Patent Publication Number: US-2021191089-A1

Title: Telephoto lens

Description:
FIELD 
     The subject matter herein generally relates to imaging, and more particularly to a telephoto lens. 
     BACKGROUND 
     Many smart phones have dual lenses or even multiple lenses. The lenses include lens for black and white, for color, and a wide-angle lens with a telephoto lens. The wide-angle lens with a telephoto lens not only has a wide field of view, but also performs long-distance capture. Thus, the wide-angle lens with a telephoto lens is the most common combination. 
     The telephoto lens needs to have the following characteristics: (1) Long focal length: the longer the focal length, the more distant the object can be. In addition, it can also be used for close-up shots, and the depth of field can be controlled to blur the background for creating a different visual hierarchy; (2) Narrow field of view: in contrast to the wide-angle lens, the narrow field of view can eliminate unnecessary background elements and reduce image distortion. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Implementations of the present disclosure will now be described, by way of embodiments, with reference to the attached figures. 
         FIG. 1  is a schematic structural diagram of a telephoto lens according to a first embodiment of the present disclosure. 
         FIG. 2  is a characteristic curve diagram of imaging field curvatures of the first embodiment of a telephoto lens. 
         FIG. 3  is a distortion characteristic curvature of the telephoto lens. 
         FIG. 4  is a characteristic curve diagram of modulation transfer function of the telephoto lens. 
         FIG. 5  is a schematic structural diagram of a telephoto lens according to a second embodiment of the present disclosure. 
         FIG. 6  is a characteristic curve diagram of imaging field curvatures of the second embodiment of a telephoto lens. 
         FIG. 7  is a distortion characteristic curvature of the telephoto lens. 
         FIG. 8  is a characteristic curve diagram of modulation transfer function of the telephoto lens. 
     
    
    
     DETAILED DESCRIPTION 
     It will be appreciated that for simplicity and clarity of illustration, where appropriate, reference numerals have been repeated among the different figures to indicate corresponding or analogous elements. Additionally, numerous specific details are set forth in order to provide a thorough understanding of the embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein can be practiced without these specific details. In other instances, methods, procedures and components have not been described in detail so as not to obscure the related relevant feature being described. The drawings are not necessarily to scale and the proportions of certain parts may be exaggerated to better illustrate details and features. The description is not to be considered as limiting the scope of the embodiments described herein. 
     The term “comprising” means “including, but not necessarily limited to”; it specifically indicates open-ended inclusion or membership in a so-described combination, group, series, and the like. 
       FIG. 1  shows an embodiment of a telephoto lens (telephoto lens  100 ). The telephoto lens  100  can be used for cameras of mobile phones, notebook computers, desktop computers, game consoles, LCD TVs, etc., or any products that require optical lenses. As a lens for image-capturing at long distances, the traditional 35 mm film focal length (35 mm EFL) has a conversion to the total focal length (F) according to formula F=(D*EFL)/43.3; the normal lens for 35 mm film has focal length of 50 mm, but when such focal length is &gt;50 mm, it is defined as a telephoto lens. 
     The 35 mm EFL=(F*43.3)/D=(6*43.3)/5.04=51.5 mm&gt;50 mm, which indicates a telephoto lens in the present disclosure. 
     The telephoto lens  100  sequentially includes from the object side to imaging side a first lens L 1  with positive refractive power, a second lens L 2  with negative refractive power, and a third lens L 3  with negative refractive power, a fourth lens L 4  with positive refractive power, a fifth lens L 5  with negative refractive power, a sixth lens L 6  with positive refractive power, a diaphragm  10 , a filter  20 , and an imaging surface  30 . 
     The convexity/concavity of the object side or of the imaging side included in the first to sixth lenses L 1  to L 6  can be determined by the radius of curvature in the following Table A or Table B being positive or negative. If an odd-numbered surface is regular, it is convex relative to the object side, and if an even-numbered surface is regular, it is concave relative to the imaging side. If the odd-numbered surface is negative, it is concave relative to the object side; if the even-numbered surface is negative, it is convex relative to the imaging side. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE A 
               
               
                   
               
               
                   
                   
                 Radius of 
                   
                   
                   
               
               
                   
                   
                 curvature 
                 thickness 
                 Refractive 
                 Abbe 
               
               
                 surface 
                 Types 
                 (mm) 
                 (mm) 
                 index 
                 number 
               
               
                   
               
             
            
               
                 Object 
                 flat 
                 gigantic 
                 gigantic 
                 — 
                 — 
               
               
                 air 
                 flat 
                 gigantic 
                 0.00 
                 — 
                 — 
               
               
                 S1 
                 Aspherical 
                 0.66 
                 0.92 
                 1.54 
                 56.00 
               
               
                 S2 
                 Aspherical 
                 −0.08 
                 0.20 
                 — 
                 — 
               
               
                 S3 
                 Aspherical 
                 0.04 
                 0.29 
                 1.66 
                 20.40 
               
               
                 S4 
                 Aspherical 
                 0.44 
                 0.22 
                 — 
                 — 
               
