Abstract:
There is provided a subminiature optical system mounted in a mobile communication terminal and a personal digital assistant (PDA) or used for a monitoring camera and a digital camera. The subminiature optical system includes: a first lens entirely having a positive refractive power and comprising a first lens element having an object-side surface convex toward the object on an optical axis; a second lens element having an object-side surface in contact with an image-side surface of the first lens element; and a third lens element having an object-side surface in contact with an image-side surface of the second lens element and an image-side surface concave toward an image on the optical axis; and a second lens entirely having a positive refractive power and comprising a fourth lens element having an object-side surface convex toward the object on the optical axis; and a fifth lens element having an object-side surface in contact with an image-side surface of the fourth lens element and an image-side surface formed of a plane.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the priority of Korean Patent Application No. 2007-0097579 filed on Sep. 27, 2007, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to an optical system, and more particularly, to a subminiature optical system mounted on a mobile communication terminal and a personal digital assistant or used for a monitoring camera and a digital camera. 
         [0004]    2. Description of the Related Art 
         [0005]    In general, early mobile communication terminals have only a communication function. However, as use thereof is increased, various services such as photographing, image transmission, and Internet, etc are provided, thereby continuously developing functions and services thereof. Recently, mobile communication terminals of a new extended concept, such as, so called, camera mobile phones come in to the spotlight, where techniques for digital cameras and mobile phones are integrated. 
         [0006]    Particularly, with respect to an optical system mounted on a camera mobile phone, a small size, light weight, and low price are required. Also, as a pixel size of an image sensor such as a charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) becomes smaller and smaller, a high resolution is required in an optical system using such image sensor. 
         [0007]    Also, to satisfy a small size and low price, it is required to reduce a number of lenses of an optical system mounted on a small device such as a mobile phone. However, there is less degree of freedom in design and it is difficult to satisfy optical performance thereof. 
         [0008]    Also, when an optical system including a plurality of refractive surfaces, a number of refractive surfaces to be managed when manufacturing and assembling lenses is increased, thereby complicating a lens manufacturing process and increasing manufacturing costs. 
         [0009]    Accordingly, there is required a subminiature optical system capable of reducing a size thereof and easily mounting lenses thereon while having a high resolution and less aberration. 
       SUMMARY OF THE INVENTION 
       [0010]    An aspect of the present invention provides a subminiature optical system in which a number of refractive surface to be managed in manufacturing and assembling lenses, thereby simplifying a lens manufacturing process and reducing manufacturing costs. 
         [0011]    An aspect of the present invention also provides a subminiature optical system capable of conveniently correcting various aberrations such as chromatic aberration, distortion, astigmatism, and spherical aberration while having a small number of lenses. 
         [0012]    An aspect of the present invention also provides a subminiature optical system using only two lenses, which is not only subminiaturized but also has a high resolution. 
         [0013]    An aspect of the present invention also provides a subminiature optical system capable of being easily mass-produced but also having various excellent optical performances. 
         [0014]    According to an aspect of the present invention, there is provided a subminiature optical system including: a first lens formed in a meniscus shape entirely convex toward an object and having a positive refractive power; and a second lens having an object-side surface convex toward the object and an image-side surface formed of a plane. 
         [0015]    The first lens may include: a first lens element having an object-side surface convex toward the object on an optical axis; a second lens element having an object-side surface in contact with an image-side surface of the first lens element; and a third lens element having an object-side surface in contact with an image-side surface of the second lens element and an image-side surface concave toward an image on the optical axis. The second lens may include: a fourth lens element having an object-side surface convex toward the object on the optical axis; and a fifth lens element having an object-side surface in contact with an image-side surface of the fourth lens element and an image-side surface formed of a plane. 
