Patent Publication Number: US-2022221687-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 
     Small optical systems suitable for medical endoscopes and the like have recently been demanded. In such optical systems, high optical performance is also demanded for accurate diagnoses and treatments. U.S. Pat. No. 9,798,115 discloses a small lens system for medical endoscopes manufactured by a wafer level process. 
     However, the lens system disclosed in U.S. Pat. No. 9,798,115 increases the cost, due to the large number of substrates and the bonding process in the wafer level process. 
     SUMMARY OF THE INVENTION 
     The present invention provides a small and inexpensive 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, a second unit, and a third 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 object side of the second substrate. The third unit includes a third substrate, and a third lens having a positive refractive power and disposed on the object side of the third substrate. An image pickup apparatus according to another aspect of the present invention includes the above optical system and an image sensor configured to receive an image formed by the optical system. 
     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. 
         FIGS. 2A to 2D  are aberration diagrams of the optical system according to Example 1. 
         FIG. 3  is a sectional view of an optical system according to Example 2. 
         FIGS. 4A  to 4D are aberration diagrams of the optical system according to Example 2. 
         FIG. 5  is a sectional view of an optical system according to Example 3. 
         FIGS. 6A to 6D  are aberration diagrams of the optical system according to Example 3. 
         FIG. 7  is a sectional view of an optical system according to Example 4. 
         FIGS. 8A to 8D  are aberration diagrams of the optical system according to Example 4. 
         FIG. 9  is a sectional view of an optical system according to Example 5. 
         FIGS. 10A to 10D  are aberration diagrams of the optical system according to Example 5. 
         FIG. 11  is a sectional view of an optical system according to Example 6. 
         FIGS. 12A to 12D  are aberration diagrams of the optical system according to Example 6. 
         FIG. 13  is a sectional view of an optical system according to Example 7. 
         FIGS. 14A to 14D  are aberration diagrams of the optical system according to Example 7. 
         FIG. 15  is a sectional view of an optical system according to Example 8. 
         FIGS. 16A to 16D  are aberration diagrams of the optical system according to Example 8. 
         FIG. 17  is a sectional view of an optical system according to a comparative example. 
         FIG. 18  is a schematic view of principal part of an electronic apparatus according to Example 5. 
         FIG. 19  is a schematic view of principal part of an image pickup apparatus according to Example 6. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Referring now to the accompanying drawings, a description will be given of embodiments according to the present invention. 
     An optical system according to each example is a small optical system obtained by using a technology called the wafer level optics. This 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, 13, and 15  are sectional views of optical systems (wafer level lenses)  1   a ,  1   b ,  1   c ,  1   d ,  1   e ,  1   f ,  1   g , and  1   h  according to Examples 1 to 8, 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 apparatus, or a photosensitive surface corresponding to a film surface of a film-based camera. 
       FIGS. 2, 4, 6, 8, 10, 12, 14, and 16  are aberration diagrams of the optical systems  1   a ,  1   b ,  1   c ,  1   d ,  1   e ,  1   f ,  1   g , and  1   h  according to Examples 1 to 8, respectively.  FIGS. 2A, 4A, 6A, 8A, 10A, 12A, 14A, and 16A  are spherical aberration diagrams,  FIGS. 2B, 4B, 6B, 8B, 10B, 12B, 14B, and 16B  are astigmatism diagrams,  FIGS. 2C, 4C, 6C, 8C, 10C, 12C, 14C, and 16C  are distortion diagrams, and  FIGS. 2D, 4D, 6D, 8D, 10D, 12D, 14D, and 16D  are lateral chromatic aberration diagrams. The spherical aberration diagram illustrate spherical aberration amounts 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 nm), respectively. In the astigmatism diagram, ΔSd and ΔSg denote astigmatism amounts on the sagittal image plane for the d-line and g-line, and ΔMd and ΔMg denote astigmatism amounts on the meridional image plane for the d-line and g-line, respectively. The distortion diagram illustrates a distortion amount for the d-line. The lateral chromatic aberration illustrates chromatic aberration amounts for the g-line, the C-line, and the F-line. 