               
                 diaphragm 
                 flat 
                 gigantic 
                 0.04 
                 — 
                 — 
               
               
                 10 
                   
                   
                   
                   
                   
               
               
                 S5 
                 Aspherical 
                 0.11 
                 0.32 
                 1.54 
                 56.00 
               
               
                 S6 
                 Aspherical 
                 0.22 
                 0.34 
                 — 
                 — 
               
               
                 S7 
                 Aspherical 
                 −0.40 
                 0.37 
                 1.66 
                 20.40 
               
               
                 S8 
                 Aspherical 
                 −0.39 
                 0.98 
                 — 
                 — 
               
               
                 S9 
                 Aspherical 
                 −0.02 
                 0.42 
                 1.54 
                 56.00 
               
               
                 S10 
                 Aspherical 
                 0.26 
                 0.11 
                 — 
                 — 
               
               
                 S11 
                 Aspherical 
                 0.15 
                 0.52 
                 1.66 
                 20.40 
               
               
                 S12 
                 Aspherical 
                 0.06 
                 0.32 
                 — 
                 — 
               
               
                 filter 20 
                 flat 
                 gigantic 
                 0.23 
                 1.52 
                 54.50 
               
               
                 air 
                 flat 
                 gigantic 
                 0.33 
                 — 
                 — 
               
               
                 Imaging 
                 flat 
                 gigantic 
                 — 
                 — 
                 — 
               
               
                 surface 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE B 
               
             
            
               
                   
               
               
                   
                   
                 Radius 
                   
               
               
                   
                   
                 of 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 curvature 
                 thickness 
                 Refractive 
                 Abbe 
               
               
                 surface 
                 Types 
                 (mm) 
                 (mm) 
                 index 
                 number 
               
               
                   
               
               
                 Object 
                 flat 
                 gigantic 
                 gigantic 
                 — 
                 — 
               
               
                 air 
                 flat 
                 gigantic 
                 0.00 
                 — 
                 — 
               
               
                 S1 
                 Aspherical 
                 0.67 
                 0.92 
                 1.54 
                 56.00 
               
               
                 S2 
                 Aspherical 
                 −0.06 
                 0.20 
                 — 
                 — 
               
               
                 S3 
                 Aspherical 
                 0.04 
                 0.2 
                 1.66 
                 20.40 
               
               
                 S4 
                 Aspherical 
                 0.45 
                 0.22 
                 — 
                 — 
               
               
                 diaphragm 
                 flat 
                 gigantic 
                 0.04 
                 — 
                 — 
               
               
                 10 
                   
                   
                   
                   
                   
               
               
                 S5 
                 Aspherical 
                 0.07 
                 0.32 
                 1.54 
                 56.00 
               
               
                 S6 
                 Aspherical 
                 0.19 
                 0.35 
                 — 
                 — 
               
               
                 S7 
                 Aspherical 
                 −0.41 
                 0.37 
                 1.66 
                 20.40 
               
               
                 S8 
                 Aspherical 
                 −0.40 
                 0.97 
                 — 
                 — 
               
               
                 S9 
                 Aspherical 
                 −0.01 
                 0.42 
                 1.54 
                 56.00 
               
               
                 S10 
                 Aspherical 
                 0.25 
                 0.12 
                 — 
                 — 
               
               
                 S11 
                 Aspherical 
                 0.15 
                 0.52 
                 1.66 
                 20.40 
               
               
                 S12 
                 Aspherical 
                 0.04 
                 0.32 
                 — 
                 — 
               
               
                 filter 20 
                 flat 
                 gigantic 
                 0.23 
                 1.52 
                 54.50 
               
               
                 air 
                 flat 
                 gigantic 
                 0.33 
                 — 
                 — 
               
               
                 Imaging 
                 flat 
                 gigantic 
                 — 
                 — 
                 — 
               
               
                 surface 
               
               
                   
               
            
           
         
       
     
     In an embodiment, the first lens L 1  is a biconvex lens, and includes a first surface S 1  convex toward the object side and a second surface S 2  convex toward the imaging side  30 . 
     The second lens L 2  is a crescent-shaped lens, and includes a third surface S 3  convex toward the object side and a fourth surface S 4  concave toward the imaging side. 
     The third lens L 3  is a crescent-shaped lens and includes a fifth surface S 5  convex toward the object side and a sixth surface S 6  concave toward the imaging side. 
     The fourth lens L 4  is a crescent-shaped lens. The fourth lens L 4  includes a seventh surface S 7  sunken toward the object side and an eighth surface S 8  convex toward the imaging side. 
     The fifth lens L 5  is a crescent-shaped lens. The fifth lens L 5  includes a ninth surface S 9  sunken toward the object side and a tenth surface S 10  sunken toward the imaging side. 
     The sixth lens L 6  is a crescent-shaped lens. The sixth lens L 6  includes an eleventh surface S 11  convex toward the object side and a twelfth surface S 12  sunken toward the imaging side  30 . 
     The first to twelfth surfaces, S 1 -S 12 , of lenses, are all aspherical. 
     The diaphragm  10  is located between the second lens L 2  and the third lens L 3 . The structure of the telephoto imaging lens  100  is symmetrical with respect to the diaphragm  10 , which effectively reduces the coma influence. The diaphragm  10  limits the light flux passing through the object into the third lens L 3 , and makes the light more symmetrical after the third lens L 3 , so that the coma of the telephoto lens  100  can be corrected. 
     The filter  20  is used to correct deviations in color. 
     In an embodiment, the light enters the first lens L 1 , the second lens L 2 , and the diaphragm  10  from the object side, and then passes through the third lens L 3 , the fourth lens L 4 , the fifth lens L 5 , the sixth lens L 6 , and the filter  20  in sequence to form an image at the imaging side  30 . It is understandable that an image sensor (not shown), such as a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), can be arranged at the imaging side  30  to complete an imaging system. 
     The telephoto lens  100  meets the conditions of formula: 
       (1) 0.85&lt; D/TTL&lt; 1.05   (formula (1));
 
