Patent Publication Number: US-2022221690-A1

Title: Optical system and image pickup apparatus

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an optical system and an image pickup apparatus. 
     Description of the Related Art 
     A technology called wafer level optics has conventionally been known as a method for manufacturing a small optical system at low cost. U.S. Pat. No. 9,798,115 discloses an optical system including three lens surfaces manufactured by the wafer level optics. PCT International Publication No. 2018/220937 discloses an optical system including two lens surfaces. 
     The optical system disclosed in U.S. Pat. No. 9,798,115 includes three lens surfaces, and thus needs many manufacturing steps and high manufacturing cost. The optical system disclosed in PCT International Publication No. 2018/220937 has such a long overall length that the miniaturization is difficult. In addition, the manufacturing process of the optical system in PCT International Publication No. 2018/220937 includes a step that does not use the wafer process, the optical system cannot be manufactured at low cost. Moreover, as a small optical system for an endoscope or a mobile phone, a wide-angle optical system having high optical performance is demanded. 
     SUMMARY OF THE INVENTION 
     The present invention provides a small, inexpensive, wide-angle optical system having high optical performance and an image pickup apparatus having the same. 
     An optical system according to one aspect of the present invention includes, in order from an object side to an image side, a first unit and a second unit. The first unit includes a first substrate, and a first lens having a negative refractive power and disposed on the image side of the first substrate. The second unit includes a second substrate, and a second lens having a positive refractive power and disposed on the image side of the second substrate. An absolute value of the refractive power on an optical axis of the second lens is larger than that of the first lens. A surface on the image side of the first lens is an aspheric surface. In the aspheric surface of the first lens, a refractive power at an outermost peripheral portion of an effective area is smaller than a refractive power on the optical axis. 
     An image pickup apparatus including the above optical system, and an image sensor configured to receive an image formed by the optical system also constitutes another aspect of the present invention. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectional view of an optical system according to Example 1. 
         FIG. 2  is an aberration diagram of the optical system according to Example 1. 
         FIG. 3  is a sectional view of an optical system according to Example 2. 
         FIG. 4  is an aberration diagram of the optical system according to Example 2. 
         FIG. 5  is a sectional view of an optical system according to Example 3. 
         FIG. 6  is an aberration diagram of the optical system according to Example 3. 
         FIG. 7  is a sectional view of an optical system according to Example 4. 
         FIG. 8  is an aberration diagram of the optical system according to Example 4. 
         FIG. 9  is a sectional view of an optical system according to Example 5. 
         FIG. 10  is an aberration diagram of the optical system according to Example 5. 
         FIG. 11  is a sectional view of an optical system according to Example 6. 
         FIG. 12  is an aberration diagram of the optical system according to Example 6. 
         FIG. 13  is a sectional view of an optical system according to Example 7. 
         FIG. 14  is an aberration diagram of the optical system according to Example 7. 
         FIG. 15  is a schematic view of principal part of an electronic apparatus according to Example 8. 
         FIG. 16  is a schematic view of principal part of an image pickup apparatus according to Example 9. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Referring now to the accompanying drawings, a detailed description will be given of embodiments according to the present invention. 
     The optical system according to each example is a small optical system obtained by using the technology called the wafer level optics. Such an optical system is called a wafer level lens, and an image pickup apparatus using the wafer level lens for an imaging optical system is called a wafer level camera. The optical system according to each example is suitable for an optical system for a built-in camera of an electronic apparatus such as a mobile phone, a smartphone, or a wearable terminal, or as an objective optical system for an endoscope because of its small size and low cost. 
       FIGS. 1, 3, 5, 7, 9, 11, and 13  are sectional views of optical systems  1   a  to  1   g  according to Examples 1 to 7, respectively. In each sectional view, a left side is an object side (front) and a right side is an image side (rear). SP denotes a diaphragm (aperture stop), and IP denotes an image plane. Disposed on the image plane IP is an imaging surface of a solid-state image sensor such as a CCD sensor or a CMOS sensor in an image pickup device, or a photosensitive surface corresponding to a film surface of a film-based camera. 
       FIGS. 2, 4, 6, 8, 10, 12, and 14  are aberration diagrams of the optical systems  1   a  to  1   g  according to Examples 1 to 7, respectively. In a spherical aberration diagram, Fno denotes an F-number, and the spherical aberration diagram illustrates a spherical aberration amount for the d-line (wavelength 587.6 nm), the g-line (wavelength 435.8 nm), the C-line (wavelength 656.3 nm), and the F-line (wavelength 486.1 mm). In an astigmatism diagram, AS denotes an astigmatism amount on a sagittal image plane (solid line), and AM denotes an astigmatism amount on a meridional image plane (broken line). A distortion diagram illustrates a distortion amount for the d-line. A lateral chromatic aberration diagram illustrates a chromatic aberration amount for the g-line. Y denotes an image height (maximum image height). 
     The optical system according to each example includes, in order from the object side to the image side, a first unit L 1  and a second unit L 2 . The first unit L 1  includes a first substrate L 11 , and a first lens L 12  having a negative refractive power and disposed on the image side of the first substrate L 11 . The second unit L 2  includes a second substrate L 21 , and a second lens L 22  having a positive refractive power and disposed on the image side of the second substrate L 21 . A diaphragm SP is disposed on the image side of the first unit L 1 . An absolute value of the refractive power on the optical axis OA of the second lens L 22  is larger than an absolute value of the refractive power on the optical axis of the first lens L 12 . A surface on the image side of the first lens L 12  is an aspherical surface S 1 . In the aspherical surface S 1  of the first lens L 12 , a refractive power of a peripheral portion (the outermost peripheral portion of an effective diameter) is smaller than a refractive power of the central portion (on the optical axis). The effective diameter (effective area) here means a diameter (area) through which effective light rays that contribute to imaging pass on the optical surface. 
     The optical system according to each example includes a cover glass  50  disposed on the image side of the second unit L 2 . The cover glass  50  is disposed to protect the image sensor and the second lens L 22 . 
     The first substrate L 11  is a flat substrate, and the first lens L 12  is a plano-concave lens. The first lens L 12  is disposed in close contact with the first substrate L 11 . The second substrate L 21  is a flat substrate, and the second lens L 22  is a plano-convex lens. The second lens L 22  is disposed in close contact with the second substrate L 21 . 
     In each example, the first unit L 1  and the second unit L 2  are manufactured by the wafer level process in order to realize a compact and inexpensive optical system. That is, each of the first unit L 1  and the second unit L 2  is manufactured by forming a lens layer made of a curable resin material on a wafer (flat substrate) made of a glass material. In the second unit L 2 , the diaphragm SP is formed on the object side of the second substrate L 21  by the same wafer process. Many wafer level lenses can be manufactured by arranging the first unit L 1  and second unit L 2  manufactured by the wafer level process, the cover glass  50 , and the image sensor at predetermined intervals, by bonding them outside of the effective diameter, and by cutting them. 
     The material forming the lens layer may be a thermoplastic resin or an ultraviolet curable resin as long as it is a curable resin material. Examples include acrylic resins, silicone resins, and cycloolefin polymers. In each example, each of the first substrate L 11  and the second substrate L 21  is made of glass, and each of the first lens L 12  and the second lens L 22  is made of resin, but the present invention is not limited to this embodiment. If the refractive indexes of the first substrate L 11  and the first lens L 12  are different from each other, for example, both of the first substrate L 11  and the first lens L 12  may be formed of resin. This is similarly applicable to the second unit L 2 . 
     The diaphragm SP can be formed on the second substrate L 21 , for example, by vapor-depositing a light-shielding film such as chromium using a mask, or by forming an opening through etching after the vapor deposition. 
     In each example, the cover glass  50  is an integral glass substrate, but the present invention is not limited to this example. For example, the cover glass may be divided into two, one of them may be bonded to the second lens L 22  in the peripheral portion through the wafer process to form a wafer lens unit, the other of them may be used as a cover glass for the image sensor to manufacture a sensor unit, and then the wafer lens unit and the sensor unit may be adhered to each other on a flat surface. 
     Each example may satisfy the following inequality (1): 
       1.10&lt;| P 2/ P 1|&lt;8.00   (1)
 
