Patent Publication Number: US-2023143770-A1

Title: Optical system, optical apparatus, and method for manufacturing optical system

Description:
FIELD 
     The present invention relates to an optical system, an optical apparatus, and a method for manufacturing an optical system. 
     BACKGROUND 
     Optical systems used in optical apparatuses, such as cameras for photographs, electronic still cameras, and video cameras, have been proposed (see, e.g., Patent Literature 1). 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: Japanese Unexamined Patent Publication No. 2018-072457 
     SUMMARY 
     An optical system of the present disclosure includes a plurality of lens groups, at focusing the distances between the lens groups are varied, a final lens group disposed closest to an image side of the lens groups includes at least one lens surface having a pole, and all of the following conditional expressions are satisfied: 
       0.020&lt; Y/f&lt; 0.120 
       0.010&lt; Bf/TL&lt; 0.150 
     where 
     Y is image height, 
     f is the focal length of the optical system, 
     TL is the total optical length of the optical system, and 
     Bf is the back focus of the optical system. 
     A method for manufacturing an optical system of the present disclosure is a method for manufacturing an optical system including a plurality of lens groups, at focusing the distances between the lens groups are varied, a final lens group disposed closest to an image side of the lens groups includes at least one lens surface having a pole, and the method includes arranging so that all of the following conditional expressions are satisfied: 
       0.020&lt; Y/f&lt; 0.120 
       0.010&lt; Bf/TL&lt; 0.150 
     where 
     Y is image height, 
     f is the focal length of the optical system, 
     TL is the total optical length of the optical system, and 
     Bf is the back focus of the optical system. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a cross-sectional view of an optical system of a first example focusing on an object at infinity. 
         FIG.  2 A  shows aberrations of the optical system of the first example focusing on an object at infinity. 
         FIG.  2 B  shows aberrations of the optical system of the first example focusing on a nearby object. 
         FIG.  3    is a cross-sectional view of an optical system of a second example focusing on an object at infinity. 
         FIG.  4 A  shows aberrations of the optical system of the second example focusing on an object at infinity. 
         FIG.  4 B  shows aberrations of the optical system of the second example focusing on a nearby object. 
         FIG.  5    is a cross-sectional view of an optical system of a third example focusing on an object at infinity. 
         FIG.  6 A  shows aberrations of the optical system of the third example focusing on an object at infinity. 
         FIG.  6 B  shows aberrations of the optical system of the third example focusing on a nearby object. 
         FIG.  7    schematically shows a camera including an optical system of the embodiment. 
         FIG.  8    is a flowchart outlining a method for manufacturing an optical system of the embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The following describes an optical system, an optical apparatus, and a method for manufacturing an optical system of an embodiment of the present application. 
     An optical system of the present embodiment includes a plurality of lens groups, at focusing the distances between the lens groups are varied, a final lens group disposed closest to an image side of the lens groups includes at least one lens surface having a pole, and all of the following conditional expressions are satisfied. A pole in the present disclosure refers to a point on a lens surface, other than on an optical axis, at which the tangent plane of the lens surface crosses the optical axis perpendicularly. 
       0.020&lt; Y/f&lt; 0.120  (1)
 
       0.010&lt; Bf/TL&lt; 0.150  (2)
 
     where 
     Y is image height, 
     f is the focal length of the optical system, 
     TL is the total optical length of the optical system, and 
     Bf is the back focus of the optical system. 
     The optical system of the present embodiment, in which the final lens group includes a lens surface having a pole, can reduce axial and off-axis aberrations effectively. 
     The optical system of the present embodiment can correct off-axis aberrations of image height, such as coma aberration, favorably by setting the value of conditional expression (1) less than the upper limit. The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (1) at 0.120. To further ensure the effect of the present embodiment, the upper limit of conditional expression (1) is preferably set at 0.110, 0.100, 0.095, 0.090, 0.085, 0.080, 0.075, 0.070, 0.065, 0.063, or 0.060, more preferably at 0.058. 
     The optical system of the present embodiment can correct chromatic aberration at an appropriate focal length favorably by setting the value of conditional expression (1) greater than the lower limit. The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (1) at 0.020. To further ensure the effect of the present embodiment, the upper limit of conditional expression (1) is preferably set at 0.025, 0.028, 0.030, or 0.033, more preferably at 0.035. 
     In the present embodiment, setting the value of conditional expression (2) less than the upper limit prevents the back focus from being too long and the optical system from upsizing. The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (2) at 0.150. To further ensure the effect of the present embodiment, the upper limit of conditional expression (2) is preferably set at 0.120, 0.100, 0.090, 0.085, or 0.080, more preferably at 0.075. 
     The optical system of the present embodiment can correct off-axis aberrations, such as coma aberration, favorably by setting the value of conditional expression (2) greater than the lower limit. The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (2) at 0.010. To further ensure the effect of the present embodiment, the lower limit of conditional expression (2) is preferably set at 0.013, 0.015, 0.018, or 0.020, more preferably at 0.022. 
     A small-sized optical system of favorable imaging performance can be achieved by the above configuration. 
     In the optical system of the present embodiment, the at least one lens surface having a pole preferably satisfies the following conditional expression: 
       0.02&lt; h/Y&lt; 1.20  (3)
 
     where 
     h is the height from an optical axis of the pole closest to the optical axis on the lens surface having a pole. 
     The optical system of the present embodiment can correct axial aberration and off-axis aberrations, such as coma aberration, distortion, and curvature of field, in a balanced manner by satisfying conditional expression (3). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (3) at 1.20. To further ensure the effect of the present embodiment, the upper limit of conditional expression (3) is preferably set at 1.15, 1.10, 1.05, or 1.00, more preferably at 0.95. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (3) at 0.02. To further ensure the effect of the present embodiment, the lower limit of conditional expression (3) is preferably set at 0.05, 0.10, 0.25, 0.30, 0.35, 0.40, or 0.45, more preferably at 0.50. 
     The optical system of the present embodiment preferably includes one or more positive lenses that are lenses including the lens surface having a pole and that have positive refractive power, and at least one of the one or more positive lenses preferably satisfies the following conditional expression: 
       −0.15&lt;( Dh−Dc )/ rK&lt; 0.00  (4)-1
 