         [0016]    In this case, the object-side surface and the image-side surface of the second lens element may be formed of planes, respectively. 
         [0017]    The first lens may include one or more refractive surface formed of aspherical surface. 
         [0018]    A refractive index of one or more of the first lens element to the third lens element may be different from a refractive index of other lens elements, and a refractive index of the fourth lens element may be different from that of the fifth lens element. 
         [0019]    On the other hand the second lens may have a positive refractive power. 
         [0020]    One or more of following Conditional Expressions may be satisfied, The following Conditional Expressions are Conditional Expression 1 related to a curvature radius r 4  of a refractive surface closest to the image in the first lens and a curvature radius r 5  closest to the object in the second lens, Conditional Expression 2 related to a distance D 12  on the optical axis from the refractive surface closest to the image in the first lens to the refractive surface closest to the object in the second lens, and Conditional Expression 3 related to a curvature radius r 1  of a refractive surface closest to the object in the first lens, 0.8&lt;r 4 /r 5 &lt;1.2 . . . Conditional Expression 1, 0.05&lt;D 12 /TL&lt;0.1 . . . Conditional Expression 2, and 0.5&lt;r 1 /f&lt;0.7 . . . Conditional Expression 3, wherein TL indicates a distance from the refractive surface closest to the object to an imaging plane and f indicates an overall focal length of the optical system. 
         [0021]    A shielding layer blocking unnecessary light may be installed on one or more of refractive surfaces included in the second lens element and fifth lens element. 
         [0022]    According to another embodiment of the present invention, there is provided a subminiature optical system including: a first lens entirely having a positive refractive power and including a first lens element having an object-side surface convex toward the object on an optical axis; a second lens element having an object-side surface in contact with an image-side surface of the first lens element; and a third lens element having an object-side surface in contact with an image-side surface of the second lens element and an image-side surface concave toward an image on the optical axis; and a second lens entirely having a positive refractive power and including a fourth lens element having an object-side surface convex toward the object on the optical axis; and a fifth lens element having an object-side surface in contact with an image-side surface of the fourth lens element and an image-side surface formed of a plane. 
         [0023]    One or more of following Conditional Expressions may be satisfied, The following Conditional Expressions are Conditional Expression 1 related to a curvature radius r 4  of a refractive surface closest to the image in the first lens and a curvature radius r 5  closest to the object in the second lens, Conditional Expression 2 related to a distance D 12  on the optical axis from the refractive surface closest to the image in the first lens to the refractive surface closest to the object in the second lens, and Conditional Expression 3 related to a curvature radius r 1  of a refractive surface closest to the object in the first lens, 0.8&lt;r 4 /r 5 &lt;1.2 . . . Conditional Expression 1, 0.05&lt;D 12 /TL&lt;0.1 . . . Conditional Expression 2, and 0.5&lt;r 1 /f&lt;0.7 . . . Conditional Expression 3, wherein TL indicates a distance from the refractive surface closest to the object to an imaging plane and f indicates an overall focal length of the optical system. 
         [0024]    According to an exemplary embodiment of the present invention, since an image surface of a second lens is formed of a plane, a number of refractive surfaces to be managed while manufacturing and assembling lenses is reduced, thereby simplifying a manufacturing process and reducing manufacturing costs. 
         [0025]    According to an exemplary embodiment of the present invention, there is also provided a subminiature optical system in which spherical, aspherical, and plane surfaces are suitably mixed and shapes of refractive lens surfaces are suitably formed, thereby being subminiaturized and having a high resolution. 
         [0026]    According to an exemplary embodiment of the present invention, there is also provided a subminiature optical system capable of efficiently correcting chromatic aberration, distortion, astigmatism, and spherical aberration while having a small number of lenses, by using first lens formed of three lens elements and a second lens formed of two lens elements. 
         [0027]    According to an exemplary embodiment of the present invention, a replica method may be used, thereby manufacturing first and second lenses in a wafer style, which is suitable for mass production. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]    The above and other aspects, features and other advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which: 