     The optical system according to each example includes, in order from an object side to an image side, a first unit L 1 , a second unit L 2 , and a third unit L 3 . The first unit L 1  includes a first substrate (front cover glass)  11 , and a first lens  12  having a negative refractive power and disposed on the image side of the first substrate  11 . The second unit L 2  includes a second substrate  21 , a second lens  22  having a positive refractive power and disposed on the object side of the second substrate  21 , and a diaphragm SP disposed on the image side of the second substrate  21 . The third unit L 3  includes a third substrate (back cover glass)  31 , and a third lens  32  disposed on the object side of the third substrate  31 . 
     In Examples 1 to 3 and 7, a fourth substrate (sensor cover glass)  41  disposed on the image side of the third substrate  31  is provided. In Examples 4 to 6 and 8, the third substrate  31  also serves as a back cover glass and a sensor cover glass. 
     The first substrate  11  is a flat substrate, and the first lens  12  is a negative lens (plano-concave lens) with a concave surface facing the image side. The first lens  12  is formed on a surface on the image side of the first substrate  11  by using the wafer level process, and is disposed in close contact with the first substrate  11 . The second substrate  21  is a flat substrate, and the second lens  22  is a positive lens (plano-convex lens) having a convex surface facing the object side. The second lens  22  is formed on a surface on the object side of the second substrate  21  by using the wafer level process, and is disposed in close contact with the second substrate  21 . The third substrate  31  is a flat substrate, and the third lens  32  is a positive lens (plano-convex lens) with a convex surface facing the object side. The third lens  32  is formed on a surface on the object side of the third substrate  31  by using the wafer level process, and is disposed in close contact with the third substrate  31 . The fourth substrate (sensor cover glass)  41  is provided to protect the image sensor. 
     In order to realize a small and inexpensive optical system, each example manufactures the first unit L 1 , the second unit L 2 , and the third unit L 3  by the wafer level process. That is, each of the first unit L 1 , the second unit L 2 , and the third unit L 3  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 image side of the second substrate  21  by the same wafer process. The first unit L 1 , the second unit L 2 , the third unit L 3 , and the image sensor manufactured by the wafer level process are disposed at desired intervals, adhered outside the effective light diameter, and then cut. Many wafer level lenses can be manufactured. 
     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  11 , the second substrate  21 , and the third substrate  31  is made of glass, and each of the first lens  12 , the second lens  22 , and the third lens  32  is made of resin, but the present invention is not limited to this example. As long as the first substrate  11  and the first lens  12  have refractive indexes different from each other, for example, both the first substrate  11  and the first lens  12  may be formed of resin. This is similarly applicable to the second unit L 2  and the third unit L 3 . 
     The diaphragm SP can be formed on the second substrate  21 , for example, by vapor-depositing a light-shielding film made of chromium or the like using a mask, or by forming an opening by etching after the vapor deposition. At that time, by forming the diaphragm SP on a flat surface such as a substrate, it becomes easy to control the mask arrangement in the thickness direction, which is advantageous to the manufacture. 
     The optical system according to each example is an optical system in which the first unit L 1 , the second unit L 2 , and the third unit L 3  are integrated. By joining the optical system according to each example and the fourth substrate (sensor cover glass)  41 , they serve as an imaging system. By forming the lens surface of the third lens  32  on the object side of the third substrate  31  (back cover glass), the back cover glass and the sensor cover glass can be directly joined. This configuration can provide a small optical system having high optical performance while suppressing the costs of materials and manufacturing process (that is, at low cost). The third substrate  31  can be used as the sensor cover glass and the lens surface of the third lens  32  can be formed on the object side of the third substrate  31 , which makes inexpensive the manufacturing process. 
     The optical system according to each example may satisfy at least one of the following inequalities (1a) and (1b). 
       1.00&lt; f 2/ f&lt; 1.50   (1a)
 