     where P 1  is a refractive power at the central portion of the first lens L 12 , and P 2  is a refractive power at the central portion of the second lens is P 2 . 
     The refractive power P of each lens is expressed by P=ΔN/R, where ΔN is a refractive index difference between the surface on the object side and the surface on the image side of each lens and R is a radius of curvature of each lens on the optical axis. 
     If the value is lower than the lower limit in the inequality (1), the refractive power of the first lens L 12  becomes large, a distance between the first lens L 1  and the diaphragm SP becomes long, and the effective diameter of the surface closest to the object becomes large. On the other hand, if the value is higher than the upper limit in the inequality (1), the refractive power of the second lens L 22  becomes large, various aberrations such as a curvature of field increase, a curvature of the lens increases, and the manufacture becomes difficult. 
     The numerical range of the inequality (1) may be set to a numerical range in the following inequality (1a). 
       1.15&lt;| P 2/ P 1|&lt;7.00   (1a)
 
     The numerical range of the inequality (1) may be set to a numerical range in the following inequality (1b). 
       1.20&lt;| P 2/ P 1|&lt;6.00 (1b) 
     Each example may satisfy the following inequality (2): 
       1.50&lt;|rp1|&lt;20.00   (2)
 
     where rp 1 is a refractive power ratio of the central portion to the peripheral portion of the first lens. 
     The refractive power ratio rp1 of the central portion to the peripheral portion of the first lens L 12  is calculated by the following expression (3). 
       rp1= R 1 e/R 1   (3)
 
     In the expression (3), R 1  is a radius of curvature of the central portion of the aspherical surface S 1  on the image side of the first lens L 12 , and R 1   e  is a radius of curvature of the peripheral portion of the aspherical surface S 1  on the image side of the first lens L 12 . 
     A shape of the aspherical surface x(h) in each example is expressed by the following expression (a): 
     
       
         
           
             
               
                 
                   
                     x 
                     ⁡ 
                     ( 
                     h 
                     ) 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             h 
                             2 
                           
                           r 
                         
                         ) 
                       
                       
                         1 
                         + 
                         
                           
                             { 
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   
                                     ( 
                                     
                                       h 
                                       r 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             } 
                           
                         
                       