           [0029]      FIG. 1  is a diagram illustrating a lens configuration of a subminiature optical system according to a first embodiment of the present invention; 
           [0030]      FIG. 2  illustrates aberration diagrams such as a spherical aberration, an astigmatism aberration, and a distortion of the optical system of  FIG. 1 ; 
           [0031]      FIG. 3  is a diagram illustrating a lens configuration of a subminiature optical system according to a second embodiment of the present invention; 
           [0032]      FIG. 4  illustrates aberration diagrams such as a spherical aberration, an astigmatism aberration, and a distortion of the optical system of  FIG. 3 ; 
           [0033]      FIG. 5  is a diagram illustrating a lens configuration of a subminiature optical system according to a third embodiment of the present invention; 
           [0034]      FIG. 6  illustrates aberration diagrams such as a spherical aberration, an astigmatism aberration, and a distortion of the optical system of  FIG. 5 ; 
           [0035]      FIG. 7  is a diagram illustrating a lens configuration of a subminiature optical system according to a fourth embodiment of the present invention; and 
           [0036]      FIG. 8  illustrates aberration diagrams such as a spherical aberration, an astigmatism aberration, and a distortion of the optical system of  FIG. 7 . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0037]    Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. 
         [0038]    The present invention provides a subminiature optical system capable of not only efficiently correcting various aberrations such as chromatic aberration, distortion, astigmatic aberration, and aspherical aberration by using a first lens formed of three lens elements and a second lens formed of two lens elements while having a small number of lenses but also reducing a number of refractive surfaces to be managed in such a way that it is possible to easily install lenses and to reduce manufacturing costs. 
         [0039]    Since it is possible to apply a replica method to the present invention, mass production is easy and a subminiature optical system having excellent performance is provided. 
         [0040]      FIG. 1  is a diagram illustrating a lens configuration of a subminiature optical system according to a first embodiment of the present invention. In  FIG. 1 , a thickness, size, and shape of a lens are a little exaggerated for description. Particularly, shapes of spherical and aspherical surfaces, which are shown in  FIG. 1 , are just an example and present invention is not limited thereto. 
         [0041]    Referring to  FIG. 1 , the subminiature optical system includes a first lens L 1 , a second lens L 2 , an image sensor (not shown) corresponding to an imaging plane IP, in an order from an object. An aperture stop AS shielding unnecessary light may be installed in a suitable position such as a front of the first lens L 1 . 
         [0042]    The first lens L 1  is formed in a meniscus shape entirely convex toward the object and having a positive refractive power. The second lens L 2  has an object-side surface convex toward the object and a top surface formed in a plane. 
         [0043]    In this case, the first lens L 1  may include a first lens element LE 1  having an object-side surface convex toward the object on an optical axis, a second lens element LE 2  having an object-side surface in contact with an image-side surface of the first lens element LE 1 , and a third lens element LE 3  having an object-side surface in contact with an image-side surface of the second lens element LE 2  and an image-side surface concave toward an image on the optical axis, which are totally three. 
         [0044]    Also, the second lens L 2  may include a fourth lens element LE 4  having an object-side surface convex toward the object on the optical axis; and a fifth lens element LE 5  having an object-side surface in contact with an image-side surface of the fourth lens element LE 4  and an image-side surface formed of a plane, which are totally two. 
         [0045]    The image sensor corresponds to the imaging plane IP and is formed of charge-coupled device (CCD) or complementary metal-oxide semiconductor (CMOS) to sense and convert a light image permeating the first lens L 1  and second lens L 2  into an electrical signal. 
         [0046]    Also, the aperture stop AS may be installed in front or inside of an object-side surface  1  of the first lens L 1  and a shielding layer capable of preventing a flare by shielding from unnecessary light may be installed on the object-side surface or the image-side surface of the second lens element LE 2 . 
         [0047]    An infrared filter or a cover glass may be installed in back of the second lens L 2 , corresponding to an optical low pass filter, color filter, and a face plate. On the object-side surface or image-side surface of the fifth lens element LE 5 , a shielding layer capable of shielding from unnecessary light may be installed (refer to M of  FIGS. 5 and 7 ). 
