 1.61411 
                 25.32 
               
               
                 6 
                 29.42935 
                 0.54246 
               
               
                 7 
                 ∞ 
                 0.51420 
               
               
                 8 
                 5.03929 
                 1.84639 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.21354 
                 1.48108 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0090]    Table 10 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 4. Since the both surfaces of the first lens  401  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.29338E−03  
                  1.14565E−04 
                 −2.13709E−06 
                 −3.36485E−09  
                 2.99138E−10 
               
               
                 4 
                 −8.62930E−01 
                 8.59319E−03 
                 −3.07143E−03 
                 −1.40132E−03 
                 1.08601E−04 
                 −2.05266E−06  
               
               
                 5 
                 −4.08338E−01 
                 2.06693E−02 
                 −1.53245E−04 
                 −5.72967E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 6.82525E−02 
                 −3.10800E−02 
                  2.10858E−02 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −1.31816E+01 
                 1.09535E−03 
                  2.27488E−03 
                 −7.47524E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −1.95324E+00 
                 −4.29912E−02  
                  1.73545E−02 
                 −2.29586E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 5 
       [0091]      FIG. 9  shows an arrangement of a wide-range optical imaging system according to Example 5. The wide-range optical imaging system according to Example 5 includes, from the object side to the image plane side, a first lens  501 , a second lens  502 , a third lens  503 , an aperture stop  505 , and a fourth lens  504 . Light which has passed through the first lens  501 , the second lens  502 , the third lens  503 , the aperture stop  505 , and the fourth lens  504  passes through a glass plate  506  and reaches an image plane  507 . 
         [0092]      FIGS. 10A to 10D  show aberrations of the wide-range optical imaging system according to Example 5.  FIG. 10A  shows astigmatism. In  FIG. 10A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 10A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 10B  shows distortion. In  FIG. 10B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 10C  shows spherical aberration. In  FIG. 10C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2010 millimeters.  FIG. 10D  shows chromatic aberration of magnification. In  FIG. 10D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0093]    Table 11 shows lens data of the wide-range optical imaging system according to Example 5. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  501 , the second lens  502  and the third lens  503 , respectively. Surface number 7 represents the aperture stop  505 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  504 , respectively. Surface number 10 represents the object side surface of the glass plate  506 , and surface number 11 represents the image plane side surface of the glass plate  506 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  501 , and the value of d (2.18306) in the row of surface number 2 represents distance between the first lens  501  and the second lens  502 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 11 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 22.60925 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 10.25067 
                 2.18306 
               
               
                 3 
                 41.30378 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.08638 
                 1.01308 
               
               
                 5 
                 2.32120 
                 3.80062 
                 1.61411 
                 25.32 
               
               
                 6 
                 21.77173 
                 0.63863 
               
               
                 7 
                 ∞ 
                 0.46823 
               
               
                 8 
                 4.16310 
                 2.09637 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.31436 
                 1.49962 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0094]    Table 12 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 5. Since the both surfaces of the first lens  501  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 12 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.10637E−03  
                 6.50201E−05 
                 −7.07830E−07 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −8.78518E−01 
                 6.85384E−03 
                 −1.25017E−03  
                 −1.12840E−03 
                 1.16052E−04 
                 −3.52543E−06  
               