                     
                     + 
                     
                       
                         A 
                         4 
                       
                       ⁢ 
                       
                         h 
                         4 
                       
                     
                     + 
                     
                       
                         A 
                         6 
                       
                       ⁢ 
                       
                         h 
                         6 
                       
                     
                     + 
                     
                       
                         A 
                         8 
                       
                       ⁢ 
                       
                         h 
                         8 
                       
                     
                     + 
                     
                       
                         A 
                         
                           1 
                           ⁢ 
                           0 
                         
                       
                       ⁢ 
                       
                         h 
                         
                           1 
                           ⁢ 
                           0 
                         
                       
                     
                     + 
                     … 
                   
                 
               
               
                 
                   ( 
                   a 
                   ) 
                 
               
             
           
         
       
     
     where x as a displacement amount from a surface apex in the optical axis direction, h is a height from the optical axis in a direction orthogonal to the optical axis, r is a paraxial radius of curvature, k is a conical constant, and Ai (i=4, 6, 8 . . . ) is an aspherical coefficient of each order. 
     A slope of the aspherical shape at the height h in the optical axis direction can be calculated from the differential of the expression (a). The differential of the expression (a) is represented by the following expression (b). 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ′ 
                     
                     ( 
                     h 
                     ) 
                   
                   = 
                   
                     
                       
                         ∂ 
                         
                           ∂ 
                           h 
                         
                       
                       
                         [ 
                         
                           x 
                           ⁡ 
                           ( 
                           h 
                           ) 
                         
                         ] 
                       
                     
                     = 
                     
                       
                         
                           r 
                           ⁢ 
                           h 
                           ⁢ 
                           
                             
                               1 
                               - 
                               
                                 
                                   
                                     ( 
                                     
                                       1 
                                       + 
                                       k 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     h 
                                     2 
                                   
                                 
                                 
                                   r 
                                   2 
                                 
                               
                             
                           
                         
                         
                           
                             r 
                             2 
                           
                           - 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 k 
                               
                               ) 
                             
                             ⁢ 
                             
                               h 
                               2 
                             
                           
                         
                       
                       + 
                       
                         4 
                         × 
                         
                           A 
                           4 
                         
                         ⁢ 
                         
                           h 
                           3 
                         
                       
                       + 
                       
                         6 
                         × 
                         
                           A 
                           6 
                         
                         ⁢ 
                         
                           h 
                           5 
                         
                       
                       + 
                       
                         8 
                         × 
                         
                           A 
                           
                               
                             8 
                           
                         
                         ⁢ 
                         
                           h 
                           7 
                         
                       
                       + 
                       
                         1 
                         ⁢ 
                         0 
                         × 
                         
                           A 
                           
                             1 
                             ⁢ 
                             0 
                           
                         
                         ⁢ 
                         
                           h 
                           9 
                         
                       
                       + 
                       … 
                     
                   
                 
               
               
                 
                   ( 
                   b 
                   ) 
                 
               
             
           
         
       
     
     A local radius of curvature Re at the height h in the optical axis direction can be obtained from the following expression (c), where the conical coefficient k of the expression (b) and the aspherical coefficient Ai of each order are set to 0. 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ′ 
                     
                     ( 
                     h 
                     ) 
                   
                   = 
                   
                     
                       
                         r 
                         e 
                       
                       ⁢ 
                       h 
                       ⁢ 
                       
                         
                           1 
                           - 
                           
                             
                               h 
                               2 
                             
                             
                               r 
                               e 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         r 
                         e 
                         2 
                       
                       - 
                       
                         h 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   c 
                   ) 
                 
               
             
           
         
       
     
     If it the value is lower than the lower limit in the inequality (2), the aspherical effect of the first lens L 12  becomes small, and it becomes difficult to suppress various aberrations (curvature of field and distortion) in the off-axis light. On the other hand, if the value is higher than the upper limit in the inequality (2), the refractive power at the central portion of the first lens L 12  becomes stronger, the effective diameter of the surface closest to the object becomes larger, and the optical system becomes larger. 
     The numerical range of the inequality (2) may be set to a numerical range in the following inequality (2a). 
       1.70&lt;|rp1|&lt;15.00   (2a)
 
     The numerical range of the inequality (2) may be set to a numerical range in the following inequality (2b). 
       1.90&lt;|rp1|&lt;12.00   (2b)
 
     Each example can more satisfactorily correct the aberration by making a refractive power of the peripheral portion in an aspherical surface S 2  that is an surface on the image side of the second lens L 22  smaller than a refractive power of the central portion in the aspherical surface S 2  of the second lens L 22 . 
     More specifically, the following inequality (4) may be satisfied: 
       1.25&lt;|rp2|&lt;10.00   (4)
 
     where rp2 is a refractive power ratio of the central portion to the peripheral portion of the second lens L 22 . 
     The refractive power ratio rp2 of the central portion to the peripheral portion of the second lens L 22  is calculated by the following expression (5). 
       rp2= R 2 e/R 2   (5)
 
     In the expression (5), R 2  is a radius of curvature of the central portion in the aspherical surface on the image side of the second lens L 22 , and R 2   e  is a radius of curvature of the peripheral portion in the aspherical surface on the image side of the second lens L 22  and is calculated similar to the expressions (a), (b), and (c). 
     The numerical range of the inequality (4) may be set to a numerical range in the following inequality (4a). 
       1.30&lt;|rp2|&lt;5.00   (4a)
 
     The numerical range of the inequality (4) may be set to a numerical range in the following inequality (4b). 
       1.30&lt;|rp2|&lt;3.00   (4b)
 