     Wherein, D is the maximum imaging circle diameter on the imaging side  30 ; TTL is the length of the entire telephoto lens  100 , that is, the distance from the center point of a lateral side of the first lens L 1  to the imaging side  30 . 
     Formula (1) limits the range of the ratio of the maximum imaging circle diameter of the telephoto lens  100  to the length of the telephoto lens  100 , which renders the telephoto lens  100  narrow in profile. 
     The telephoto lens  100  further meets the conditions of formula: 
       (2) 0.37&lt;(D*0.5)/F&lt;0.45   (formula (2));
 
     Wherein, F is the focal length of the telephoto lens  100 . The conversion relationship between the field of view (FOV) and the focal length (F) and the maximum imaging circle diameter (D) is: FOV=2*arc tan((D*0.5)/F. That is, the field of view is determined by the focal length (F) and the maximum imaging circle diameter (D). 
     The formula (2) limits the range of the ratio between the maximum imaging circle diameter and the focal length of the telephoto lens  100  to limit the viewing angle range of the telephoto lens. The telephoto lens  100  can have a narrow viewing angle, to eliminate unnecessary background elements and reduce image distortion. 
     The telephoto lens  100  further meets the conditions of this formula: 
       (3) 0.95&lt;| EFL 2/( EFL 1*2)|&lt;1.35   (formula (3));
 
     Wherein, EFL 1  is the combined focal length of the first lens group formed by the first lens L 1  to the fourth lens L 4 , and EFL 2  is the combined focal length of the second lens group formed by the fifth lens L 5  to the sixth lens L 6 . By controlling the ratio of the combined focal length of the first lens L 1 , the second lens L 2 , the third lens L 3  and the fourth lens L 4  to the combined focal length of the fifth lens L 5  and the sixth lens L 6  within a certain range, the fringe field of view can be reduced. Since each surface of the lens has different power of refraction, when the focus position of the front and rear surfaces of the lens is inconsistent with the light, the image will be blurred, which is seen as an aberration. Formula (3) guarantees correction of such aberration by limiting the ratio range between focal lengths. 
     In addition, the formula (3) can also ensure that the power distribution of the telephoto lens  100  is appropriate, thereby reducing the decentering sensitivity of the telephoto lens  100 . 
     The telephoto lens  100  further meets the conditions of this formula: 
       (4) 0.95&lt;(| F 1|+| F 2|+| F 3|)/(| F 5|+| F 6|)&lt;1.05   (formula (4));
 
     Wherein, F 1  is the focal length of the first lens L 1 , F 2  is the focal length of the second lens L 2 , F 3  is the focal length of the third lens L 3 , F 5  is the focal length of the fifth lens L 5 , and F 6  is the focal length of the sixth lens L 6 . A reasonable ratio of the effective focal length of the first lens L 1 , the second lens L 2 , and the third lens L 3  to the effective focal length of the fifth lens L 5  and the sixth lenses lens can effectively reduce the size of the telephoto lens  100 , and avoids concentration of the optical power, facilitating correction of system aberrations. 
     The telephoto lens  100  further meets the conditions of formula: 
       (5) 1.35&lt;| T 5/ ET 5|&lt;1.55   (formula (5));
 
       (6) 1.85&lt;| T 6/ ET 6|&lt;2.15   (formula (6)).
 
     Wherein, T 5  is the center thickness of the fifth lens L 5  on the optical axis, ET 5  is the edge thickness of the fifth lens L 5 , T 6  is the center thickness of the sixth lens L 6 , and ET 6  is the edge thickness of the sixth lens L 6 . 
     Formula (5) limits the ratio range between the center thickness and the edge thickness of the fifth lens L 5 , which limits the size of the fifth lens L 5  to ensure that the fifth lens L 5  has good processability. Formula (6) limits the ratio range between the center thickness and the edge thickness of the sixth lens L 6 , which limits the size of the sixth lens L 6  to ensure that the sixth lens L 6  has good processability. This allows the telephoto lens  100  to have a better ability to balance chromatic aberrations difficulties in processing would exist for fifth and sixth lens which were too thin. Formulas (5) and (6) enable the telephoto lens  100  to have good correction of aberration, and at the same time have a small curvature of field. 
     The telephoto lens  100  further meets the conditions of formula: 
       (7) −1.05&lt; SF 5&lt;−0.75   (formula (7)); and
 