     where 
     Dh is the thickness on an optical axis of a lens including the lens surface having a pole, 
     Dc is the thickness at the pole of the lens including the lens surface having a pole, and 
     rK is the effective radius of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can correct curvature of field favorably and control the position of an exit pupil appropriately by satisfying conditional expression (4)-1. 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (4)-1 at 0.00. To further ensure the effect of the present embodiment, the upper limit of conditional expression (4)-1 is preferably set at −0.03, −0.05, or −0.08, more preferably at −0.10. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (4)-1 at −0.15. To further ensure the effect of the present embodiment, the lower limit of conditional expression (4)-1 is preferably set at −0.13. 
     The optical system of the present embodiment preferably includes one or more negative lenses that are lenses including the lens surface having a pole and that have negative refractive power, and at least one of the one or more negative lenses preferably satisfies the following conditional expression: 
       0.000&lt;( Dh−Dc )/ rK&lt; 0.100  (4)-2
 
     where 
     Dh is the thickness on an optical axis of a lens including the lens surface having a pole, 
     Dc is the thickness at the pole of the lens including the lens surface having a pole, and 
     rK is the effective radius of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can correct curvature of field favorably and control the position of an exit pupil appropriately by satisfying conditional expression (4)-2. 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (4)-2 at 0.100. To further ensure the effect of the present embodiment, the upper limit of conditional expression (4)-2 is preferably set at 0.095, 0.090, 0.085, or 0.080, more preferably at 0.075. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (4)-2 at 0.000. To further ensure the effect of the present embodiment, the lower limit of conditional expression (4)-2 is preferably set at 0.003, more preferably at 0.005. 
     The optical system of the present embodiment preferably satisfies the following conditional expression: 
       0.020&lt; KML/TL&lt; 0.140  (5)
 
     where 
     KML is the distance from the lens surface having a pole closest to an image plane to the image plane. 
     The optical system of the present embodiment can correct curvature of field favorably by setting the value of conditional expression (5) less than the upper limit. The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (5) at 0.140. To further ensure the effect of the present embodiment, the upper limit of conditional expression (5) is preferably set at 0.135, 0.130, 0.125, or 0.120, more preferably at 0.118. 
     The optical system of the present embodiment can prevent reduction in the amount of ambient light by setting the value of conditional expression (5) greater than the lower limit. The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (5) at 0.020. To further ensure the effect of the present embodiment, the lower limit of conditional expression (5) is preferably set at 0.025, 0.030, 0.035, 0.040, 0.045, or 0.050, more preferably at 0.055. 
     In the optical system of the present embodiment, at least one lens including the lens surface having a pole preferably satisfies the following conditional expression: 
       0.70&lt; rK/Y&lt; 1.10  (6)
 
     where 
     rK is the effective radius of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can correct off-axis aberrations, such as coma aberration, distortion, and curvature of field, favorably by satisfying conditional expression (6). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (6) at 1.10. To further ensure the effect of the present embodiment, the upper limit of conditional expression (6) is preferably set at 1.05, 1.00, or 0.98, more preferably at 0.95. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (6) at 0.70. To further ensure the effect of the present embodiment, the lower limit of conditional expression (6) is preferably set at 0.73, 0.75, 0.78, or 0.80, more preferably at 0.82. 
     In the optical system of the present embodiment, at least one lens including the lens surface having a pole preferably satisfies the following conditional expression: 
       −0.40&lt; Bf/fK&lt; 0.40  (7)
 
     where 
     fK is the focal length of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can control the position of an exit pupil appropriately and correct curvature of field favorably by satisfying conditional expression (7). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (7) at 0.40. To further ensure the effect of the present embodiment, the upper limit of conditional expression (7) is preferably set at 0.38, 0.35, or 0.33, more preferably at 0.30. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (7) at −0.40. To further ensure the effect of the present embodiment, the lower limit of conditional expression (7) is preferably set at −0.35, −0.30, −0.25, −0.20, or −0.15, more preferably at −0.10. 
     In the optical system of the present embodiment, at least one lens including the lens surface having a pole preferably satisfies the following conditional expression: 
       25.00&lt;ν dK&lt; 70.00  (8)
 
     where 
     νdK is the Abbe number for d-line of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can correct chromatic aberration favorably by satisfying conditional expression (8). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (8) at 70.00. To further ensure the effect of the present embodiment, the upper limit of conditional expression (8) is preferably set at 68.00 or 66.00, more preferably at 65.00. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (8) at 25.00. To further ensure the effect of the present embodiment, the lower limit of conditional expression (8) is preferably set at 30.00, 35.00, 38.00, or 40.00, more preferably at 42.00. 
     In the optical system of the present embodiment, at least one lens including the lens surface having a pole preferably satisfies the following conditional expression: 
       −1.00&lt; fR/fK&lt; 0.60  (9)
 
     where 
     fR is the focal length of the final lens group, and 
     fK is the focal length of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can control the position of an exit pupil appropriately and correct curvature of field favorably by satisfying conditional expression (9). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (9) at 0.60. To further ensure the effect of the present embodiment, the upper limit of conditional expression (9) is preferably set at 0.55, 0.50, 0.45, or 0.40, more preferably at 0.35. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (9) at −1.00. To further ensure the effect of the present embodiment, the lower limit of conditional expression (9) is preferably set at −0.98, −0.95, or −0.93, more preferably at −0.90. 
     The optical system of the present embodiment preferably satisfies the following conditional expression: 
       −0.50&lt; Bf/rR&lt; 0.20  (10)
 
     where 
     rR is the radius of curvature of a lens surface disposed closest to the image side. 
     The optical system of the present embodiment can control the position of an exit pupil appropriately and correct curvature of field favorably by satisfying conditional expression (10). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (10) at 0.20. To further ensure the effect of the present embodiment, the upper limit of conditional expression (10) is preferably set at 0.15, 0.10, or 0.05, more preferably at 0.02. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (10) at −0.50. To further ensure the effect of the present embodiment, the lower limit of conditional expression (10) is preferably set at −0.48, −0.45, −0.43, −0.40, or −0.38, more preferably at −0.35. 
     In the optical system of the present embodiment, at least one lens including the lens surface having a pole preferably satisfies the following conditional expression: 
       −2.00&lt; fK/f&lt; 0.50  (11)
 
     where 
     fK is the focal length of the lens including the lens surface having a pole. 
     The optical system of the present embodiment can correct axial aberration and off-axis aberrations, such as coma aberration, distortion, and curvature of field, in a balanced manner by satisfying conditional expression (11). 
     The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (11) at 0.50. To further ensure the effect of the present embodiment, the upper limit of conditional expression (11) is preferably set at 0.45, 0.40, 0.35, or 0.30, more preferably at 0.28. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (11) at −2.00. To further ensure the effect of the present embodiment, the lower limit of conditional expression (11) is preferably set at −1.95, −1.90, −1.85, or −1.80, more preferably at −1.75. 
     The optical system of the present embodiment preferably satisfies the following conditional expression. 
       0.20&lt; TL/f&lt; 1.10  (12)
 