     In the optical system according to each example, lens surfaces are disposed before and after the diaphragm SP, and a refractive power of each lens surface is properly set to realize the miniaturization and suppression of various aberrations. Therefore, the second unit L 2  may include the diaphragm SP. The diaphragm SP may be disposed close to the second substrate L 21  (for example, disposed on the second substrate L 21 ). By disposing the diaphragm SP close to the second substrate L 21  of the second unit L 2 , the diaphragm SP can be formed in the wafer process and the structure is easy to manufacture. The diaphragm SP may be located on either the surface on the object side of the second substrate L 21  opposite to an air surface or the surface on the image side of the second substrate L 21  facing the second lens L 22 . Each configuration promotes easy manufacturing. 
     Each example may satisfy the following inequality (5): 
       1.00&lt;R1 e/d 1&lt;30.00   (5)
 
     where R 1   e  is a radius of curvature of the peripheral portion of the first lens L 12 , and d1 is a distance on the optical axis from the surface on the image side of the first lens L 12  to the diaphragm SP. 
     If the value is lower than the lower limit in the inequality (5), the refractive power of the peripheral portion of the first lens L 12  becomes large (close to the refractive power of the central portion), the aspherical effect becomes weak, and it becomes difficult to suppress various aberrations such as a curvature of field. On the other hand, if the value is higher than the upper limit in the inequality (5), a distance between the diaphragm SP and the first lens L 12  becomes small, and the spherical aberration of the on-axis luminous flux and the aberration of the off-axis luminous flux become unbalanced, and it becomes difficult to suppress various aberrations. 
     The numerical range of the inequality (5) may be set to a numerical range in the following inequality (5a). 
       1.10&lt; R 1 e/d 1&lt;25.00   (5a)
 
     The numerical range of the inequality (5) may be set to a numerical range in the following inequality (5b). 
       1.30&lt; R 1 e/d 1&lt;22.00   (5b)
 
     Each example may satisfy the following inequality (6): 
       0.53&lt; d 0/ R 1&lt;5.00   (6)
 
     where d0 is a distance on the optical axis from the surface on the object side of the first unit L 1  to the diaphragm SP, and R 1  is a radius of curvature of the central portion in the surface on the image side of the first lens L 12 . 
     If the value is lower than the lower limit in the inequality (6), the refractive power of the first lens L 12  becomes stronger or a distance to the diaphragm SP becomes smaller, and it becomes difficult to suppress various aberrations. On the other hand, if the value is higher than the upper limit in the inequality (6), the effective diameter of the surface closest to the object becomes large, and the optical system becomes large. 
     The numerical range of the inequality (6) is set to a numerical range in the following inequality (6a). 
       0.65&lt; d 0/ R 1&lt;3.00   (6a)
 
     The numerical range of the inequality (6) is set to a numerical range in the following inequality (6b). 
       0.70&lt; d 0/ R 1&lt;2.50   (6b)
 
     In each example, each of the first lens L 12  and the second lens L 22  is made of a curable resin, so that the structure can be easily manufactured. In the wafer level optics, wiring is installed by soldering or the like after joining the wafer level lens and the image sensor, a resin may need to withstand a certain high temperature. When the optical system according to each example is used for an imaging optical system, a material having less birefringence may be used. Thus, a resin material having a refractive index of about 1.5 may be selected as the resin material used for the wafer level lens. 
     Each example may satisfy the following inequality (7): 
       1.40&lt;N1&lt;1.65   (7)
 
     where N 1  is a refractive index of the first lens L 12  for the d-line. 
     The numerical range of the inequality (7) may be set to a numerical range in the following inequality (7a). 
       1.45&lt;N1&lt;1.63   (7a)
 
     Each example may satisfy the following inequality (8): 
       1.40&lt;N2&lt;1.65   (8)
 
     where N 2  is a refractive index of the second lens L 22  for the d-line. 
     The numerical range of the inequality (8) may be set to a numerical range in the following inequality (8a). 
       1.45&lt;N2&lt;1.63   (8a)
 
     If the value is lower than the lower limit in each of the inequalities (7) and (8), a curvature of each lens becomes large, the manufacture becomes difficult, and the curvature of field becomes difficult to correct. On the other hand, if the value is higher than the upper limit in each of the inequalities (7) and (8), the dispersion of the material becomes large, and the chromatic aberration becomes unacceptably increases, and the birefringence becomes large. 
     The optical system according to each example has such a configuration that aberrations are canceled by the first lens L 12  having a negative refractive power and the second lens L 22  having a positive refractive power before and after the diaphragm SP. Therefore, by using a low-dispersion material for both the first lens L 12  and the second lens L 22 , longitudinal and lateral chromatic aberrations can be satisfactorily corrected. 
     Each example may satisfy the following inequality (9): 
       40&lt;ν1&lt;80   (9)
 
     where ν1 is an Abbe number of the first lens L 12  based on the d-line. 
     The numerical range of the inequality (9) may be set to a numerical range in the following inequality (9a). 
       45&lt;ν1&lt;70   (9a)
 
     Each example may satisfy the following inequality (10): 
       40&lt;ν2&lt;80   (10)
 
     where ν2 is an Abbe number of the second lens L 22  based on the d-line. 
     The numerical range of the inequality (10) may be set to a numerical range in the following inequality (10a). 
       45&lt;ν2&lt;70   (10a)
 