         [0048]    In  FIGS. 5 and 7 , the shielding layer M is installed on the object-side surface of the fifth lens element LE 5 . However, the shielding layer M may be installed on the object-side surface or image-side surface of the second lens element LE 2  or the image-side surface of the fifth lens element LE 5 . In this case, the shielding layer M may be installed in a portion out of a path of light incident from the object, may be installed instead of the aperture stop AS, and may be installed separately from the aperture stop AS. 
         [0049]    The subminiature optical system may embody subminiaturization by reducing an overall length thereof by using the first lens L 1  having the positive refractive power and the second lens L 2  having the positive refractive power. 
         [0050]    Also, one or more of refractive surfaces included in the first to third lens elements LE 1 , LE 2 , and LE 3  is formed of an aspherical surface and one of refractive surfaces included in the fourth and fifth lens elements LE 4  and LE 5  is formed of an aspherical surface, thereby correcting a spherical aberration, astigmatism, and distortion. 
         [0051]    As shown in  FIG. 1 , the first lens element LE 1  and second lens element LE 2  are cemented to an object-side surface  2  and an image-side surface  3  of the second lens element LE 2 , respectively. 
         [0052]    In this case, the first lens L 1  may be formed by using a replica method of laminating polymers on both surfaces of the second lens element LE 2  corresponding to a lens substrate, to form the first lens element LE 1  and the third lens element LE 3 . As described above, when a lens of a wafer style is formed by using the replica method, mass production is possible. 
         [0053]    However, when one or more of the first lens element LE 1 , the second lens element LE 2 , and the third lens element LE 3  has a different refractive index from others, the first lens L 1  is not limited to be manufactured by using the replica method. That is, aberration correction is capable of being performed by making a refractive index of some of the three lens element forming the first lens L 1  be different from others, the first lens L 1  may be manufactured by using a general method of manufacturing a cemented lens. 
         [0054]    Also, as shown in  FIG. 1 , in the case of the second lens L 2 , the fourth lens element LE 4  is cemented to an object-side surface  6  of the fifth lens element LE 5 . 
         [0055]    In this case, similar to the first lens L 1 , the second lens L 2  may be formed by using the replica method of laminating polymers on both surfaces of the fifth lens element LE 5  corresponding to a lens substrate, to form the fourth lens element LE 4 . However, when the fourth lens element LE 4  and the fifth lens element LE 5  are capable of having a different refractive index from each other, the second lens L 2  may be manufactured by using the general method of manufacturing a cemented lens. 
         [0056]    When the fourth lens LE 4  and the fifth lens element LE 5  are capable of having a different refractive index from each other, the second lens L 2  is not limited to be manufactured by using the replica method. That is, when aberration correction is capable of being performed by making refractive indexes of the tow lens element forming the second lens L 2  be different from each other, the second lens L 2  may be manufactured by using the general method of manufacturing a cemented lens. 
         [0057]    Also, when an image-side surface  7  of the fifth lens element LE 5  is formed of a plane, since a number of refractive surfaces to be managed when manufacturing and assembling lenses is reduced, a lens manufacturing process may be simplified and manufacturing costs may be reduced. 
         [0058]    On the other hand, all of the object-side surfaces  2  and  6  and the image-side surfaces  3  and  7  of the second lens element LE 2  and the fifth lens element LE 5  are formed in planes in  FIG. 1  but not limited thereto. 
         [0059]    That is, to apply a general replica method of easily mass producing, the both surfaces of the second lens element LE 2  and the fifth lens element LE 5  may be formed in planes, respectively. However, when applying the general method of manufacturing a cemented lens, one or more of the refractive surfaces  2 ,  3 , and  6  of the second lens element LE 2  and the fifth lens element LE 5  may be formed in one of a spherical and an aspherical surfaces. As described above, when some of the refractive surfaces are formed in a curved surface, a number of refractive surfaces is increased, thereby improving a degree of freedom and forming an optical system having various excellent optical characteristics. 
         [0060]    Also, the subminiature optical system may embody excellent aberration characteristics and a high resolution by forming a curved line in an aspherical surface and optimizing a curvature radius of a refractive surface. 