     The optical system of the present embodiment can be prevented from upsizing by setting the value of conditional expression (12) less than the upper limit. The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (12) at 1.10. To further ensure the effect of the present embodiment, the upper limit of conditional expression (12) is preferably set at 1.08, 1.05, or 1.03, more preferably at 1.00. 
     The optical system of the present embodiment can correct aberrations favorably by setting the value of conditional expression (12) greater than the lower limit. The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (12) at 0.20. To further ensure the effect of the present embodiment, the lower limit of conditional expression (12) is preferably set at 0.25, 0.30, 0.35, 0.40, or 0.43, more preferably at 0.45. 
     The optical system of the present embodiment preferably satisfies the following conditional expression. 
       0.005&lt; Bf/f&lt; 0.100  (13)
 
     In the present embodiment, setting the value of conditional expression (13) less than the upper limit prevents the back focus from being too long and the optical system from upsizing. The effect of the optical system of the present embodiment can be further ensured by setting the upper limit of conditional expression (13) at 0.100. To further ensure the effect of the present embodiment, the upper limit of conditional expression (13) is preferably set at 0.095, 0.090, 0.085, or 0.080, more preferably at 0.075. 
     The optical system of the present embodiment can prevent an exit pupil from being too near the image plane and correct off-axis aberrations, such as coma aberration, favorably by setting the value of conditional expression (13) greater than the lower limit. The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (13) at 0.005. To further ensure the effect of the present embodiment, the lower limit of conditional expression (13) is preferably set at 0.008, 0.010, or 0.013, more preferably at 0.015. 
     The optical system of the present embodiment preferably includes at least one lens Z satisfying all of the following conditional expressions: 
         ndLZ +(0.01425×ν dLZ )&lt;2.12  (14)
 
       ν dLZ&lt; 35.00  (15)
 
       0.702&lt;θ gFLZ +(0.00316×ν dLZ )  (16)
 
     where 
     ndLZ is the refractive index for d-line of the lens Z, 
     νdLZ is the Abbe number for d-line of the lens Z, and 
     θgFLZ is a partial dispersion ratio of the lens Z and is defined by the following equation: 
       θ gFLZ =( ngLZ−nFLZ )/( nFLZ−nCLZ )
 
     where the refractive indices for g-line, F-line, and C-line of the lens Z are denoted by ngLZ, nFLZ, and nCLZ, respectively. 
     The optical system of the present embodiment having such a configuration can correct aberrations favorably. 
     Setting the value of conditional expression (14) less than the upper limit prevents the Petzval sum from being too small and enables the optical system of the present embodiment to correct curvature of field favorably. The effect of the present embodiment can be further ensured by setting the upper limit of conditional expression (14) at 2.12. To further ensure the effect of the present embodiment, the upper limit of conditional expression (14) is preferably set at 2.10, more preferably at 2.08. 
     The optical system of the present embodiment can correct quadratic variance of axial chromatic aberration favorably by setting the value of conditional expression (15) less than the upper limit. The effect of the present embodiment can be further ensured by setting the upper limit of conditional expression (15) at 35.00. To further ensure the effect of the present embodiment, the upper limit of conditional expression (15) is preferably set at 33.50, 32.50, 31.00, or 30.00, more preferably at 28.50. 
     The optical system of the present embodiment can correct quadratic variance of axial chromatic aberration favorably by setting the value of conditional expression (16) greater than the lower limit. The effect of the present embodiment can be further ensured by setting the lower limit of conditional expression (16) at 0.702. To further ensure the effect of the present embodiment, the upper limit of conditional expression (17) is preferably set at 0.705, 0.708, 0.710, 0.712, or 0.714, more preferably at 0.716. 
     The optical system of the present embodiment preferably includes at least one lens X satisfying the following conditional expression: 
       80.00&lt;ν dLX   (18)
 
     where 
     νdLX is the Abbe number for d-line of the lens X. 
     The optical system of the present embodiment including the lens X satisfying conditional expression (18) can correct chromatic aberration favorably. 
     The effect of the optical system of the present embodiment can be further ensured by setting the lower limit of conditional expression (18) at 80.00. To further ensure the effect of the present embodiment, the lower limit of conditional expression (18) is preferably set at 83.00, 85.00, 88.00, or 90.00, more preferably at 92.50. 
     In the optical system of the present embodiment, a lens group disposed closest to an object side preferably has positive refractive power. 
     A small-sized optical system of favorable imaging performance can be achieved by the above configuration. 
     An optical apparatus of the present embodiment includes the optical system having the above configuration. This enables achieving a small-sized optical apparatus of favorable imaging performance. 
     A method for manufacturing an optical system of the present embodiment is a method for manufacturing an optical system including a plurality of lens groups, at focusing the distances between the lens groups are varied, a final lens group disposed closest to an image side of the lens groups includes at least one lens surface having a pole, and the method includes arranging so that all of the following conditional expressions are satisfied: 
       0.020&lt; Y/f&lt; 0.120  (1)
 
       0.010&lt; Bf/TL&lt; 0.150  (2)
 