     If the value is lower than the lower limit in each of the inequalities (9) and (10), it becomes difficult to correct the chromatic aberration. On the other hand, if the value is higher than the upper limit in each of the inequalities (9) and (10), the refractive index becomes low, the curvature of field increases, and the material becomes expensive. 
     The Abbe numbers ν1 and ν2 of the first lens L 12  and the second lens L 22  may be close to each other in terms of a good balance of the chromatic aberration correction. More specifically, each example may satisfy the following inequality (11): 
       0≤|ν1−ν2|&lt;15   (11)
 
     The Abbe number v based on the d-line is expressed by the following expression: 
       ν=( nd− 1)/( nF−nC )
 
     where nd, nF, and nC are refractive indexes for the d-line (wavelength 587.6 nm), F-line (wavelength 486.1 nm), and C-line (wavelength 656.3 nm) in the Fraunhofer lines. 
     A detailed description will be given of the optical system according to each example. 
     EXAMPLE 1 
     Referring now to  FIG. 1 , a description will be given of an optical system  1   a  according to Example 1 (numerical example 1). The optical system  1   a  according to this example includes, in order from the object side to the image side, a first unit L 1  and a second unit L 2 . The first unit L 1  includes a first substrate (flat substrate) L 11  and a first lens (planar-concave lens) L 12  having a negative refractive power and disposed on the image side of the first substrate L 11 . The second unit L 2  includes second substrate (flat substrate) L 21 , a second lens (planar convex lens) L 22  having a positive refractive power and disposed on the image side of the second substrate L 21 , and a diaphragm SP disposed on the object side of the second substrate L 21 . The optical system  1   a  further includes a cover glass  50  disposed on the image side of the second unit L 2 . The cover glass  50  is disposed to protect an image sensor and the second lens L 22 . 
     The optical system  1   a  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 59°, an F-number of 2.8, and an image height of 0.28 mm. In miniaturizing a wide-angle optical system having a half angle of view of 50° or more as in this example, it is necessary to shorten the overall length and to control various aberrations while reducing the effective diameter on the surface closest to the object. If the effective diameter of the surface closest to the object becomes large, the size of one optical system becomes large, so that the number of optical systems that can be manufactured from one wafer is reduced and the manufacturing method becomes expensive. 
     When the wafer level optics is used for a small image pickup apparatus such as an endoscope or a smartphone, a surface closest to the object may be made of a hard material having strong environmental resistance such as a glass material. Since it is difficult to make the surface of the glass material a curved surface in the wafer process, the surface closest to the object may be a glass flat surface. 
     In this example, an absolute value of the refractive power on the optical axis OA of the second lens L 22  is larger than that of the first lens L 12 . The surface on the image side of the first lens L 12  is an aspherical surface S 1 . In the aspherical surface S 1  of the first lens L 12 , a refractive power of the peripheral portion (the outermost peripheral portion of the effective diameter) is smaller than that of the central portion (on the optical axis). This configuration can realize a wide-angle, bright, and compact optical system with a simple configuration of two lens surfaces. That is, the optical system  1   a  according to this example can reduce a distance between the diaphragm and the surface closest to the object side while satisfactorily correcting various aberrations of off-axis light having a large incident angle. As a result, the effective diameter of the surface closest to the object side can be made small, and thereby a compact optical system can be realized. 
     As illustrated in the aberration diagram of  FIG. 2 , the optical system  1   a  according to this example satisfactorily corrects a chromatic aberration and various aberrations up to the periphery of the image even though the optical system is small. 
     EXAMPLE 2 
     Referring now to  FIG. 3 , a description will be given of an optical system  1   b  according to Example 2 (numerical example 2). The basic configuration of the optical system  1   b  according to this example is the same as that of the optical system  1   a  according to Example 1. In the optical system  1   b  according to this example, the thickness of the first substrate L 11  of the first unit L 1  (thickness in the optical axis direction), the thickness of the second substrate L 21  of the second unit L 2 , and thickness of the cover glass  50  are larger than those of the optical system  1   a  according to Example 1. The optical system  1   b  according to this example has a configuration that is easy to manufacture because cracks and deformations during feeding are unlikely to occur in the wafer process. The optical system  1   b  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 59°, an F-number of 2.9, and an image height of 0.28 mm. As illustrated in  FIG. 4 , the optical system  1   b  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux, even though the optical system is small, bright, and wide-angle. 
     EXAMPLE 3 
     Referring now to  FIG. 5 , a description will be given of an optical system  1   c  according to Example 3 (numerical example 3). The basic configuration of the optical system  1   c  according to this example is the same as that of the optical system  1   a  according to Example 1. In the optical system  1   c  according to this example, a minimum thickness (thickness in the optical axis direction) of the first lens L 12  is larger than that of the optical system  1   a  according to Example 1. Therefore, in the wafer process, resin molding is satisfactorily stable and the structure is easy to manufacture. The optical system  1   c  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 59°, an F-number of 2.9, and an image height of 0.28 mm. As illustrated in  FIG. 6 , the optical system  1   c  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux, even though the optical system is small, bright, and wide-angle. 
     EXAMPLE 4 
     Referring now to  FIG. 7 , a description will be given of an optical system  1   d  according to Example 4 (numerical example 4). In the optical system  1   d  according to this example, a diaphragm SP of the second unit L 2  is disposed on the image side of the second substrate L 21  of the second unit L 2 . The optical system  1   d  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 59°, an F-number of 2.8, and an image height of 0.28 mm. As illustrated in  FIG. 8 , the optical system  1   d  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux, even though the optical system is small, bright, and wide-angle. 
     EXAMPLE 5 
     Referring now to  FIG. 9 , a description will be given of an optical system  1   e  according to Example 5 (numerical example 5). The basic configuration of the optical system  1   e  according to this example is the same as that of the optical system  1   a  according to Example 1. The optical system  1   e  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 50°, an F-number of 2.9, and an image height of 0.28 mm. As illustrated in  FIG. 10 , the optical system  1   e  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux, even though the optical system is small, bright, and wide-angle. 
     EXAMPLE 6 
     Referring now to  FIG. 11 , a description will be given of an optical system  1   f  according to Example 6 (numerical example 6). The basic configuration of the optical system  1   f  according to this example is the same as that of the optical system  1   a  according to Example 1. The optical system  1   f  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 70°, an F-number of 2.9, and an image height of 0.28 mm. As illustrated in  FIG. 12 , the optical system  1   f  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux even though the optical system is small, bright, and wide-angle. 
     EXAMPLE 7 
     Referring now to  FIG. 13 , a description will be given of an optical system  1   g  according to Example 7 (numerical example 7). The basic configuration of the optical system  1   g  according to this example is the same as that of the optical system  1   a  according to Example 1. The optical system  1   g  according to this example is a compact yet bright and wide-angle optical system having a half angle of view of 70°, an F-number of 2.8, and an image height of 0.28 mm. As illustrated in  FIG. 14 , the optical system  1   g  according to this example satisfactorily corrects various aberrations from the on-axis luminous flux to the off-axis luminous flux even though the optical system is small, bright, and wide-angle. 
     A description will now be given of numerical examples 1 to 7 corresponding to Examples 1 to 7. In each numerical example, m denotes the number of a surface or optical element counted from the light incident side. For example, Rm denotes a radius of curvature (mm) of an m-th optical surface (m-th surface). Dm denotes an on-axis distance (mm) between an m-th surface and an (m+1)-th surface. Nd is a refractive index of a material of an optical element for the d-line. νd is an Abbe number based on the d-line of a material of an optical element. “E±XX” means “×10 ±XX ”. f denotes a focal length, and Fno denotes an effective F-number. ω denotes a half angle of view (degrees). BF denotes a backfocus, which is a distance from the final surface of the optical system to the image plane. 
     NUMERICAL EXAMPLE 1 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.209 Fno = 2.84 2ω = 118° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective  
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.60 
               