               
                 5 
                 −2.70728E−01 
                 1.27211E−02 
                 1.93895E−04 
                 −2.63428E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 3.78411E−02 
                 5.99255E−03 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −2.12783E+01 
                 1.46965E−02 
                 −3.05382E−03  
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −9.15902E−01 
                 2.19561E−02 
                 5.61012E−03 
                 −1.13058E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 6 
       [0095]      FIG. 11  shows an arrangement of a wide-range optical imaging system according to Example 6. The wide-range optical imaging system according to Example 6 includes, from the object side to the image plane side, a first lens  601 , a second lens  602 , a third lens  603 , an aperture stop  605 , and a fourth lens  604 . Light which has passed through the first lens  601 , the second lens  602 , the third lens  603 , the aperture stop  605 , and the fourth lens  604  passes through a glass plate  606  and reaches an image plane  607 . 
         [0096]      FIGS. 12A to 12D  show aberrations of the wide-range optical imaging system according to Example 6.  FIG. 12A  shows astigmatism. In  FIG. 12A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 12A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 12B  shows distortion. In  FIG. 12B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 12C  shows spherical aberration. In  FIG. 12C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2194 millimeters.  FIG. 12D  shows chromatic aberration of magnification. In  FIG. 12D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0097]    Table 13 shows lens data of the wide-range optical imaging system according to Example 6. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  601 , the second lens  602  and the third lens  603 , respectively. Surface number 7 represents the aperture stop  605 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  604 , respectively. Surface number 10 represents the object side surface of the glass plate  606 , and surface number 11 represents the image plane side surface of the glass plate  606 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  601 , and the value of d (1.45955) in the row of surface number 2 represents distance between the first lens  601  and the second lens  602 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 13 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 13 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 27.71033 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 13.01884 
                 1.45955 
               
               
                 3 
                 13.75461 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.10647 
                 1.28331 
               
               
                 5 
                 2.59395 
                 3.90834 
                 1.61411 
                 25.32 
               
               
                 6 
                 7.94643 
                 0.62198 
               
               
                 7 
                 ∞ 
                 0.41613 
               
               
                 8 
                 4.83107 
                 2.03879 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.35219 
                 1.86272 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0098]    Table 14 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 6. Since the both surfaces of the first lens  601  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 14 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.97552E−03  
                 7.13172E−05 
                 −6.44309E−07 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −8.86496E−01 
                 9.97494E−03 
                 −6.90209E−05  
                 −1.19228E−03 
                 1.13045E−04 
                 −3.65037E−06  
               
               
                 5 
                 −4.19892E−01 
                 1.48154E−02 
                 1.86290E−04 
                 −6.38113E−05 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 4.20669E−02 
                 1.15479E−02 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −3.93753E+01 
                 1.39544E−02 
                 −3.11138E−03  
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −8.57300E−01 
                 1.62311E−02 
                 1.46591E−03 
                 −2.68728E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 7 
       [0099]      FIG. 13  shows an arrangement of a wide-range optical imaging system according to Example 7. The wide-range optical imaging system according to Example 7 includes, from the object side to the image plane side, a first lens  701 , a second lens  702 , a third lens  703 , an aperture stop  705 , and a fourth lens  704 . Light which has passed through the first lens  701 , the second lens  702 , the third lens  703 , the aperture stop  705 , and the fourth lens  704  passes through a glass plate  706  and reaches an image plane  707 . 
         [0100]      FIGS. 14A to 14D  show aberrations of the wide-range optical imaging system according to Example 7.  FIG. 14A  shows astigmatism. In  FIG. 14A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 14A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 14B  shows distortion. In  FIG. 14B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 14C  shows spherical aberration. In  FIG. 14C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2203 millimeters.  FIG. 14D  shows chromatic aberration of magnification. In  FIG. 14D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0101]    Table 15 shows lens data of the wide-range optical imaging system according to Example 7. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  701 , the second lens  702  and the third lens  703 , respectively. Surface number 7 represents the aperture stop  705 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  704 , respectively. Surface number 10 represents the object side surface of the glass plate  706 , and surface number 11 represents the image plane side surface of the glass plate  706 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  701 , and the value of d (1.65090) in the row of surface number 2 represents distance between the first lens  701  and the second lens  702 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 15 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 15 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 27.35113 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 14.05922 
                 1.65090 
               
               
                 3 
                 68.87686 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 0.97437 
                 0.94944 
               
               
                 5 
                 2.21926 
                 3.24120 
                 1.61411 
                 25.32 
               
               
                 6 
                 41.27478 
                 0.77280 
               
               
                 7 
                 ∞ 
                 0.54338 
               
               
                 8 
                 4.38156 
                 1.85566 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.43698 
                 1.71384 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0102]    Table 16 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 7. Since the both surfaces of the first lens  701  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 16 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.35577E−03 
                  9.89470E−05 
                 −1.73543E−06 
                 1.54087E−09 
                 2.59811E−10 
               