     where 
     Y is image height, 
     f is the focal length of the optical system, 
     TL is the total optical length of the optical system, and 
     Bf is the back focus of the optical system. 
     A small-sized optical system of favorable imaging performance can be manufactured by such a method for manufacturing an optical system. 
     Numerical Examples 
     Examples of the present application will be described below with reference to the drawings. 
     First Example 
       FIG.  1    is a cross-sectional view of an optical system of a first example focusing on an object at infinity. 
     The optical system of the present example includes a first lens group G 1  having positive refractive power, a second lens group G 2  having positive refractive power, and a third lens group G 3  having negative refractive power, in order from the object side. 
     The first lens group G 1  includes a biconvex positive lens L 1 , a positive meniscus lens L 2  convex on the object side, a biconvex positive lens L 3 , a biconcave negative lens L 4 , a biconvex positive lens L 5 , and a positive cemented lens composed of a biconcave negative lens L 6  and a biconvex positive lens L 7 , in order from the object side. 
     The second lens group G 2  includes a positive meniscus lens L 8  convex on the object side. 
     The third lens group G 3  includes a negative cemented lens composed of a biconvex positive lens L 9  and a biconcave negative lens L 10 ; an aperture stop S; a negative cemented lens composed of a positive meniscus lens L 11  convex on the image side and a biconcave negative lens L 12 ; a biconcave negative lens L 13 ; a biconvex positive lens L 14 ; a positive cemented lens composed of a biconvex positive lens L 15  and a negative meniscus lens L 16  convex on the image side; a biconvex positive lens L 17 ; and a biconcave negative lens L 18 , in order from the object side. 
     An imaging device (not shown) constructed from CCD, CMOS or the like is disposed on an image plane I. 
     A filter FL 1  is disposed between the optical system of the present example and the image plane I. 
     The optical system of the present example focuses by moving the second lens group G 2  along the optical axis. When the focus is shifted from infinity to a nearby object, the second lens group G 2  moves from the image side toward the object side. 
     In the optical system of the present example, the negative cemented lens composed of the positive meniscus lens L 11  and the negative lens L 12  and the negative lens L 13 , which are lenses included in the third lens group G 3 , are configured as a vibration reduction lens group movable so that movement has a component in a direction perpendicular to the optical axis to correct an image blur. 
     In the optical system of the present example, the object-side lens surface of the positive meniscus lens L 17  and the image-side lens surface of the negative meniscus lens L 18  included in the third lens group G 3  have a pole. The positive meniscus lens L 17  corresponds to a positive lens that is a lens including a lens surface having a pole and that has positive refractive power. In the optical system of the present example, the positive lens L 5  corresponds to the lens Z, and the positive meniscus lens L 2  and the positive lens L 3  each correspond to the lens X. 
     Table 1 below shows specifications of the optical system of the present example. In Table 1, f, Fno, and TL denote the focal length, the f-number, and the total optical length of the optical system focusing on infinity, respectively, and Bf denotes the back focus of the optical system. 
     In [Lens specifications], m denotes the positions of optical surfaces counted from the object side, r the radii of curvature, d the surface-to-surface distances, nd the refractive indices for d-line (wavelength 587.6 nm), and νd the Abbe numbers for d-line. In [Lens specifications], the radius of curvature r=∞ means a plane. In [Lens specifications], the optical surfaces with “*” are aspherical surfaces. 
     In [Aspherical surface data], ASP denotes the optical surface corresponding to the aspherical surface data, K the conic constant, and A4 to A20 the spherical constants. 
     The aspherical surfaces are expressed by expression (a) below, where the height in a direction perpendicular to the optical axis is denoted by y, the distance along the optical axis from the tangent plane at the vertex of an aspherical surface to the aspherical surface at height y (a sag) by S (y), the radius of curvature of a reference sphere (paraxial radius of curvature) by r, the conic constant by K, and the nth-order aspherical coefficient by An. In the examples, the second-order aspherical coefficient A2 is 0. “E-n” denotes “×10 −n .” 
         S ( y )=( y   2   /r )/{1+(1− K×y   2   /r   2 ) 1/2   }+A 4× y 4+ A 6× y 6+ A 8× y   8   +A 10× y   10   +A 12× y   12   +A 14× y   14   +A 16× y   16   +A 18× y   18   +A 20× y   20   (a)
 
     The unit of the focal lengths f, the radii of curvature r, and the other lengths listed in Table 1 is “mm.” However, the unit is not limited thereto because the optical performance of a proportionally enlarged or reduced optical system is the same as that of the original optical system. 
     The above reference symbols in Table 1 will also be used similarly in the tables of the other examples described below. 
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
             
            
               
                 [General specifications] 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 f 
                 390.00 
               
               
                   
                 Fno 
                 2.90 
               
               
                   
                 Bf 
                 28.455 
               
               
                   
                 image height 
                 21.700 
               
               
                   
                 TL 
                 387.455 
               
               
                   
                 2ω 
                 6.34 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Lens specifications] 
               
            
           
           
               
               
               
               
               
               
            
               
                 m 
                 r 
                 d 
                 nd 
                 νd 
                 θgF 
               
               
                   
               
               
                  1) 
                 480.771 
                 9.450 
                   
                 1.518600 
                 69.89 
               
               
                  2) 
                 −1180.201 
                 18.368 
               
               
                  3) 
                 190.470 
                 12.100 
                   
                 1.433837 
                 95.16 
               
               
                  4) 
                 1088.433 
                 88.972 
               
               
                  5) 
                 121.568 
                 12.850 
                   
                 1.433837 
                 95.16 
               
               
                  6) 
                 −317.679 
                 1.750 
               
               
                  7) 
                 −279.152 
                 2.600 
                   
                 1.737999 
                 32.26 
               
               
                  8) 
                 211.486 
                 38.050 
               
               
                  9) 
                 226.884 
                 7.300 
                 1.663820 
                 27.35 
                 0.632 
               
               
                 10) 
                 −226.482 
                 0.300 
               
               
                 11) 
                 −382.831 
                 1.900 
                   
                 1.749504 
                 35.33 
               
               
                 12) 
                 64.198 
                   
                 8.350 
                 1.437001 
                 95.10 
               
               
                 13) 
                 −3151.863 
                 D13 
               
               
                 14) 
                 79.158 
                   
                 5.700 
                 1.627496 
                 59.24 
               
               
                 15) 
                 889.670 
                 D15 
               
               
                 16) 
                 87.296 
                   
                 4.800 
                 1.698950 
                 30.13 
               
               
                 17) 
                 −247.699 
                 1.200 
                   
                 1.881003 
                 40.14 
               
               
                 18) 
                 52.070 
                   
                 7.100 
               
            
           
           
               
               
               
               
               
            
               
                 19&gt; 
                 ∞ 
                 7.032 
                 (aperture stop) 
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 20) 
                 −370.162 
                 2.900 
                   
                 1.846663 
                 23.78 
               
               
                 21) 
                 −85.379 
                 1.200 
                   
                 1.496997 
                 81.61 
               
               
                 22) 
                 78.949 
                   
                 3.884 
               
               
                 23) 
                 −106.294 
                 1.200 
                   
                 1.593190 
                 67.90 
               
               
                 24) 
                 126.247 
                 7.883 
               
               
                 25) 
                 84.389 
                   
                 3.000 
                 1.720467 
                 34.71 
               
               
                 26) 
                 −937.027 
                 35.448 
               
               
                 27) 
                 126.616 
                 7.600 
                   
                 1.595510 
                 39.21 
               
               
                 28) 
                 −67.347 
                 1.200 
                   
                 1.945944 
                 17.98 
               
               
                 29) 
                 −126.151 
                 22.187 
               
               
                 *30)  
                 111.791 
                 6.100 
                   
                 1.612660 
                 44.46 
               
               
                 *31)  
                 −126.654 
                 9.374 
               
               
                 *32)  
                 −69.987 
                 1.200 
                   
                 2.001003 
                 29.13 
               
               
                 *33)  
                 240.688 
                 6.450 
               
               
                 34) 
                 ∞ 
                 2.000 
                   
                 1.516800 
                 63.88 
               
               
                 35) 
                 ∞ 
                 20.005 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 [Aspherical surface data] 
               