       (8) 1.65&lt; SF 6&lt;2.65, where  SFi =( C 1 i+C 2 i )/( C 1 i−C 2 i ),  i= 5, 6   (formula (8))
 
     C1i is the radius of curvature of the lens adjacent to the object side, and C2i is the radius of curvature of the lens adjacent to the imaging side. Formulas (7) and (8) enable the telephoto lens  100  to have good correction of aberrations. That is, through the ratio between the radius of curvature of the fifth lens and sixth lens adjacent to the imaging side and the object side, astigmatism and coma of the fifth lens and sixth lens can be effectively balanced, and by constraining the radius of curvature of the imaging side and the object side, the refraction angle of the light beam in the fifth/sixth lens of the telephoto lens  100  can be effectively controlled, so that the lens group can maintain a better imaging quality, and the telephoto lens  100  can have a good processability. 
     The telephoto lens  100  further meets the conditions of formulas: 
       (9) 0.25&lt;| T 56/ ET 56|&lt;0.35   (formula (9)); and
 
       (10) 0.75&lt;( T 56*7)/ T 45&lt;0.95   (formula (10)).
 
     Wherein, T 56  is the center interval thickness between the fifth lens L 5  and the sixth lens L 6 , ET 56  is the edge interval thickness between the fifth lens L 5  and the sixth lens L 6 , T 45  is the center interval thickness between the fourth lens L 4  and the fifth lens L 5 . Control within reasonable limits of the ratio of the center interval thickness between the fifth lens L 5  and the sixth lens L 6  to the edge interval thickness between the fifth lens L 5  and the sixth lens L 6 , and the ratio of the edge interval thickness between the fifth lens L 5  and the sixth lens L 6  to center interval thickness between the fourth lens L 4  and the fifth lens L 5  results in reducing the risk of ghosting caused by the telephoto lens  100 , that is, formulas (9) and (10) make the telephoto lens  100  effective in correcting aberrations. 
     By this disclosure, the volume of the lenses is reduced, and the processability of the lenses is improved by reasonably distributing the focal power, surface shape, center thickness of each lens, and distance between each lens. The lenses in the group herein can be applied to portable electronic products. The lens group is also ultra-thin, with long focal length, and narrow viewing angle to produce excellent imaging quality. 
     All lens surfaces, S 1 -S 12 , are aspherical, and satisfy the aspherical surface formula: 
     
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       
                         c 
                          
                         
                           r 
                           2 
                         
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   K 
                                 
                                 ) 
                               
                                
                               
                                 c 
                                 2 
                               
                                
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         A 
                         4 
                       
                        
                       
                         h 
                         4 
                       
                     
                     + 
                     
                       
                         A 
                         6 
                       
                        
                       
                         h 
                         6 
                       
                     
                     + 
                     
                       
                         A 
                         8 
                       
                        
                       
                         h 
                         8 
                       
                     
                     + 
                     
                       
                         A 
                         10 
                       
                        
                       
                         h 
                         
                           1 
                            
                           0 
                         
                       
                     
                     + 
                     
                       
                         A 
                         12 
                       
                        
                       
                         h 
                         
                           1 
                            
                           2 
                         
                       
                     
                     + 
                     
                       
                         A 
                         14 
                       
                        
                       
                         h 
                         
                           1 
                            
                           4 
                         
                       
                     
                     + 
                     
                       
                         A 
                         16 
                       
                        
                       
                         h 
                         
                           1 
                            
                           6 
                         
                       
                     
                     + 
                     
                       
                         A 
                         18 
                       
                        
                       
                         h 
                         18 
                       
                     
                     + 
                     
                       
                         A 
                         
                           2 
                            
                           0 
                         
                       
                        
                       
                         h 
                         
                           2 
                            
                           0 
                         
                       
                     
                     + 
                     
                       
                         A 
                         
                           2 
                            
                           2 
                         
                       
                        
                       
                         h 
                         
                           2 
                            
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   
                     ( 
                     
                       formula 
                        
                       
                           
                       
                        
                       
                         ( 
                         AS 
                         ) 
                       
                     
                     ) 
                   
                   . 
                 