               
                 4 
                 −8.70889E−01 
                 −1.16524E−02 
                 −1.03014E−03 
                 −1.15553E−03 
                 1.12473E−04 
                 −6.26676E−06  
               
               
                 5 
                 −2.03752E−01 
                  9.24031E−03 
                  3.49531E−04 
                 −3.52603E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                  3.42814E−02 
                 −8.94593E−04 
                  3.90563E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −7.42499E+00 
                  3.00377E−03 
                 −5.68834E−04 
                 −3.60652E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −2.36160E+00 
                 −3.61764E−02 
                  1.69052E−02 
                 −2.76105E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 8 
       [0103]      FIG. 15  shows an arrangement of a wide-range optical imaging system according to Example 8. The wide-range optical imaging system according to Example 8 includes, from the object side to the image plane side, a first lens  801 , a second lens  802 , a third lens  803 , an aperture stop  805 , and a fourth lens  804 . Light which has passed through the first lens  801 , the second lens  802 , the third lens  803 , the aperture stop  805 , and the fourth lens  804  passes through a glass plate  806  and reaches an image plane  807 . 
         [0104]      FIGS. 16A to 16D  show aberrations of the wide-range optical imaging system according to Example 8.  FIG. 16A  shows astigmatism. In  FIG. 16A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 16A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 16B  shows distortion. In  FIG. 16B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 16C  shows spherical aberration. In  FIG. 16C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2149 millimeters.  FIG. 16D  shows chromatic aberration of magnification. In  FIG. 16D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0105]    Table 17 shows lens data of the wide-range optical imaging system according to Example 8. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  801 , the second lens  802  and the third lens  803 , respectively. Surface number 7 represents the aperture stop  805 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  804 , respectively. Surface number 10 represents the object side surface of the glass plate  806 , and surface number 11 represents the image plane side surface of the glass plate  806 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  801 , and the value of d (1.56238) in the row of surface number 2 represents distance between the first lens  801  and the second lens  802 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 17 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 17 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 32.84835 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 17.22412 
                 1.56238 
               
               
                 3 
                 36.17811 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 0.95701 
                 1.01209 
               
               
                 5 
                 2.35021 
                 3.30349 
                 1.61411 
                 25.32 
               
               
                 6 
                 13.86311 
                 0.76606 
               
               
                 7 
                 ∞ 
                 0.51293 
               
               
                 8 
                 4.32708 
                 1.89289 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.42727 
                 1.87056 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0106]    Table 18 shows conic constants and coefficients of the polynomials of the Equation (A) representing the both surfaces of the second to the fourth lenses of Example 8. Since the both surfaces of the first lens  801  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 18 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.41591E−03 
                 9.68422E−05 
                 −1.77092E−06 
                 1.60303E−09 
                 3.01185E−10 
               
               
                 4 
                 −8.76398E−01 
                 −1.49919E−02 
                 −3.27279E−04  
                 −1.10838E−03 
                 1.12054E−04 
                 −7.30915E−06  
               
               
                 5 
                 −1.18950E−01 
                  9.89425E−03 
                 1.43611E−04 
                 −2.41306E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                  3.74205E−02 
                 9.43402E−04 
                  3.95133E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −5.87569E+00 
                  2.70169E−03 
                 −1.15503E−03  
                 −1.33142E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −2.35215E+00 
                 −3.71341E−02 
                 1.67916E−02 
                 −2.69036E−03 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 9 
       [0107]      FIG. 17  shows an arrangement of a wide-range optical imaging system according to Example 9. The wide-range optical imaging system according to Example 9 includes, from the object side to the image plane side, a first lens  901 , a second lens  902 , a third lens  903 , an aperture stop  905 , and a fourth lens  904 . Light which has passed through the first lens  901 , the second lens  902 , the third lens  903 , the aperture stop  905 , and the fourth lens  904  passes through a glass plate  906  and reaches an image plane  907 . 
         [0108]      FIGS. 18A to 18D  show aberrations of the wide-range optical imaging system according to Example 9.  FIG. 18A  shows astigmatism. In  FIG. 18A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 18A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 18B  shows distortion. In  FIG. 18B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 18C  shows spherical aberration. In  FIG. 18C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2512 millimeters.  FIG. 18D  shows chromatic aberration of magnification. In  FIG. 18D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0109]    Table 19 shows lens data of the wide-range optical imaging system according to Example 9. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  901 , the second lens  902  and the third lens  903 , respectively. Surface number 7 represents the aperture stop  905 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  904 , respectively. Surface number 10 represents the object side surface of the glass plate  906 , and surface number 11 represents the image plane side surface of the glass plate  906 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  901 , and the value of d (1.87630) in the row of surface number 2 represents distance between the first lens  901  and the second lens  902 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 19 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 19 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 34.68339 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 17.98798 
                 1.87630 
               