               
                   
                   
               
            
           
           
               
            
               
                 ASP: 30th surface 
               
               
                 K: −0.0945 
               
               
                 A4: 0.00E+00 A6: −3.70E−06 A8: 6.64E−10 A10: −4.66E−11 
               
               
                 A12: 3.48E−14 
               
               
                 A14: −1.08E−16 A16: −2.85E−20 A18: 4.77E−23 A20: 3.35E−26 
               
               
                 ASP: 31st surface 
               
               
                 K: 2.8122 
               
               
                 A4: 0.00E+00 A6: −4.69E−06 A8: −1.35E−09 A10: −3.95E−11 
               
               
                 A12: −1.64E−14 
               
               
                 A14: 8.73E−17 A16: −6.66E−20 A18: −6.27E−23 A20: −2.46E−26 
               
               
                 ASP: 32nd surface 
               
               
                 K: 3.0000 
               
               
                 A4: 0.00E+00 A6: −7.94E−06 A8: 9.42E−09 A10: 1.32E−11 
               
               
                 A12: 2.48E−15 
               
               
                 A14: 9.89E−17 A16: 4.73E−29 A18: 6.43E−32 A20: −3.53E−25 
               
               
                 ASP: 33rd surface 
               
               
                 K: −1.0000 
               
               
                 A4: 0.00E+00 A6: −8.82E−06 A8: 1.08E−08 A10: 5.92E−12 
               
               
                 A12: 4.61E−14 
               
               
                 A14: −6.54E−17 A16: −3.08E−29 A18: −7.29E−32 A20: 3.36E−25 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 [Focal length data of groups] 
               
            
           
           
               
               
               
               
            
               
                   
                 Groups 
                 Starting surfaces 
                 Focal lengths 
               
               
                   
                   
               
               
                   
                 G1 
                 1 
                 379.315 
               
               
                   
                 G2 
                 14 
                 138.094 
               
               
                   
                 G3 
                 16 
                 −85.999 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Variable distance data] 
               
            
           
           
               
               
               
            
               
                   
                 At focusing on infinity 
                 At focusing on a nearby object 
               
               
                   
               
               
                 D13 
                 24.000 
                 4.100 
               
               
                 D15 
                 4.000 
                 23.900 
               
               
                   
               
            
           
         
       
     
       FIG.  2 A  shows aberrations of the optical system of the first example focusing on an object at infinity.  FIG.  2 B  shows aberrations of the optical system of the first example focusing on a nearby object. 
     In the graphs of aberrations, FNO and Y denote f-number and image height, respectively. More specifically, the graph of spherical aberration shows the f-number corresponding to the maximum aperture, the graphs of astigmatism and distortion show the maximum of image height, and the graph of coma aberration shows the values of image height. d and g denote d-line and g-line (wavelength 435.8 nm), respectively. In the graph of astigmatism, the solid lines and the broken lines show a sagittal plane and a meridional plane, respectively. The reference symbols in the graphs of aberrations of the present example will also be used in those of the other examples described below. 
     The graphs of aberrations suggest that the optical system of the present example effectively reduces variations in aberrations at focusing and has high optical performance. 
     Second Example 
       FIG.  3    is a cross-sectional view of an optical system of a second example focusing on an object at infinity. 
     The optical system of the present example includes a first lens group G 1  having positive refractive power, a second lens group G 2  having positive refractive power, and a third lens group G 3  having negative refractive power, in order from the object side. 
     The first lens group G 1  includes a positive meniscus lens L 1  convex on the object side, a biconvex positive lens L 2 , a biconvex positive lens L 3 , a biconcave negative lens L 4 , a biconvex positive lens L 5 , and a negative cemented lens composed of a biconcave negative lens L 6  and a positive meniscus lens L 7  convex on the object side, in order from the object side. 
     The second lens group G 2  includes a biconvex positive lens L 8 . 
     The third lens group G 3  includes a positive meniscus lens L 9  convex on the object side; an aperture stop S; a negative cemented lens composed of a biconvex positive lens L 10  and a biconcave negative lens L 11 ; a biconcave negative lens L 12 ; a positive meniscus lens L 13  convex on the object side; a negative cemented lens composed of a biconvex positive lens L 14  and a biconcave negative lens L 15 ; a biconvex positive lens L 16 ; a biconcave negative lens L 17 ; and a biconcave negative lens L 18 , in order from the object side. 
     An imaging device (not shown) constructed from CCD, CMOS or the like is disposed on an image plane I. 
     Filters FL 1  and FL 2  are disposed between the optical system of the present example and the image plane I. 
     The optical system of the present example focuses by moving the second lens group G 2  along the optical axis. When the focus is shifted from infinity to a nearby object, the second lens group G 2  moves from the image side toward the object side. 
     In the optical system of the present example, the object-side lens surface of the negative lens L 18  included in the third lens group G 3  has a pole. The negative lens L 18  corresponds to a negative lens that is a lens including a lens surface having a pole and that has negative refractive power. In the optical system of the present example, the positive lens L 5  corresponds to the lens Z, the positive lenses L 2  and L 3  each correspond to the lens X. 
     Table 2 below shows specifications of the optical system of the present example. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 [General specifications] 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 f 
                 588.00 
               
               
                   
                 Fno 
                 4.09 
               
               
                   
                 Bf 
                 24.200 
               
               
                   
                 image height 
                 21.700 
               
               
                   
                 TL 
                 458.000 
               
               
                   
                 2ω 
                 4.14 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Lens specifications] 
               
            
           
           
               
               
               
               
               
               
            
               
                 m 
                 r 
                 d 
                 nd 
                 νd 
                 θgF 
               
               
                   
               
               
                  1) 
                 318.082 
                 10.293 
                   
                 1.518600 
                 69.89 
               
               
                  2) 
                 2767.474 
                 70.000 
               
               
                  3) 
                 250.000 
                 11.741 
                   
                 1.433837 
                 95.16 
               
               
                  4) 
                 −2625.391 
                 76.022 
               
               
                  5) 
                 117.178 
                 13.094 
                   
                 1.433837 
                 95.16 
               
               
                  6) 
                 −358.058 
                 0.243 
               
               
                  7) 
                 −326.721 
                 2.600 
                   
                 1.737999 
                 32.26 
               
               
                  8) 
                 219.472 
                 44.906 
               
               
                  9) 
                 136.873 
                 7.129 
                 1.663820 
                 27.35 
                 0.632 
               