         [0061]    As described above, effects of Conditional Expressions 1 to 3 under the described configuration will be described. 
         [0000]      0.8 &lt;r 4 /r 5&lt;1.2  Conditional Expression 1 
         [0062]    wherein r 4  indicates a curvature radius of a refractive surface closest to the object from the first lens L 1 , that is, the image-side surface  4  of the third lens element LE 3 , and r 5  indicates a curvature radius of a refractive surface closest to the object from the second lens L 2 , that is, the object-side surface  5  of the fourth lens element LE 4 . 
         [0063]    Conditional Expression 1 is a condition on shapes of the first lens L 1  and second lens L 2 . 
         [0064]    When r 4 /r 5  becomes smaller than a lower limit of Conditional Expression 1, it is difficult to assemble the first lens L 1  and the second lens L 2 . On the other hand, r 4 /r 5  becomes greater than an upper limit of Conditional Expression 1, it is difficult to correct astigmatism. 
         [0000]      0.05 &lt;D 12 /TL&lt; 0.1  Conditional Expression 2 
         [0065]    wherein D 12  indicates a distance on an optical axis from a refractive surface closest to the image from the first lens L 1 , that is, the image-side surface  4  of the third lens element LE 3  to a refractive surface closest to the object from the second lens L 2 , that is, the object-side surface  5  of the fourth lens element LE 4 , and TL indicates a distance from a refractive surface closest to the object in the first lens to an imaging plane. 
         [0066]    Conditional Expression 2 is a condition on a distance between the first lens L 1  and the second lens L 2 . 
         [0067]    When the distance between the first lens L 1  and the second lens L 2  becomes smaller than a lower limit of Conditional Expression 2, it is difficult to assemble the first lens L 1  and the second lens L 2  due to lack of a distance for assembling. On the other hand, when the distance between the first lens L 1  and the second lens L 2  becomes greater than an upper limit of Conditional Expression 2, it is impossible to provide a satisfactory back focal length. 
         [0000]      0.5 &lt;r 1 /f&lt; 0.7  Conditional Expression 3 
         [0068]    wherein r 1  indicates a curvature radius of a refractive surface closest to the object in the first lens L 1 , that is the object-side surface  1  of the first lens element LE 1 , and f indicates an overall focal length of the optical system. 
         [0069]    Conditional Expression 3 is a condition on a shape of the first lens L 1 . 
         [0070]    When smaller than a lower limit of Conditional Expression 3, sensitivity of the object-side of the first lens L 1  is decreased. On the other hand, when greater than an upper limit, the overall length of the optical system becomes great. 
         [0071]    Hereinafter, detailed numerical values of embodiments according to the present invention will be described. 
         [0072]    As described above, following first to fourth embodiments include the aperture stop AS, the first lens L 1 , the second L 2 , the image sensor corresponding to the imaging plane IP sequentially from the object. 
         [0073]    The first lens L 1  is formed in a meniscus shape entirely convex toward the object and having a positive refractive power. The second lens L 2  has an object-side surface convex toward the object and a top surface formed in a plane. 
         [0074]    In this case, the first lens L 1  includes a first lens element LE 1  having an object-side surface convex toward the object on an optical axis, a second lens element LE 2  having an object-side surface in contact with an image-side surface of the first lens element LE 1 , and a third lens element LE 3  having an object-side surface in contact with an image-side surface of the second lens element LE 2  and an image-side surface concave toward an image on the optical axis, which are totally three. 
         [0075]    Also, the second lens L 2  may include a fourth lens element LE 4  having an object-side surface convex toward the object on the optical axis; and a fifth lens element LE 5  having an object-side surface in contact with an image-side surface of the fourth lens element LE 4  and an image-side surface formed of a plane, which are totally two. 
         [0076]    Also, the aperture stop AS may be installed in front the object-side surface  2  of the first lens L 1  and a shielding layer capable of preventing a flare by shielding from unnecessary light may be installed on one or more of refractive surfaces of the second lens element LE 2  and fifth lens element LE 5  (refer to M in  FIGS. 5 and 7 ). 
         [0077]    Aspherical surfaces used in the respective following examples are obtained from well-known Equation 1. 
         [0000]    
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       
                         cY 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   K 
                                 