               
                 3 
                 22.99130 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.07363 
                 1.01983 
               
               
                 5 
                 2.52174 
                 3.29986 
                 1.61411 
                 25.32 
               
               
                 6 
                 4.82586 
                 0.77129 
               
               
                 7 
                 ∞ 
                 0.28999 
               
               
                 8 
                 4.44392 
                 2.17685 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.49653 
                 2.51254 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0110]    Table 20 shows conic constants and coefficients of the polynomials of Equation (A) representing the both surfaces of the second to the fourth lenses of Example 9. Since the both surfaces of the first lens  901  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 20 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −2.54218E−03  
                 6.38775E−05 
                 −5.16375E−07  
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −8.80556E−01 
                 −2.82753E−03  
                 1.54520E−03 
                 −9.90661E−04  
                 1.17042E−04 
                 −9.44078E−06  
               
               
                 5 
                 −1.52064E−01 
                 1.32350E−02 
                 −2.72710E−04  
                 1.88632E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                  0.00000E+00 
                 4.21157E−02 
                 1.98431E−02 
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −3.59698E+01 
                 2.29596E−02 
                 −4.72105E−03  
                 0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −7.73343E−01 
                 1.38362E−02 
                 9.77197E−04 
                 2.47537E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Example 10 
       [0111]      FIG. 19  shows an arrangement of a wide-range optical imaging system according to Example 10. The wide-range optical imaging system according to Example 10 includes, from the object side to the image plane side, a first lens  1001 , a second lens  1002 , a third lens  1003 , an aperture stop  1005 , and a fourth lens  1004 . Light which has passed through the first lens  1001 , the second lens  1002 , the third lens  1003 , the aperture stop  1005 , and the fourth lens  1004  passes through a glass plate  1006  and reaches an image plane  1007 . 
         [0112]      FIGS. 20A to 20D  show aberrations of the wide-range optical imaging system according to Example 10.  FIG. 20A  shows astigmatism. In  FIG. 20A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. In  FIG. 20A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 20B  shows distortion. In  FIG. 20B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees.  FIG. 20C  shows spherical aberration. In  FIG. 20C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.2509 millimeters.  FIG. 20D  shows chromatic aberration of magnification. In  FIG. 20D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. 
         [0113]    Table 21 shows lens data of the wide-range optical imaging system according to Example 10. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  1001 , the second lens  1002  and the third lens  1003 , respectively. Surface number 7 represents the aperture stop  1005 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  1004 , respectively. Surface number 10 represents the object side surface of the glass plate  1006 , and surface number 11 represents the image plane side surface of the glass plate  1006 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.20000) in the row of surface number 1 represents thickness of the first lens  1001 , and the value of d (1.42500) in the row of surface number 2 represents distance between the first lens  1001  and the second lens  1002 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 21 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 21 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 19.98824 
                 1.20000 
                 1.79999 
                 29.84 
               
               
                 2 
                 6.81679 
                 1.42500 
               
               
                 3 
                 −66.66544 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.03328 
                 0.78600 
               
               
                 5 
                 2.26766 
                 2.52000 
                 1.61411 
                 25.32 
               