               
                 10) 
                 −279.195 
                 0.100 
               
               
                 11) 
                 −417.537 
                 1.900 
                   
                 1.800999 
                 34.97 
               
               
                 12) 
                 57.256 
                   
                 8.730 
                 1.437001 
                 95.10 
               
               
                 13) 
                 422.344 
                 D13 
               
               
                 14) 
                 75.383 
                   
                 6.241 
                 1.518230 
                 58.82 
               
               
                 15) 
                 −1118.853 
                 D15 
               
               
                 16) 
                 121.757 
                 1.200 
                   
                 1.497820 
                 82.57 
               
               
                 17) 
                 42.268 
                   
                 8.586 
               
            
           
           
               
               
               
               
               
            
               
                 18&gt; 
                 ∞ 
                 6.500 
                   
                 (aperture stop) 
               
            
           
           
               
               
               
               
               
               
            
               
                 19) 
                 153.272 
                 5.178 
                   
                 1.808090 
                 22.74 
               
               
                 20) 
                 −85.972 
                 1.200 
                   
                 1.772500 
                 49.62 
               
               
                 21) 
                 74.810 
                   
                 3.582 
               
               
                 22) 
                 −107.276 
                 1.200 
                   
                 1.816000 
                 46.59 
               
               
                 23) 
                 255.014 
                 4.500 
               
               
                 24) 
                 45.618 
                   
                 4.111 
                 1.698950 
                 30.13 
               
               
                 25) 
                 130.848 
                 35.282 
               
               
                 26) 
                 102.108 
                 7.814 
                   
                 1.698950 
                 30.13 
               
               
                 27) 
                 −26.600 
                 1.260 
                   
                 1.922860 
                 20.88 
               
               
                 28) 
                 212.812 
                 0.460 
               
               
                 *29)  
                 50.919 
                   
                 10.000 
                 1.647690 
                 33.72 
               
               
                 *30)  
                 −30.632 
                 0.100 
               
               
                 31) 
                 −43.062 
                 1.200 
                   
                 1.593190 
                 67.90 
               
               
                 32) 
                 52.042 
                   
                 50.049 
               
               
                 *33)  
                 −119.867 
                 3.013 
                   
                 1.848500 
                 43.79 
               
               
                 *34)  
                 221837.780 
                   
                 6.000 
               
               
                 35) 
                 ∞ 
                 2.000 
                   
                 1.516800 
                 64.13 
               
               
                 36) 
                 ∞ 
                 14.500 
               
               
                 37) 
                 ∞ 
                 1.600 
                   
                 1.516800 
                 64.13 
               
               
                 38) 
                 ∞ 
                 0.100 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 [Aspherical surface data] 
               
               
                   
                   
               
            
           
           
               
            
               
                 ASP: 29th surface 
               
               
                 K: −3.5347 
               
               
                 A4: 0.00E+00 A6: 3.84E−06 A8: 6.41E−10 A10: −3.33E−12 
               
               
                 A12: 1.1E−14 
               
               
                 ASP: 30th surface 
               
               
                 K: 1.24E+00 
               
               
                 A4: 0.00E+00 A6: 8.39E−06 A8: 4.06E−09 A10: −3.49E−12 
               
               
                 A12: 1.88E−14 
               
               
                 ASP: 33rd surface 
               
               
                 K: 2.32E+01 
               
               
                 A4: 0.00E+00 A6: 6.44E−06 A8: 2.40E−08 A10: −6.37E−11 
               
               
                 A12: 5.19E−14 
               
               
                 ASP: 34th surface 
               
               
                 K: −2.27E+29 
               
               
                 A4: 0.00E+00 A6: 2.46E−06 A8: 2.50E−08 A10: −5.95E−11 
               
               
                 A12: 3.75E−14 
               
               
                   
               
            
           
           
               
            
               
                 [Focal length data of groups] 
               
            
           
           
               
               
               
               
            
               
                   
                 Groups 
                 Starting surfaces 
                 Focal lengths 
               
               
                   
                   
               
               
                   
                 G1 
                 1 
                 445.504 
               
               
                   
                 G2 
                 14 
                 136.523 
               
               
                   
                 G3 
                 16 
                 −44.174 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Variable distance data] 
               
            
           
           
               
               
               
            
               
                   
                 At focusing on infinity 
                 At focusing on a nearby object 
               
               
                   
               
               
                 D13 
                 31.468 
                 17.198 
               
               
                 D15 
                 4.100 
                 18.370 
               
               
                   
               
            
           
         
       
     
       FIG.  4 A  shows aberrations of the optical system of the second example focusing on an object at infinity.  FIG.  4 B  shows aberrations of the optical system of the second example focusing on a nearby object. 
     The graphs of aberrations suggest that the optical system of the present example effectively reduces variations in aberrations at focusing and has high optical performance. 
     Third Example 
       FIG.  5    is a cross-sectional view of an optical system of a third example focusing on an object at infinity. 
     The optical system of the present example includes a first lens group G 1  having positive refractive power, a second lens group G 2  having negative refractive power, and a third lens group G 3  having negative refractive power, in order from the object side. An aperture stop S is disposed between the first lens group G 1  and the second lens group G 2 . 
     The first lens group G 1  includes a positive meniscus lens L 1  convex on the object side; a positive meniscus lens L 2  convex on the object side; a negative meniscus lens L 3  convex on the object side and having a multilayered and glued diffractive optical element GD made of two different materials on the image-side lens surface; a negative cemented lens composed of a biconvex positive lens L 4  and a biconcave negative lens L 5 ; a positive meniscus lens L 6  convex on the object side; and a positive cemented lens composed of a negative meniscus lens L 7  convex on the object side and a positive meniscus lens L 8  convex on the object side, in order from the object side. 
     The second lens group G 2  includes a biconcave negative lens L 9 . 
     The third lens group G 3  includes a positive cemented lens composed of a negative meniscus lens L 10  convex on the object side and a biconvex positive lens L 11 ; a negative cemented lens composed of a biconvex positive lens L 12  and a biconcave negative lens L 13 ; a biconcave negative lens L 14 ; a positive cemented lens composed of a biconvex positive lens L 15  and a biconcave negative lens L 16 ; a negative cemented lens composed of a biconvex positive lens L 17  and a biconcave negative lens L 18 ; a positive cemented lens composed of a biconvex positive lens L 19  and a negative meniscus lens L 20  convex on the image side; and a negative meniscus lens L 21  convex on the image side, in order from the object side. 
     An imaging device (not shown) constructed from CCD, CMOS or the like is disposed on an image plane I. 
     The optical system of the present example focuses by moving the second lens group G 2  along the optical axis. When the focus is shifted from infinity to a nearby object, the second lens group G 2  moves from the object side toward the image side. 
     In the optical system of the present example, the negative cemented lens composed of the positive lens L 12  and the negative lens L 13  and the negative lens L 14 , which are lenses included in the third lens group G 3 , are configured as a vibration reduction lens group movable so that movement has a component in a direction perpendicular to the optical axis to correct an image blur. 
     In the optical system of the present example, the object-side and image-side lens surfaces of the negative meniscus lens L 21  included in the third lens group G 3  has a pole. The negative meniscus lens L 21  corresponds to a negative lens that is a lens including a lens surface having a pole and that has negative refractive power. In the optical system of the present example, the positive meniscus lens L 8  corresponds to the lens Z. 
     Table 3 below shows specifications of the optical system of the present example. 
     [Diffracting optical surface data] shows n (order of diffracted light), λ0 (designed wavelength), and C2 and C4 (phase coefficients) in the following equation (b) representing the phase shape ψ of the diffracting optical surface. 
       ψ( h,n )=(2π/( n×λ 0))×( C 2 h   2   +C 4 h   4 )  (b)
 