                                 ) 
                               
                                
                               
                                 c 
                                 2 
                               
                                
                               
                                 Y 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       AY 
                       4 
                     
                     + 
                     
                       BY 
                       6 
                     
                     + 
                     
                       CY 
                       8 
                     
                     + 
                     
                       DY 
                       10 
                     
                     + 
                     
                       EY 
                       12 
                     
                     + 
                     
                       FY 
                       14 
                     
                     + 
                     … 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0078]    wherein Z indicates a distance from a fixed point on a lens in a direction of an optical axis, Y indicates a distance in a direction vertical to the optical axis, c indicates a reciprocal of a curvature radius at the fixed point on the lens, K indicates a conic constant, and A, B, C, D, E, and F indicate aspherical coefficients. 
       First Embodiment 
       [0079]    Following Table 1 illustrates numerical values according to the first example of the present invention. 
         [0080]    Also,  FIG. 1  is a diagram illustrating a lens configuration of the subminiature optical system according to the first embodiment of the present invention and  FIG. 2  illustrates aberrations of the optical system of  FIG. 1 , in which (a) illustrates a spherical aberration, (b) illustrates astigmatism, and (c) illustrates a distortion, respectively. In (b), “S” indicates sagittal and “T” indicates tangential. 
         [0081]    In the present embodiment, a viewing angle is 66 degrees, a f-number is 3.0, a distance TL from the object-side surface  1  of the first lens element LE 1  to the imaging plane  8  is 1.883 mm, and an effective focal length f of the optical system is 1.343 mm. 
         [0082]    In Table 1, a unit of a curvature radius R, a thickness, and a distance t is mm. 
         [0000]    
       
         
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 Thickness 
                   
                   
                   
               
               
                   
                 Curvature 
                 or 
                   
                 Abbe 
               
               
                 Number of 
                 radius 
                 distance 
                 Refractive 
                 number 
               
               
                 surface 
                 (R) 
                 (t) 
                 index (N d ) 
                 (V d ) 
                 Remarks 
               
               
                   
               
             
             
               
                 1 
                 0.8645 
                 0.166 
                 1.59 
                 34.0 
                 First 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 2 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 3 
                 ∞ 
                 0.123 
                 1.48 
                 48.5 
               
               
                 *4  
                 0.7106 
                 0.100 
               
               
                 *5  
                 0.7466 
                 0.224 
                 1.59 
                 34.0 
                 Second 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 6 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 7 
                 ∞ 
                 0.470 
               
               
                 8 
                 ∞ 
                 — 
                   
                   
                 Imaging 
               
               
                   
                   
                   
                   
                   
                 plane 
               
               
                   
               
               
                 wherein * indicates an aspherical surface, and a fourth surface that is the image-side surface of the third lens element and a fifth surface that is the object-side surface of the fourth lens element are formed of aspherical surfaces in the first embodiment. 
               
             
          
         
       
     
         [0083]    Aspherical coefficients of the first embodiment, obtained by Equation 1, are as shown in following Table 2. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
               
               
                 surface 
                 K 
                 A 
                 B 
                 C 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 4 
                 −14.2594 
                 0.5923 
                 3.2874 
                 −7.8026 
               
               
                 5 
                 −10.8461 
                 0.0399 
                 0.4377 
                 −0.3847 
               
               
                   
               
             
          
         
       
     
       Second Embodiment 
       [0084]    Following Table 3 illustrates numerical values according to the second embodiment of the present invention. 
         [0085]    Also,  FIG. 3  is a diagram illustrating a lens configuration of a subminiature optical system according to the second embodiment of the present invention and  FIG. 4  illustrates aberrations of the optical system of  FIG. 3 , in which (a) illustrates a spherical aberration, (b) illustrates astigmatism, and (c) illustrates a distortion, respectively. 
         [0086]    In the present embodiment, a viewing angle is 66 degrees, a f-number is 3.0, a distance TL from the object-side surface  1  of the first lens element LE 1  to the imaging plane  8  is 1.935 mm, and an effective focal length f of the optical system is 1.41 mm. 
         [0087]    In Table 3, a unit of a curvature radius R, a thickness, and a distance t is mm. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                 Thickness 
                   
                   
                   
               
               
                   
                 Curvature 
                 or 
                   
                 Abbe 
               
               
                 Number of 
                 radius 
                 distance 
                 Refractive 
                 number 
               