               
             
           
         
       
     
     Wherein, Z is the displacement value from the optical axis at the height of h along the optical axis, c is the radius of curvature, h is the lens height, K is the conical constant, and A4 is four times power of aspheric coefficient, A6 is six times power of aspheric coefficient, A8 is eight times power of aspheric coefficient, A10 is ten times power of aspheric coefficient, A12 is twelve times of aspheric coefficient, A14 is fourteen times of aspheric coefficient, and A16 is sixteen times aspheric coefficient, A18 is eighteen times of aspherical coefficient, A20 is twenty times of aspherical coefficient, and A22 is twenty-two times of aspherical coefficient. 
     By substituting the data in Tables 1-4 (see below) into the formula (AS), the aspheric shape of each lens in the telephoto lens  100  of the first embodiment can be obtained. By substituting the data in Tables 5-7 into the formula (AS), the aspherical shape of each lens in the telephoto lens  100  of the second embodiment can be obtained. 
     The First Embodiment 
     The lenses of the telephoto lens  100  in the first embodiment satisfy the conditions in Table 1 to Table 4. F# in Table 4 and Table 8 refers to the diaphragm value of the telephoto lens  100 . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 (repeating Table A) 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 Radius of 
                   
                   
                   
               
               
                   
                   
                 curvature 
                 thickness 
                 Refractive 
                 Abbe 
               
               
                 surface 
                 Types 
                 (mm) 
                 (mm) 
                 index 
                 number 
               
               
                   
               
               
                 Object 
                 flat 
                 gigantic 
                 gigantic 
                 — 
                 — 
               
               
                 air 
                 flat 
                 gigantic 
                 0.00 
                 — 
                 — 
               
               
                 S1 
                 Aspherical 
                 0.66 
                 0.92 
                 1.54 
                 56.00 
               
               
                 S2 
                 Aspherical 
                 −0.08 
                 0.20 
                 — 
                 — 
               
               
                 S3 
                 Aspherical 
                 0.04 
                 0.29 
                 1.66 
                 20.40 
               
               
                 S4 
                 Aspherical 
                 0.44 
                 0.22 
                 — 
                 — 
               
               
                 diaphragm 
                 flat 
                 gigantic 
                 0.04 
                 — 
                 — 
               
               
                 10 
                   
                   
                   
                   
                   
               
               
                 S5 
                 Aspherical 
                 0.11 
                 0.32 
                 1.54 
                 56.00 
               
               
                 S6 
                 Aspherical 
                 0.22 
                 0.34 
                 — 
                 — 
               
               
                 S7 
                 Aspherical 
                 −0.40 
                 0.37 
                 1.66 
                 20.40 
               
               
                 S8 
                 Aspherical 
                 −0.39 
                 0.98 
                 — 
                 — 
               
               
                 S9 
                 Aspherical 
                 −0.02 
                 0.42 
                 1.54 
                 56.00 
               
               
                 S10 
                 Aspherical 
                 0.26 
                 0.11 
                 — 
                 — 
               
               
                 S11 
                 Aspherical 
                 0.15 
                 0.52 
                 1.66 
                 20.40 
               
               
                 S12 
                 Aspherical 
                 0.06 
                 0.32 
                 — 
                 — 
               
               
                 filter 20 
                 flat 
                 gigantic 
                 0.23 
                 1.52 
                 54.50 
               
               
                 air 
                 flat 
                 gigantic 
                 0.33 
                 — 
                 — 
               
               
                 Imaging 
                 flat 
                 gigantic 
                 — 
                 — 
                 — 
               
               
                 surface 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Aspheric 
                   
                   
                   
                   
                   
                   
               
               
                 coefficient 
                 S1 
                 S2 
                 S3 
                 S4 
                 S5 
                 S6 
               
               
                   
               
             
            
               
                 K 
                 −2.2567E−01 
                 −3.8382E+01  
                 0.0000E+00 
                 −4.3802E+01 
                 −2.0641E+01 
                 2.4572E+01 
               
               
                 A 4   
                  5.4348E−03 
                 3.9799E−02 
                 7.9517E−02 
                  5.4539E−01 
                  6.2961E−02 
                 2.4691E−02 
               
               
                 A 6   
                 −6.3037E−03 
                 8.4132E−03 
                 −3.4107E−02  
                 −1.2874E+00 
                 −3.5280E−02 
                 1.9198E−01 
               
               
                 A 8   
                  2.4569E−02 
                 −3.6821E−02  
                 −5.8847E−03  
                  2.8748E+00 
                  3.7640E−02 
                 −1.1079E+00  
               
               
                 A 10   
                 −2.7786E−02 
                 1.1489E−02 
                 1.1073E−02 
                 −2.9311E+00 
                 −2.8006E−01 
                 1.8933E+00 
               
               
                 A 12   
                  1.4707E−02 
                 3.3158E−02 
                 9.9948E−02 
                 −1.0826E+00 
                  4.7747E−01 
                 −6.0149E−01  
               
               
                 A 14   
                 −2.4706E−03 
                 −3.3223E−02  
                 −1.5342E−01  
                  5.9003E+00 
                  3.4171E−01 
                 −1.2185E+00  
               
               
                 A 16   
                 −1.9611E−04 
                 9.1330E−03 
                 6.3332E−02 
                 −3.9463E+00 
                 −7.8465E−01 
                 6.3845E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Aspheric 
                   
                   
                   
                   
                   
                   
               
               
                 coefficient 
                 S7 
                 S8 
                 S9 
                 S10 
                 S11 
                 S12 
               
               
                   
               
             
            
               
                 K 
                 −4.3895E+01 
                 −3.3607E+01 
                 6.7322E+01 
                  5.8863E−01 
                  7.8402E+00 
                 −1.3159E+01  
               