               
                 6 
                 −23.86513 
                 0.65000 
               
               
                 7 
                 ∞ 
                 0.21000 
               
               
                 8 
                 2.41680 
                 2.33000 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.26398 
                 1.02000 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0114]    Table 22 shows conic constants and coefficients of the polynomials of Equation (A) representing the both surfaces of the second to the fourth lenses of Example 10. Since the both surfaces of the first lens  1001  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 22 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                  0.00000E+00 
                 −4.23779E−04 
                 −5.54694E−04 
                  4.09594E−05 
                 1.34478E−06 
                 −1.38659E−07 
               
               
                 4 
                 −1.22720E+00 
                  1.32346E−01 
                 −4.15241E−02 
                 −5.47769E−03 
                 3.98464E−03 
                 −4.37293E−04 
               
               
                 5 
                 −2.14572E−02 
                  7.59370E−02 
                 −3.40240E−02 
                  1.04045E−02 
                 −2.16403E−03  
                  2.10608E−04 
               
               
                 6 
                  0.00000E+00 
                  9.78230E−02 
                 −1.10081E−01 
                  1.50493E−01 
                 −1.17334E−01  
                  3.48643E−02 
               
               
                 8 
                  3.38431E−01 
                 −9.83116E−02 
                  4.15837E−01 
                 −9.56059E−01 
                 1.10356E+00 
                 −5.01897E−01 
               
               
                 9 
                 −9.49515E+00 
                 −3.57088E−01 
                  5.21990E−01 
                 −3.99269E−01 
                 1.65993E−01 
                 −2.76393E−02 
               
               
                   
               
             
          
         
       
     
       Example 11 
       [0115]      FIG. 21  shows an arrangement of a wide-range optical imaging system according to Example 11. The wide-range optical imaging system according to Example 11 includes, from the object side to the image plane side, a first lens  1001 , a second lens  1002 , a third lens  1003 , an aperture stop  1005 , and a fourth lens  1004 . Light which has passed through the first lens  1001 , the second lens  1002 , the third lens  1003 , the aperture stop  1005 , and the fourth lens  1004  passes through a glass plate  1106  and reaches an image plane  1107 . 
         [0116]      FIGS. 22A to 22D  show aberrations of the wide-range optical imaging system according to Example 11.  FIG. 22A  shows astigmatism. In  FIG. 22A , distance (in millimeters) from the image plane to the paraxial image surface is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 100 degrees. In  FIG. 22A , S represents the sagittal image surface while T represents the tangential image surface.  FIG. 22B  shows distortion. In  FIG. 22B , distortion is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 89 degrees. The maximum angle of view is 100 degrees in half angle. However, since distortion cannot be defined for 90 degrees or more, angle of view is normalized by 89 degrees.  FIG. 22C  shows spherical aberration. In  FIG. 22C , for a ray bundle with angle of view of 0 degree, distance (in millimeters) from the image plane to points at which rays of the ray bundle intersect with the optical axis is represented as a function of normalized pupil coordinate. The maximum value of normalized pupil coordinate corresponds to 0.1759 millimeters.  FIG. 22D  shows chromatic aberration of magnification. In  FIG. 22D , image height difference (in micrometer) of each of F-line and C-line with reference to image height of d-line is represented as a function of normalized angle of view. The maximum value of normalized angle of view corresponds to 100 degrees. 
         [0117]    Table 23 shows lens data of the wide-range optical imaging system according to Example 11. Surface numbers 1 to 6 represent the object side surface and the image plane side surface of each of the first lens  1101 , the second lens  1102  and the third lens  1103 , respectively. Surface number 7 represents the aperture stop  1105 . Surface numbers 8 and 9 represent the object side surface and the image plane side surface of the fourth lens  1104 , respectively. Surface number 10 represents the object side surface of the glass plate  1106 , and surface number 11 represents the image plane side surface of the glass plate  1106 . R represents the radius of curvature in Equation (A) which represents each lens surface. d represents thickness of a lens or the glass plate, or distance between elements. By way of example, the value of d (1.00000) in the row of surface number 1 represents thickness of the first lens  1101 , and the value of d (3.09747) in the row of surface number 2 represents distance between the first lens  1101  and the second lens  1102 . n represents refractive index at d-line of each lens or element, and v represents an Abbe number at d-line of the material of each lens or element. Unit of length in Table 23 is millimeter. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 23 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 R 
                 d 
                 n 
                 v 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 15.57408 
                 1.00000 
                 1.80400 
                 46.57 
               