               
                 surface 
                 (R) 
                 (t) 
                 index (N d ) 
                 (V d ) 
                 Remarks 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 *1 
                 0.9178 
                 0.110 
                 1.59 
                 34.0 
                 First 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 2 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 3 
                 ∞ 
                 0.150 
                 1.48 
                 48.5 
               
               
                 *4 
                 0.6762 
                 0.105 
               
               
                 *5 
                 0.7212 
                 0.220 
                 1.59 
                 34.0 
                 Second 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 6 
                 ∞ 
                 0.400 
                 1.52 
                 54.6 
               
               
                 7 
                 ∞ 
                 0.550 
               
               
                 8 
                 ∞ 
                 — 
                   
                   
                 Imaging 
               
               
                   
                   
                   
                   
                   
                 plane 
               
               
                   
               
               
                 wherein * indicates an aspherical surface, and a first surface that is the object-side surface of the first lens element, a fourth surface that is the image-side surface of the third lens element and a fifth surface that is the object-side surface of the fourth lens element are formed of aspherical surfaces in the second embodiment. 
               
             
          
         
       
     
         [0088]    The aspherical coefficients of the second embodiment, obtained by Equation 3, are as shown in following Table 4. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
               
               
                 surface 
                 K 
                 A 
                 B 
                 C 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 0.1600 
                 −0.0803 
                   
                   
               
               
                 4 
                 −20.6679 
                 1.1443 
                 −0.3321 
                 −2.1492 
               
               
                 5 
                 −12.3249 
                 0.2591 
                 −0.1614 
                 0.0952 
               
               
                   
               
             
          
         
       
     
       Third Embodiment 
       [0089]    Following Table 5 illustrates numerical values according to the third example of the present invention. 
         [0090]    Also,  FIG. 5  is a diagram illustrating a lens configuration of the subminiature optical system according to the second embodiment of the present invention and  FIG. 6  illustrates aberrations of the optical system of  FIG. 5 , in which (a) illustrates a spherical aberration, (b) illustrates astigmatism, and (c) illustrates a distortion, respectively. 
         [0091]    In the present embodiment, a viewing angle is 66 degrees, a f-number is 3.0, a distance TL from the object-side surface  1  of the first lens element LE 1  to the imaging plane  8  is 1.908 mm, and an effective focal length f of the optical system is 1.33 mm. 
         [0092]    In Table 5, a unit of a curvature radius R, a thickness, and a distance t is mm. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
               
                   
                   
                 Thickness 
                   
                   
                   
               
               
                   
                 Curvature 
                 or 
                   
                 Abbe 
               
               
                 Number of 
                 radius 
                 distance 
                 Refractive 
                 number 
               
               
                 surface 
                 (R) 
                 (t) 
                 index (N d ) 
                 (V d ) 
                 Remarks 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 0.8759 
                 0.220 
                 1.59 
                 34.0 
                 First 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 2 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 3 
                 ∞ 
                 0.150 
                 1.48 
                 48.5 
               
               
                 *4 
                 0.7693 
                 0.108 
               
               
                 *5 
                 0.7640 
                 0.230 
                 1.59 
                 34.0 
                 Second 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 6 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 7 
                 ∞ 
                 0.400 
               
               
                 8 
                 ∞ 
                 — 
                   
                   
                 Imaging 
               
               
                   
                   
                   
                   
                   
                 plane 
               
               
                   
               
               
                 wherein * indicates an aspherical surface, and a fourth surface that is the image-side surface of the third lens element and a fifth surface that is the object-side surface of the fourth lens element are formed of aspherical surfaces in the third embodiment. 
               