               
                 A 4   
                 −3.3648E−01 
                 −2.8432E−01 
                 −1.3957E−01  
                 −1.1865E−01 
                 −4.4021E−02 
                 −8.0288E−02  
               
               
                 A 6   
                  3.1238E−01 
                  3.7696E−01 
                 −3.7621E−02  
                 −7.7590E−02 
                 −4.5890E−02 
                 8.8717E−03 
               
               
                 A 8   
                  1.7834E−01 
                 −4.2433E−01 
                 4.3644E−02 
                  7.0548E−02 
                  5.4046E−02 
                 2.2964E−02 
               
               
                 A 10   
                 −1.1057E+00 
                  2.6303E−01 
                 5.4427E−02 
                 −1.6763E−02 
                 −1.9084E−02 
                 −1.0979E−02  
               
               
                 A 12   
                  1.0530E+00 
                  9.8941E−02 
                 −6.1810E−02  
                 −2.7879E−04 
                  2.7563E−04 
                 6.2354E−04 
               
               
                 A 14   
                  9.4359E−01 
                 −1.5690E−01 
                 2.2237E−02 
                  4.2424E−04 
                  1.0021E−03 
                 4.2331E−04 
               
               
                 A 16   
                 −1.2667E+00 
                  3.5525E−02 
                 −2.9017E−03  
                 −4.0149E−05 
                 −1.3754E−04 
                 −6.1998E−05  
               
               
                 A 18   
                 — 
                 — 
                 −1.3489E−05  
                  7.4282E−06 
                 −8.7886E−07 
                 −1.8963E−07  
               
               
                 A 20   
                 — 
                 — 
                 2.8986E−06 
                  1.6583E−06 
                 −4.5188E−08 
                 6.6173E−08 
               
               
                 A 22   
                 — 
                 — 
                 4.2959E−06 
                 −4.9203E−07 
                  8.7817E−08 
                 2.5940E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 F(mm) 
                 F/# 
                 FOV(2ω°) 
                 TTL(mm) 
                 D(mm) 
                 EFL1(mm) 
                 EFL2(mm) 
               
               
                 6.01 
                 2.41 
                  47.41 
                 5.61 
                 5.04 
                 5.38 
                 −10.57  
               
               
                 F1(mm) 
                 F2(mm) 
                 F3(mm) 
                 F5(mm) 
                 F6(mm) 
                 SF5 
                 SF6 
               
               
                 2.55 
                 −3.73  
                 −17.19 
                 −6.54  
                 16.93  
                 −0.84  
                 2.43 
               
               
                 T5(mm) 
                 ET5(mm) 
                 T6(mm) 
                 ET6(mm) 
                 T45(mm) 
                 T56(mm) 
                 ET56(mm) 
               
               
                 0.42 
                 0.29 
                  0.52 
                 0.27 
                 0.98 
                 0.11 
                 0.43 
               
               
                   
               
            
           
         
       
     
       FIG. 1  is a structural diagram of a telephoto lens  100  of the first embodiment. In this embodiment, the field of view of the telephoto lens  100  is 47.41°, and the focal length of the telephoto lens  100  is 6.01 millimeters. That is, when formulas (1) and (2) are satisfied, a telephoto lens  100  with long focal length and narrow field of view can be obtained. In this embodiment, the field curvature and distortion of the telephoto lens  100  are respectively shown in  FIG. 2  to  FIG. 3 . 
     As shown in  FIG. 2 , the curves T and S are the characteristic curves of tangential field curvature and sagittal field curvature. It can be seen from  FIG. 2  that the tangential field curvature and sagittal field curvature of the telephoto lens  100  are controlled within the range of −0.20 mm to 0.20 mm. 
     The curve shown in  FIG. 3  is a distortion characteristic curve of the telephoto lens  100 , and it can be seen from  FIG. 3  that the optical distortion amount of the telephoto lens  100  is controlled within the range of −3.00% to 3.00%. 
       FIG. 4  is a Modulation Transfer Function (MTF) diagram of the telephoto lens  100 , the MTF representing lens resolution. The units of MTF frequency are Line Pair/mm, which means the number of resolvable line pairs per millimeter (mm). One pair of line pairs contains 2 pixels. MTF full frequency is LinePair/2*(Pixel Size). In this embodiment, the maximum imaging circle diameter D=5.04 mm, where 0.5*D=2.52 mm is defined as 1.0 field of view, and 0.8 field of view is 2.52 mm*0.8=2.016 mm. Under the ¼ Nyquist frequency condition (the ¼ frequency in this embodiment is 125 lp/mm), the MTF of the central field of view is &gt;75% (as shown by the curve mc), the MTF of eighty percent of view field is &gt;60% (as shown by the curve mp), and the MTF between the center view field and eighty percent of view field is between 60% and 75%. The telephoto lens  100  of the first embodiment has a high resolution. 
     The Second Embodiment 
     The lenses of a telephoto lens in a second embodiment satisfy the conditions in Table 5 to Table 8. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 (repeating Table B) 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Radius 
                   