               
                 2 
                 ∞ 
                 0.030 
                 1.5100 
                 57.5 
                 0.46 
               
               
                 3 (aspheric) 
                   0.3592 
                 0.149 
                   
                   
                 0.39 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.000 
                   
                   
                 0.09 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.18 
               
               
                 6 
                 ∞ 
                 0.160 
                 1.5100 
                 57.5 
                 0.18 
               
               
                 7 (aspheric) 
                 −0.1199 
                 0.030 
                   
                   
                 0.28 
               
               
                 8 
                 ∞ 
                 0.400 
                 1.5168 
                 64.2 
                 0.36 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.57 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −8.17811E+00 
                 −9.10764E+00 
               
               
                 A4 
                 −2.48232E+01 
                 −3.58329E+02 
               
               
                 A6 
                   4.32682E+02 
                   3.50904E+04 
               
               
                 A8 
                   7.37237E+03 
                 −2.23556E+06 
               
               
                 A10 
                 −4.16420E+05 
                   7.54984E+07 
               
               
                 A12 
                   4.63866E+06 
                 −1.02744E+09 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 2 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.222 Fno = 2.89 2ω =118° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective  
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.70 
               
               
                 2 
                 ∞ 
                 0.011 
                 1.5100 
                 57.5 
                 0.43 
               
               
                 3 (aspheric) 
                   0.2255 
                 0.193 
                   
                   
                 0.35 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.000 
                   
                   
                 0.10 
               
               
                 5 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.10 
               
               
                 6 
                 ∞ 
                 0.103 
                 1.5300 
                 56.0 
                 0.29 
               
               
                 7 (aspheric) 
                 −0.1478 
                 0.015 
                   
                   
                 0.31 
               
               
                 8 
                 ∞ 
                 0.600 
                 1.5168 
                 64.2 
                 0.36 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.58 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −3.66634E+01 
                 −1.10654E+01 
               
               
                 A4 
                   1.09167E+02 
                 −2.29816E+02 
               
               
                 A6 
                 −8.23526E+03 
                   1.79179E+04 
               
               
                 A8 
                   3.42649E+05 
                 −9.56015E+05 
               
               
                 A10 
                 −7.57580E+06 
                   2.76785E+07 
               
               
                 A12 
                   6.83791E+07 
                 −3.27104E+08 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 3 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.183 Fno = 2.9 2ω = 118° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.64 
               
               
                 2 
                 ∞ 
                 0.050 
                 1.5200 
                 47.0 
                 0.50 
               
               
                 3 (aspheric) 
                   0.2439 
                 0.144 
                   
                   
                 0.40 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.000 
                   
                   
                 0.08 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.08 
               
               
                 6 
                 ∞ 
                 0.175 
                 1.5200 
                 47.0 
                 0.20 
               