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                 [General specifications] 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 f 
                 581.97 
               
               
                   
                 Fno 
                 8.06 
               
               
                   
                 Bf 
                 16.167 
               
               
                   
                 image height 
                 21.600 
               
               
                   
                 TL 
                 269.235 
               
               
                   
                 2ω 
                 4.17 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Lens specifications] 
               
            
           
           
               
               
               
               
               
               
            
               
                 m 
                 r 
                 d 
                 nd 
                 νd 
                 θgF 
               
               
                   
               
               
                  1) 
                 134.048 
                 7.530 
                   
                 1.518600 
                 69.89 
               
               
                  2) 
                 975.941 
                 0.600 
               
               
                  3) 
                 93.756 
                 8.246 
                   
                 1.518600 
                 69.89 
               
               
                  4) 
                 332.255 
                 9.686 
               
               
                  5) 
                 136.607 
                 4.312 
                   
                 1.516800 
                 64.13 
               
               
                  6) 
                 120.104 
                 0.300 
                   
                 1.528300 
                 36.18 
               
               
                  7) 
                 119.767 
                 0.200 
                   
                 1.548900 
                 51.30 
               
               
                  8) 
                 120.755 
                 41.847 
               
               
                  9) 
                 88.622 
                 5.436 
                   
                 1.518600 
                 69.89 
               
               
                 10) 
                 −416.992 
                 2.000 
                   
                 1.903660 
                 31.27 
               
               
                 11) 
                 41.602 
                 5.323 
               
               
                 12) 
                 42.525 
                 5.649 
                   
                 1.518600 
                 69.89 
               
               
                 13) 
                 143.662 
                 14.506 
               
               
                 14) 
                 47.751 
                 2.000 
                   
                 1.903660 
                 31.27 
               
               
                 15) 
                 28.892 
                 4.794 
                 1.663820 
                 27.35 
                 0.632 
               
               
                 16) 
                 112.282 
                 11.734 
               
               
                 17&gt; 
                 ∞ 
                 D17 
                 (aperture stop) 
               
               
                 18) 
                 −1154.419 
                 1.200 
                   
                 1.487490 
                 70.32 
               
               
                 19) 
                 62.576 
                 D19 
               
               
                 20) 
                 310.300 
                 1.200 
                   
                 2.000690 
                 25.46 
               
               
                 21) 
                 26.935 
                 3.449 
                   
                 1.603420 
                 38.03 
               
               
                 22) 
                 −47.327 
                 1.500 
               
               
                 23) 
                 48.394 
                 3.086 
                   
                 1.672700 
                 32.18 
               
               
                 24) 
                 −44.128 
                 1.100 
                   
                 1.497820 
                 82.57 
               
               
                 25) 
                 26.495 
                 2.410 
               
               
                 26) 
                 −53.275 
                 1.100 
                   
                 1.696800 
                 55.52 
               
               
                 27) 
                 43.809 
                 1.500 
               
               
                 28) 
                 24.114 
                 4.701 
                   
                 1.603420 
                 38.03 
               
               
                 29) 
                 −25.443 
                 1.200 
                   
                 1.497820 
                 82.57 
               
               
                 30) 
                 29.757 
                 8.994 
               
               
                 31) 
                 27.240 
                 5.426 
                   
                 1.603420 
                 38.03 
               
               
                 32) 
                 −31.131 
                 1.200 
                   
                 1.772500 
                 49.62 
               
               
                 33) 
                 19.933 
                 0.100 
               
               
                 34) 
                 20.086 
                 7.524 
                   
                 1.603420 
                 38.03 
               
               
                 35) 
                 −18.471 
                 1.200 
                   
                 1.922860 
                 20.88 
               
               
                 36) 
                 −83.172 
                 44.826 
               
               
                 *37)  
                 −82.638 
                 4.000 
                   
                 1.516800 
                 64.13 
               
               
                 *38)  
                 −100.000 
                 16.167 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 [Aspherical surface data] 
               
               
                   
                   
               
            
           
           
               
            
               
                 ASP: 37th surface 
               
               
                 K: 1.0000 
               
               
                 A4: 0.00E+00 A6: 2.01E−05 
               
               
                 ASP: 38th surface 
               
               
                 K: −3.4854 
               
               
                 A4: 0.00E+00 A6: 1.93E−05 A8: −8.37E−09 A10: 7.40E−11 
               
               
                 A12: −1.81E−13 
               
               
                   
               
            
           
           
               
            
               
                 [Diffracting optical surface data] 
               
               
                 GD: 7th surface 
               
            
           
           
               
               
               
               
               
            
               
                   
                 n 
                 λ0 
                 C2 
                 C4 
               
               
                   
                   
               
               
                   
                 1 
                 587.6 
                 −3.59E−05 
                 −9.39E−10 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Focal length data of groups] 
               
            
           
           
               
               
               
               
            
               
                   
                 Groups 
                 Starting surfaces 
                 Focal lengths 
               
               
                   
                   
               
               
                   
                 G1 
                 1 
                 173.592 
               
               
                   
                 G2 
                 18 
                 −121.724 
               
               
                   
                 G3 
                 20 
                 −78.037 
               
               
                   
                   
               
            
           
           
               
            
               
                 [Variable distance data] 
               
            
           
           
               
               
               
            
               
                   
                 At focusing on infinity 
                 At focusing on a nearby object 
               
               
                   
               
               
                 D17 
                 2.053 
                 20.426 
               
               
                 D19 
                 31.136 
                 12.840 
               
               
                   