               
                 2 
                 3.80440 
                 3.09747 
               
               
                 3 
                 −11.31314 
                 1.00000 
                 1.52512 
                 56.28 
               
               
                 4 
                 1.31541 
                 0.34371 
               
               
                 5 
                 2.06950 
                 2.81526 
                 1.61411 
                 25.32 
               
               
                 6 
                 −6.65472 
                 0.86000 
               
               
                 7 
                 ∞ 
                 0.83234 
               
               
                 8 
                 3.73788 
                 2.06174 
                 1.52512 
                 56.28 
               
               
                 9 
                 −1.50486 
                 1.41744 
               
               
                 10 
                 ∞ 
                 0.30000 
                 1.51680 
                 64.17 
               
               
                 11 
                 ∞ 
                 0.50000 
               
               
                   
               
             
          
         
       
     
         [0118]    Table 24 shows conic constants and coefficients of the polynomials of Equation (A) representing the both surfaces of the second to the fourth lenses of Example 11. Since the both surfaces of the first lens  1101  are spherical, the conic constants k and the coefficients of the polynomials Ai are zero. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 24 
               
               
                   
               
               
                 Surface 
                   
                   
                   
                   
                   
                   
               
               
                 number 
                 k 
                 α4 
                 α6 
                 α8 
                 α10 
                 α12 
               
               
                   
               
             
             
               
                 3 
                 −5.54890E+01 
                 −2.26773E−03  
                 2.18198E−04 
                 −9.22124E−06 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 4 
                 −7.38061E−01 
                 7.87204E−03 
                 −1.88960E−03  
                 −1.71441E−03 
                 5.72044E−05 
                 5.55846E−06 
               
               
                 5 
                 −3.52456E−01 
                 3.82096E−02 
                 −4.18552E−03  
                 −5.14153E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 6 
                 −2.51134E+02 
                 1.11483E−02 
                 1.00709E−03 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 8 
                 −2.58306E+00 
                 7.17679E−03 
                 2.48357E−04 
                  0.00000E+00 
                 0.00000E+00 
                 0.00000E+00 
               
               
                 9 
                 −1.54839E+00 
                 2.43559E−02 
                 3.15157E−03 
                 −4.21975E−04 
                 0.00000E+00 
                 0.00000E+00 
               
               
                   
               
             
          
         
       
     
       Comparison Between Aberrations of Examples of the Present Invention and Aberrations of Examples of JP2006259704A 
       [0119]    As described below, values of longitudinal chromatic aberration and chromatic aberration of magnification of examples of the present invention are made smaller than those of examples of JP2006259704A. Values of distortion of examples of the present invention are greater than those of examples of JP2006259704A. The reason is that the maximum angle of view of Examples 1 to 10 of the present invention is 179.6 degrees (89.8 degrees in half angle) and the maximum angle of view of Example 11 is 200 degrees (100 degrees in half angle) while the maximum angle of examples of JP2006259704A rages from 139.4 (69.7 degrees in half angle) degrees to 165.2 degrees (82.6 degrees in half angle). Thus, the present invention is applicable to a wider angle of view than the value of angle of view to which conventional optical systems are applicable. 
       Longitudinal Chromatic Aberration 
       [0120]    According to  FIG. 2C  and other drawings, longitudinal chromatic aberration of Examples 1 to 11 of the present invention remains within limits of ±0.1 millimeters. On the other hand, longitudinal chromatic aberration of Examples 1 to 12 of JP2006259704A does not remain within limits of ±0.1 millimeters, but is within limits of ±0.25 millimeters. 
       Chromatic Aberration of Magnification 
       [0121]    According to  FIG. 2D  and other drawings, chromatic aberration of magnification of Examples 1 to 11 of the present invention remains within limits of ±5 micrometers. On the other hand, chromatic aberration of magnification of Examples 1 to 12 of JP2006259704A does not remain within limits of ±5 micrometers, but is within limits of ±10 micrometers.