               
                 7 (aspheric) 
                 −0.1158 
                 0.030 
                   
                   
                 0.30 
               
               
                 8 
                 ∞ 
                 0.400 
                 1.5168 
                 64.2 
                 0.38 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.55 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −1.88497E+01 
                 −6.73952E+00 
               
               
                 A4 
                 −4.96067E+00 
                 −2.86470E+02 
               
               
                 A6 
                 −4.54092E+02 
                   2.34926E+04 
               
               
                 A8 
                   2.32049E+04 
                 −1.28204E+06 
               
               
                 A10 
                 −4.38925E+05 
                   3.83506E+07 
               
               
                 A12 
                   3.06454E+06 
                 −4.68543E+08 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 4 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.211 Fno = 2.84 2ω = 118° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective  
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.150 
                 1.5168 
                 64.2 
                 0.68 
               
               
                 2 
                 ∞ 
                 0.025 
                 1.5100 
                 57.5 
                 0.47 
               
               
                 3 (aspheric) 
                   0.5339 
                 0.050 
                   
                   
                 0.42 
               
               
                 4 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.32 
               
               
                 5 (Diaphragm) 
                 ∞ 
                 0.226 
                 1.5100 
                 57.5 
                 0.09 
               
               
                 6 (aspheric) 
                 −0.1180 
                 0.015 
                   
                   
                 0.26 
               
               
                 7 
                 ∞ 
                 0.400 
                 1.5168 
                 64.2 
                 0.33 
               
               
                 8 
                 ∞ 
                   
                   
                   
                 0.57 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 6th Surface 
               
               
                   
               
               
                 K 
                   2.45135E−01 
                 −1.28390E+01 
               
               
                 A4 
                 −1.95476E+01 
                 −4.40719E+02 
               
               
                 A6 
                 −1.87107E+02 
                   5.05215E+04 
               
               
                 A8 
                   2.19302E+04 
                 −3.75675E+06 
               
               
                 A10 
                 −5.09987E+05 
                   1.48835E+08 
               
               
                 A12 
                   4.02848E+06 
                 −2.39036E+09 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 5 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.268 Fno= 2.9 2ω = 100° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective  
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.67 
               
               
                 2 
                 ∞ 
                 0.011 
                 1.5310 
                 55.7 
                 0.43 
               
               
                 3 (aspheric) 
                   0.3687 
                 0.200 
                   
                   
                 0.39 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.000 
                   
                   
                 0.11 
               
               
                 5 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.11 
               
               
                 6 
                 ∞ 
                 0.095 
                 1.5310 
                 55.7 
                 0.30 
               
               
                 7 (aspheric) 
                 −0.1609 
                 0.015 
                   
                  0.0 
                 0.32 
               
               
                 8 
                 ∞ 
                 0.600 
                 1.5168 
                 64.2 
                 0.36 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.58 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −1.33499E+02 
                 −1.49030E+01 
               
               
                 A4 
                   6.35073E+01 
                 −2.23781E+02 
               
               
                 A6 
                 −4.34973E+03 
                   1.80786E+04 
               
               
                 A8 
                   1.54981E+05 
                 −9.75225E+05 
               
               
                 A10 
                 −2.86138E+06 
                   2.82757E+07 
               
               
                 A12 
                   2.13758E+07 
                 −3.32787E+08 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 6 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.184 Fno = 2.89 2ω = 140° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.70 
               
               
                 2 
                 ∞ 
                 0.011 
                 1.5100 
                 57.5 
                 0.54 
               
               
                 3 (aspheric) 
                   0.1839 
                 0.264 
                   
                   
                 0.40 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.005 
                   
                   
                 0.11 
               
               
                 5 
                 ∞ 
                 0.200 
                 1.5168 
                 64.2 
                 0.11 
               
               
                 6 
                 ∞ 
                 0.099 
                 1.5300 
                 56.0 
                 0.29 
               
               
                 7 (aspheric) 
                 −0.1481 
                 0.015 
                   
                   
                 0.31 
               
               
                 8 
                 ∞ 
                 0.600 
                 1.5168 
                 64.2 
                 0.35 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.55 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −1.39743E+01 
                 −8.78131E+00 
               
               
                 A4 
                   6.66364E+01 
                 −1.85785E+02 
               
               
                 A6 
                 −2.34970E+03 
                   1.20004E+04 
               
               
                 A8 
                   4.16853E+04 
                 −5.58397E+05 
               
               
                 A10 
                 −3.11553E+05 
                   1.45240E+07 
               
               
                 A12 
                   1.89095E+05 
                 −1.57007E+08 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE 7 
       
     
       
         
           
               
             
               
                   
               
             
            
               
                 f = 0.186 Fno = 2.89 2ω =140° 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 R 
                 D 
                 Nd 
                 νd 
                 diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.69 
               
               
                 2 
                 ∞ 
                 0.020 
                 1.5100 
                 57.5 
                 0.54 
               
               
                 3 (aspheric) 
                   0.3070 
                 0.166 
                   
                   
                 0.44 
               
               
                 4 (Diaphragm) 
                 ∞ 
                 0.010 
                   
                   
                 0.08 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.5168 
                 64.2 
                 0.08 
               
               
                 6 
                 ∞ 
                 0.091 
                 1.5100 
                 57.5 
                 0.21 
               
               
                 7 (aspheric) 
                 −0.1090 
                 0.015 
                   
                   
                 0.24 
               
               
                 8 
                 ∞ 
                 0.399 
                 1.5168 
                 64.2 
                 0.32 
               