               
            
           
         
       
     
       FIG.  6 A  shows aberrations of the optical system of the third example focusing on an object at infinity.  FIG.  6 B  shows aberrations of the optical system of the third example focusing on a nearby object. 
     The graphs of aberrations suggest that the optical system of the present example effectively reduces variations in aberrations at focusing and has high optical performance. 
     A small-sized optical system of favorable imaging performance can be achieved according to the above examples. 
     The following is a list of the conditional expressions and the values for the conditional expressions in the examples. 
     Y is image height, f is the focal length of the optical system, TL is the total optical length of the optical system, and Bf is the back focus of the optical system. h is the height from an optical axis of the pole closest to the optical axis on the lens surface having a pole. Dh is the thickness on an optical axis of a lens including the lens surface having a pole, Dc is the thickness at the pole of the lens including the lens surface having a pole, and rK is the effective radius of the lens including the lens surface having a pole. 
     KML is the distance from the lens surface having a pole closest to an image plane to the image plane. fK is the focal length of the lens including the lens surface having a pole. νdK is the Abbe number for d-line of the lens including the lens surface having a pole. fR is the focal length of the final lens group. rR is the radius of curvature of a lens surface disposed closest to the image side. 
     ndLZ is the refractive index for d-line of the lens Z, and θgFLZ is a partial dispersion ratio of the lens Z and is defined by the following equation: 
       θ gFLZ =( ngLZ−nFLZ )/( nFLZ−nCLZ )
 
     where the refractive indices for g-line, F-line, and C-line of the lens Z are denoted by ngLZ, nFLZ, and nCLZ, respectively. 
     νdLX is the Abbe number for d-line of the lens X. 
     [List of Conditional Expressions and their Values] 
     
       
         
           
               
               
               
               
             
               
                   
               
               
                 Conditional expressions: 
                 First example 
                 Second example 
                 Third example 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 (1) 
                 Y/f: 
                 0.056 
                 0.037 
                 0.037 
               
               
                 (2) 
                 Bf/TL: 
                 0.073 
                 0.053 
                 0.060 
               
               
                 (3) 
                 h/Y: 
                 0.724 
                 0.915 
                 0.571 
               
               
                 (4) 
                 (Dh-Dc)/rK: 
                 −0.105 
                 0.073 
                 0.009 
               
               
                 (5) 
                 KML/TL: 
                 0.073 
                 0.053 
                 0.060 
               
               
                 (6) 
                 rK/Y: 
                 0.943 
                 0.924 
                 0.838 
               
               
                 (7) 
                 Bf/fK: 
                 0.291 
                 −0.171 
                 −0.016 
               
               
                 (8) 
                 vdK: 
                 29.13 
                 43.79 
                 64.13 
               
               
                 (9) 
                 fR/fK: 
                 −0.879 
                 0.313 
                 0.078 
               
               
                 (10)  
                 Bf/rR: 
                 0.118 
                 0.000 
                 −0.162 
               
               
                 (11)  
                 fK/f: 
                 0.251 
                 −0.240 
                 −1.717 
               
               
                 (12)  
                 TL/f: 
                 0.993 
                 0.779 
                 0.463 
               
               
                 (13)  
                 Bf/f: 
                 0.073 
                 0.041 
                 0.028 
               
               
                 (14)  
                 ndLZ + (0.01425*vdLZ): 
                 2.054 
                 2.054 
                 2.054 
               
               
                 (15)  
                 vdLZ: 
                 27.35 
                 27.35 
                 27.35 
               
               
                 (16)  
                 θgFLZ + (0.00316*vdLZ: 
                 0.718 
                 0.718 
                 0.718 
               
               
                 (17)  
                 vdLX: 
                 95.16 
                 95.16 
               
               
                   
               
            
           
         
       
     
     The above examples illustrate specific examples of the present invention, and the present invention is not limited thereto. The following details can be appropriately employed unless the optical performance of the optical system of the embodiment of the present application is lost. 
     The lens surfaces of the lenses constituting any of the optical systems of the above examples may be covered with antireflection coating having high transmittance in a wide wavelength range. This reduces flares and ghosts, and enables achieving optical performance with high contrast. 
     Next, a camera including the optical system of the present embodiment is described with reference to  FIG.  23   . 
       FIG.  23    schematically shows a camera including the optical system of the present embodiment. 
     The camera  1  is a “mirror-less camera” of an interchangeable lens type including the optical system according to the first example as an imaging lens  2 . 
     In the camera  1 , light from an object (subject) (not shown) is condensed by the imaging lens  2  and reaches an imaging device  3 . The imaging device  3  converts the light from the subject to image data. The image data is displayed on an electronic view finder  4 . This enables a photographer who positions his/her eye at an eye point EP to observe the subject. 
     When a release button (not shown) is pressed by the photographer, the image data is stored in a memory (not shown). In this way, the photographer can take a picture of the subject with the camera  1 . 
     The optical system of the first example included in the camera  1  as the imaging lens  2  is a small-sized optical system of favorable optical performance. Thus the camera  1  can be small and achieve favorable optical performance. A camera configured by including the optical system of the second or third example as the imaging lens  2  can have the same effect as the camera  1 . 
     Finally, a method for manufacturing an optical system of the present embodiment is described in outline with reference to  FIG.  8   . 
       FIG.  8    is a flowchart outlining a method for manufacturing an optical system of the present embodiment. 
     The method for manufacturing an optical system of the present embodiment shown in  FIG.  8    is a method for manufacturing an optical system including a plurality of lens groups and includes the following steps S 1  to S 4 : 
     Step S 1 : preparing a plurality of lens groups; 
     Step S 2 : arranging so that at focusing the distances between the lens groups are varied; 
     Step S 3 : arranging so that a final lens group disposed closest to an image side of the lens groups includes at least one lens surface having a pole; and 
     Step S 3 : making the optical system satisfy all of the following conditional expressions: 
       0.020&lt; Y/f&lt; 0.120  (1)
 
       0.010&lt; Bf/TL&lt; 0.150  (2)
 
     where 
     Y is image height, 
     f is the focal length of the optical system, 
     TL is the total optical length of the optical system, and 
     Bf is the back focus of the optical system. 
     A small-sized optical system of favorable imaging performance can be manufactured by the method for manufacturing an optical system of the present embodiment. 
     Note that those skilled in the art can make various changes, substitutions, and modifications without departing from the spirit and scope of the present invention. 
     REFERENCE SIGNS LIST 
     
         
         
           
             S aperture stop 
             I image plane 
               1  camera 
               2  imaging lens 
               3  imaging device