               
               
                   
                   
                 of 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 curvature 
                 thickness 
                 Refractive 
                 Abbe 
               
               
                 surface 
                 Types 
                 (mm) 
                 (mm) 
                 index 
                 number 
               
               
                   
               
               
                 Object 
                 flat 
                 gigantic 
                 gigantic 
                 — 
                 — 
               
               
                 air 
                 flat 
                 gigantic 
                 0.00 
                 — 
                 — 
               
               
                 S1 
                 Aspherical 
                 0.67 
                 0.92 
                 1.54 
                 56.00 
               
               
                 S2 
                 Aspherical 
                 −0.06 
                 0.20 
                 — 
                 — 
               
               
                 S3 
                 Aspherical 
                 0.04 
                 0.2 
                 1.66 
                 20.40 
               
               
                 S4 
                 Aspherical 
                 0.45 
                 0.22 
                 — 
                 — 
               
               
                 diaphragm 
                 flat 
                 gigantic 
                 0.04 
                 — 
                 — 
               
               
                 10 
                   
                   
                   
                   
                   
               
               
                 S5 
                 Aspherical 
                 0.07 
                 0.32 
                 1.54 
                 56.00 
               
               
                 S6 
                 Aspherical 
                 0.19 
                 0.35 
                 — 
                 — 
               
               
                 S7 
                 Aspherical 
                 −0.41 
                 0.37 
                 1.66 
                 20.40 
               
               
                 S8 
                 Aspherical 
                 −0.40 
                 0.97 
                 — 
                 — 
               
               
                 S9 
                 Aspherical 
                 −0.01 
                 0.42 
                 1.54 
                 56.00 
               
               
                 S10 
                 Aspherical 
                 0.25 
                 0.12 
                 — 
                 — 
               
               
                 S11 
                 Aspherical 
                 0.15 
                 0.52 
                 1.66 
                 20.40 
               
               
                 S12 
                 Aspherical 
                 0.04 
                 0.32 
                 — 
                 — 
               
               
                 filter 20 
                 flat 
                 gigantic 
                 0.23 
                 1.52 
                 54.50 
               
               
                 air 
                 flat 
                 gigantic 
                 0.33 
                 — 
                 — 
               
               
                 Imaging 
                 flat 
                 gigantic 
                 — 
                 — 
                 — 
               
               
                 surface 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Aspheric 
                   
                   
                   
                   
                   
                   
               
               
                 coefficient 
                 S1 
                 S2 
                 S3 
                 S4 
                 S5 
                 S6 
               
               
                   
               
             
            
               
                 K 
                 −2.4080E−01 
                 −3.8382E+01  
                 0.0000E+00 
                 −4.3802E+01 
                 −2.0641E+01 
                  1.8861E+01 
               
               
                 A 4   
                  5.7762E−03 
                 3.5611E−02 
                 8.5869E−02 
                  5.6433E−01 
                  2.9959E−02 
                 −7.1170E−03 
               
               
                 A 6   
                 −6.2811E−03 
                 9.7832E−03 
                 −3.7965E−02  
                 −1.2854E+00 
                 −8.1250E−04 
                  2.2393E−01 
               
               
                 A 8   
                  2.4436E−02 
                 −3.7379E−02  
                 −4.1524E−03  
                  2.8622E+00 
                  5.0177E−02 
                 −1.0618E+00 
               
               
                 A 10   
                 −2.7831E−02 
                 1.1100E−02 
                 1.4478E−02 
                 −2.9095E+00 
                 −3.1037E−01 
                  1.9140E+00 
               
               
                 A 12   
                  1.4735E−02 
                 3.3423E−02 
                 9.8992E−02 
                 −1.0471E+00 
                  5.0052E−01 
                 −6.0452E−01 
               
               
                 A 14   
                 −2.5137E−03 
                 −3.3303E−02  
                 −1.5973E−01  
                  6.0497E+00 
                  5.3083E−01 
                 −1.2473E+00 
               
               
                 A 16   
                 −2.3118E−04 
                 9.1921E−03 
                 6.8619E−02 
                 −4.2319E+00 
                 −1.1580E+00 
                  7.5891E−01 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 Aspheric 
                   
                   
                   
                   
                   
                   
               
               
                 coefficient 
                 S7 
                 S8 
                 S9 
                 S10 
                 S11 
                 S12 
               
               
                   
               
             
            
               
                 K 
                 −4.3895E+01 
                 −3.1039E+01 
                 6.7322E+01 
                  1.1799E+00 
                  7.8727E+00 
                 −1.3159E+01  
               
               
                 A 4   
                 −4.1320E−01 
                 −3.1646E−01 
                 −1.3426E−01  
                 −1.2103E−01 
                 −4.6393E−02 
                 −7.5507E−02  
               
               
                 A 6   
                  3.2834E−01 
                  3.6145E−01 
                 −3.9164E−02  
                 −7.9265E−02 
                 −4.5810E−02 
                 8.0252E−03 
               