               
                 9 
                 ∞ 
                   
                   
                   
                 0.57 
               
               
                 BF = 0.02 
               
               
                   
               
            
           
           
               
            
               
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
            
               
                   
                 3rd Surface 
                 7th Surface 
               
               
                   
               
               
                 K 
                 −1.62113E+01 
                 −1.22192E+01 
               
               
                 A4 
                   3.44701E+01 
                 −5.53837E+02 
               
               
                 A6 
                 −2.60774E+03 
                   7.11976E+04 
               
               
                 A8 
                   8.06761E+04 
                 −5.89167E+06 
               
               
                 A10 
                 −1.19531E+06 
                   2.63097E+08 
               
               
                 A12 
                   6.91564E+06 
                 −4.81501E+09 
               
               
                   
               
            
           
         
       
     
     Table 1 shows a relationship between the numerical values regarding the above inequalities (1) to (11) and the numerical examples. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Numerical Example 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Inequality 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 P1 
                 −1.420 
                 −2.262 
                 −2.132 
                 −0.955 
                 −1.440 
                 −2.774 
                 −1.661 
               
               
                 P2 
                 4.254 
                 3.587 
                 4.492 
                 4.324 
                 3.299 
                 3.578 
                 4.680 
               
               
                 P2/P1 
                 −2.996 
                 −1.586 
                 −2.107 
                 −4.527 
                 −2.291 
                 −1.290 
                 −2.817 
               
               
                 R1e 
                 1.935 
                 0.493 
                 2.548 
                 3.780 
                 0.929 
                 0.390 
                 1.357 
               
               
                 R1/R1e 
                 5.385 
                 2.187 
                 10.447 
                 7.079 
                 2.520 
                 2.119 
                 4.420 
               
               
                 R2e 
                 −0.183 
                 −0.208 
                 −0.193 
                 −0.175 
                 −0.218 
                 −0.208 
                 −0.163 
               
               
                 R2/R2e 
                 1.522 
                 1.406 
                 1.671 
                 1.482 
                 1.355 
                 1.407 
                 1.498 
               
               
                 d1 
                 0.149 
                 0.193 
                 0.144 
                 0.250 
                 0.200 
                 0.264 
                 0.166 
               
               
                 R1e/d1 
                 12.983 
                 2.561 
                 17.685 
                 15.149 
                 4.648 
                 1.478 
                 8.155 
               
               
                 d0 
                 0.279 
                 0.403 
                 0.294 
                 0.425 
                 0.411 
                 0.374 
                 0.286 
               
               
                 d0/R1 
                 0.777 
                 1.788 
                 1.206 
                 0.795 
                 1.114 
                 2.036 
                 0.933 
               
               
                 N1 
                 1.510 
                 1.510 
                 1.520 
                 1.510 
                 1.531 
                 1.510 
                 1.510 
               
               
                 ν1 
                 57.5 
                 57.5 
                 47.0 
                 57.5 
                 55.7 
                 57.5 
                 57.5 
               
               
                 N2 
                 1.510 
                 1.530 
                 1.520 
                 1.510 
                 1.531 
                 1.530 
                 1.510 
               
               
                 ν2 
                 57.5 
                 56.0 
                 47.0 
                 57.5 
                 55.7 
                 56.0 
                 57.5 
               
               
                 |ν1 − ν2| 
                 0.0 
                 1.5 
                 0.0 
                 0.0 
                 0.0 
                 1.5 
                 0.0 
               
               
                   
               
            
           
         
       
     
     While the imaging optical system has been described in Examples 1 to 7, the optical system according to each example is suitably used for a built-in camera of an electronic apparatus such as a mobile phone, a smartphone, and a wearable terminal, an objective optical system of an endoscope, and the like. 
     EXAMPLE 8 
     Referring now to  FIG. 15 , a description will be given of an electronic apparatus according to Example 8 of the present invention.  FIG. 15  is a schematic view of principal part of the electronic apparatus (smartphone  70 ) according to this example. The smartphone  70  includes an image pickup apparatus  71  as a front camera module. The image pickup apparatus  71  includes an optical system  72  corresponding to any of the optical systems according to Examples 1 to 7, and an image sensor  73  that receives an image formed by the optical system  72 . Thus, by applying the optical system according to each of the above examples to an image pickup apparatus such as a smartphone, a compact image pickup apparatus having high optical performance can be realized. 
     EXAMPLE 9 
     Referring now to  FIG. 16 , a description will be given of an image pickup apparatus according to Example 9 of the present invention.  FIG. 16  is a schematic view of principal part of the image pickup apparatus  100  according to this example. The image pickup apparatus  100  is used for a small endoscope and includes a camera head  120  and an electric cable  150 . The camera head  120  includes a lens housing  121  including an optical system according to any one according to Examples 1 to 7, an image sensor  122 , and a ceramic substrate  123 . Wires of the electric cable  150  are connected to the image sensor  122  via the ceramic substrate  123 . Thus, by applying the optical system according to each of the above examples to the image pickup apparatus of the endoscope, a compact image pickup apparatus having high optical performance can be realized. 
     Each of the above examples can provide a compact wide-angle optical system having high optical performance and an image pickup apparatus having the same. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2021-003688, filed on Jan. 13, 2021, which is hereby incorporated by reference herein in its entirety.