             
          
         
       
     
         [0093]    The aspherical coefficients of the third embodiment, obtained by Equation 1, are as shown in following Table 6. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
               
               
                 surface 
                 K 
                 A 
                 B 
                 C 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 4 
                 −20.8658 
                 0.7448 
                 3.5191 
                 −13.3958 
               
               
                 5 
                 −13.4559 
                 0.2062 
                 0.0203 
                 −0.0589 
               
               
                   
               
             
          
         
       
     
       Fourth Embodiment 
       [0094]    Following Table 7 illustrates numerical values according to the fourth example of the present invention. 
         [0095]    Also,  FIG. 7  is a diagram illustrating a lens configuration of the subminiature optical system according to the fourth embodiment of the present invention and  FIG. 8  illustrates aberrations of the optical system of  FIG. 7 , in which (a) illustrates a spherical aberration, (b) illustrates astigmatism, and (c) illustrates a distortion, respectively. 
         [0096]    In the present embodiment, a viewing angle is 66 degrees, an f-number is 3.0, a distance TL from the object-side surface  1  of the first lens element LE 1  to the imaging plane  8  is 1.922 mm, and an effective focal length f of the optical system is 1.42 mm. 
         [0097]    In Table 7, a unit of a curvature radius R, a thickness, and a distance t is mm. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 7 
               
               
                   
               
               
                   
                   
                 Thickness 
                   
                   
                   
               
               
                   
                 Curvature 
                 or 
                   
                 Abbe 
               
               
                 Number of 
                 radius 
                 distance 
                 Refractive 
                 number 
               
               
                 surface 
                 (R) 
                 (t) 
                 index (N d ) 
                 (V d ) 
                 Remarks 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 0.8866 
                 0.140 
                 1.59 
                 34.0 
                 First 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 2 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 3 
                 ∞ 
                 0.130 
                 1.48 
                 48.5 
               
               
                 *4 
                 0.6959 
                 0.110 
               
               
                 *5 
                 0.7703 
                 0.220 
                 1.59 
                 34.0 
                 Second 
               
               
                   
                   
                   
                   
                   
                 lens 
               
               
                 6 
                 ∞ 
                 0.400 
                 1.52 
                 54.5 
               
               
                 7 
                 ∞ 
                 0.522 
               
               
                 8 
                 ∞ 
                 — 
                   
                   
                 Imaging 
               
               
                   
                   
                   
                   
                   
                 plane 
               
               
                   
               
               
                 wherein * indicates an aspherical surface, and a fourth surface that is the image-side surface of the third lens element and a fifth surface that is the object-side surface of the fourth lens element are formed of aspherical surfaces in the fourth embodiment. 
               
             
          
         
       
     
         [0098]    The aspherical coefficients of the fourth embodiment, obtained by Equation 1, are as shown in following Table 8. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Number of 
                   
                   
                   
                   
               
               
                 surface 
                 K 
                 A 
                 B 
                 C 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 4 
                 −18.5495 
                 1.3462 
                 −0.5564 
                 −2.9774 
               
               
                 5 
                 −12.1209 
                 0.2851 
                 −0.1210 
                 0.0225 
               
               
                   
               
             
          
         
       
     
         [0099]    On the other hand, values obtained by Conditional Expressions 1 to 3 with respect to the first to fourth embodiments are as following Table 9. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
               
                   
                 Conditional 
                 Conditional 
                 Conditional 
               
               
                   
                 Expression 1 
                 Expression 2 
                 Expression 3 
               
               
                   
                 (r4/r5) 
                 (D12/TL) 
                 (r1/f) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 First 
                 0.9518 
                 0.0531 
                 0.6437 
               
               
                   
                 Embodiment 
               
               
                   
                 Second 
                 0.9376 
                 0.0543 
                 0.6509 
               
               
                   
                 Embodiment 
               
               
                   
                 Third 
                 1.0069 
                 0.0566 
                 0.6586 
               
               
                   
                 Embodiment 
               
               
                   
                 Fourth 
                 0.9035 
                 0.0572 
                 0.6243 
               
               
                   
                 Embodiment 
               
               
                   
                   
               
             
          
         
       
     
         [0100]    Via the described embodiments, it may be known that it is possible to obtain the subminiature optical system having excellent aberration characteristics as illustrated in  FIGS. 2 ,  4 ,  6 , and  8 . 
         [0101]    While the present invention has been shown and described in connection with the exemplary embodiments, it will be apparent to those skilled in the art that modifications and variations can be made without departing from the spirit and scope of the invention as defined by the appended claims.