               
                 A 8   
                  1.2053E−01 
                 −4.2313E−01 
                 4.4243E−02 
                  7.1799E−02 
                  5.4003E−02 
                 2.2464E−02 
               
               
                 A 10   
                 −1.1344E+00 
                  2.6377E−01 
                 5.4505E−02 
                 −1.6601E−02 
                 −1.9102E−02 
                 −1.0882E−02  
               
               
                 A 12   
                  1.1426E+00 
                  9.9028E−02 
                 −6.1843E−02  
                 −2.8951E−04 
                  2.7645E−04 
                 6.3469E−04 
               
               
                 A 14   
                  1.1175E+00 
                 −1.5729E−01 
                 2.2208E−02 
                  4.0956E−04 
                  1.0037E−03 
                 4.2388E−04 
               
               
                 A 16   
                 −1.4035E+00 
                  3.7440E−02 
                 −2.9149E−03  
                 −4.5140E−05 
                 −1.3702E−04 
                 −6.2173E−05  
               
               
                 A 18   
                 — 
                 — 
                 −1.7332E−05  
                  6.4596E−06 
                 −7.8478E−07 
                 −2.5556E−07  
               
               
                 A 20   
                 — 
                 — 
                 2.8026E−06 
                  1.6496E−06 
                 −4.5990E−08 
                 5.5896E−08 
               
               
                 A 22   
                 — 
                 — 
                 5.1215E−06 
                 −3.8483E−07 
                  7.8470E−08 
                 2.7032E−08 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 8 
               
               
                   
               
             
            
               
                 F(mm) 
                 F/# 
                 FOV(2ω°) 
                 TTL(mm) 
                 D(mm) 
                 EFL1(mm) 
                 EFL2(mm) 
               
               
                 6.00 
                 2.38 
                  47.62 
                 5.61 
                 5.04 
                 5.48 
                 −14.06  
               
               
                 F1(mm) 
                 F2(mm) 
                 F3(mm) 
                 F5(mm) 
                 F6(mm) 
                 SF5 
                 SF6 
               
               
                 2.53 
                 −3.65  
                 −15.47 
                 −7.00  
                 13.96  
                 −0.93  
                 1.78 
               
               
                 T5(mm) 
                 ET5(mm) 
                 T6(mm) 
                 ET6(mm) 
                 T45(mm) 
                 T56(mm) 
                 ET56(mm) 
               
               
                 0.42 
                 0.28 
                  0.52 
                 0.26 
                 0.97 
                 0.12 
                 0.41 
               
               
                   
               
            
           
         
       
     
       FIG. 5  is a structural diagram of a telephoto lens  100  of the second embodiment. In this embodiment, the field of view (FOV) of the telephoto lens  100  is 47.62°, and the focal length of the telephoto lens  100  is 6.0 millimeters. That is, when formulas (1) and (2) are satisfied, a telephoto lens  100  with long focal length and narrow field of view can be obtained. The field curvature and distortion of the telephoto lens  100  of the second embodiment are respectively shown in  FIG. 6  and  FIG. 7 . As shown in  FIG. 6 , the curves T and S are respectively the characteristic curve of tangential field curvature and the characteristic curve of sagittal field curvature. It can be seen from  FIG. 6  that the tangential field curvature and sagittal field curvature of the telephoto lens  100  are controlled within the range of −0.20 mm to 0.20 mm. 
     Further, the curve shown in  FIG. 7  is the distortion characteristic curve of the telephoto lens  100 . It can be seen from  FIG. 7  that the optical distortion amount of the telephoto lens  100  is controlled within the range of −3.00% to 3.00%. 
     The MTF of the telephoto lens  100  is shown in  FIG. 8 . Under the condition of ¼ Nyquist frequency (the ½ frequency of this embodiment is 125 lp/mm), the MTF of the central field of view is &gt;75% (as shown by the curve mc), the MTF of eighty percent of view field is &gt;60% (as shown by the curve mp), and the MTF between the center view field and eighty percent of view field is between 60% and 75%. In summary, it can be seen that the telephoto lens  100  of the second embodiment has a relatively high resolution. 
     The telephoto lens of the disclosure meets the formulas (1) and (2) and can achieve a long focal length (F) and a narrow field of view (FOV). A longer focal length can be used to shoot distant objects. The longer the focal length, the farther away the target object can be. In addition, it can also be used to zoom in and close-up the subject, and control the depth of field to blur the background, creating a different sense of visual hierarchy. The narrow field of view can eliminate unnecessary background elements and reduce image distortion. Formulas (3)-(10) are used to adjust the aberration of the telephoto lens  100 , ensure that the power distribution of the telephoto lens  100  is appropriate, reduce the decentering sensitivity of the lens system, and have good aberration correction effect. 
     The embodiments shown and described above are only examples. Even though numerous characteristics and advantages of the present technology have been set forth in the foregoing description, together with details of the structure and function of the present disclosure, the disclosure is illustrative only, and changes may be made in the detail, including in matters of shape, size and arrangement of the parts within the principles of the present disclosure up to, and including, the full extent established by the broad general meaning of the terms used in the claims.