       0.60&lt; f 2/ f&lt; 1.60   (1b)
 
     where f is a focal length of the optical system (entire system), and f2 is a focal length of the second lens  22 . The inequality (1a) or (1b) enables the spherical aberration to be corrected a proper value. 
     The numerical range of the inequality (1a) or (1b) may be set to that in the following inequality (1c). 
       0.75&lt; f 2/ f&lt; 1.55   (1c)
 
     The numerical range of the inequality (1a) or (1b) may be set to that in the following inequality (1d). 
       0.85&lt; f 2/ f&lt; 1.52   (1d)
 
     The optical system according to each example may satisfy at least one of the following inequality (2a) and (2b). 
       −2.50&lt; f 3/ f 1&lt;−1.80   (2a)
 
       −3.50&lt; f 3/ f 1&lt;−1.50   (2b)
 
     where f1 is a focal length of the first lens  12 , and f3 is a focal length of the third lens  32 . The inequality (2a) or (2b) enables the astigmatism and distortion to be corrected to proper values. 
     The numerical range of the inequality (2a) or (2b) may be set to that in the following inequality (2c). 
       −3.20&lt; f 3/ f 1&lt;−1.60   (2c)
 
     The numerical range of the inequality (2a) or (2b) may be set to that in the following inequality (2d). 
       −3.00&lt; f 3/ f 1&lt;−1.65   (2d)
 
     The optical system according to each example may satisfy the following inequality (3a) or (3b). 
       0.10&lt; d/f&lt; 0.50   (3a)
 
       0.07&lt; d/f&lt; 0.65   (3b)
 
     where d is a distance on the optical axis OA from the diaphragm SP to a surface on the object side of the third lens  32 . The inequality (3a) or (3b) enables the astigmatism and distortion to be corrected to proper values. 
     The numerical range of the inequality (3a) or (3b) may be set to that in the following inequality (3c). 
       0.10&lt; d/f&lt; 0.62   (3c)
 
     The optical system according to each example may satisfy the following inequality (4a) or (4b). 
       1.20&lt; L/f&lt; 2.40   (4a)
 
       1.00&lt; L/f&lt; 2.40   (4b)
 
     where L is a distance from the third lens  32  to the image plane IP. The inequality (4a) or (4b) enables the spherical aberration and the astigmatism to be corrected to proper values. 
     The numerical range of the inequality (4a) or (4b) may be set to that in the following inequality (4c). 
       1.20&lt; L/f&lt; 2.20   (4c)
 
     The optical system according to each example is configured to cancel various aberrations between the first lens L 12  and the second lens L 22  existing on the object side of the diaphragm SP, and to maintain a balance with the aberrations that are generated in the third lens L 32  on the image side of the diaphragm SP. Therefore, the following inequality (5) may be satisfied. 
       0.30&lt;( f 2− f 1)/ f 3&lt;1.60   (5)
 
     If the value is lower than the lower limit in the inequality (5), the refractive power of the third lens L 32  becomes small and the balance of the aberration correction before and after the diaphragm SP is lost. On the other hand, if the value is higher than the upper limit in the inequality (5), the refractive power of the third lens L 32  becomes large and it becomes difficult to correct various aberrations. In addition, at the same time, the diameter of the third lens L 32  becomes so large that it becomes difficult to secure a width outside the effective diameter and the manufacture becomes difficult. 
     The numerical range of the inequality (5) may be set to that in the following inequality (5a). 
       0.50&lt;( f 2− f 1)/ f 3&lt;1.60   (5a)
 
     The numerical range of the inequality (5) may be set to that in the following inequality (5b). 
       0.60&lt;( f 2− f 1)/ f 3&lt;1.55   (5b)
 
     In the optical system according to each example, only the third lens L 32  is responsible for the aberration correction on the image side of the diaphragm SP. The outer peripheral portion of the third lens L 32  significantly bends the light ray and corrects high-order aberrations. Therefore, the distance d from the diaphragm SP to the third lens L 32  and the refractive power of the third lens L 32  may be properly set. More specifically, the following inequality (6) may be satisfied. 
       0.03&lt; d/f 3&lt;0.40   (6)
 
     If the value is lower than the lower limit in the inequality (6), the refractive power of the third lens L 32  becomes small, so that it becomes difficult to correct the aberration generated on the image side of the diaphragm SP. On the other hand, if the value is higher than the upper limit in the inequality (6), the angle of light ray incident on the outer peripheral portion of the third lens L 32  becomes so gentle that it becomes difficult to correct higher-order aberrations. 
     The numerical range of the inequality (6) may be set to that in the following inequality (6a). 
       0.04&lt; d/f 3&lt;0.35   (6a)
 
     The numerical range of the inequality (6) may be set to that in the following inequality (6b). 
       0.05&lt; d/f 3&lt;0.34   (6b)
 
     Various aberrations may be corrected satisfactorily by satisfying the following inequality (7). 
       1.50&lt; f 3/ f&lt; 3.00   (7)
 
     The numerical range of the inequality (7) may be set to that in the following inequality (7a). 
       1.60&lt; f 3/ f&lt; 2.80   (7a)
 
     In the wafer level lens manufacturing process according to each example, the first lens L 12  and the second lens L 22  are structurally opposite to each other via an air layer. Therefore, in joining the first unit L 1  including the first lens L 12  and the second unit L 2  including the second lens L 22 , it is necessary to bond the outer peripheral portions of the first lens L 12  and the second lens L 22  to each other. Since the first lens L 12  and the second lens L 22  are usually made of resin, it is a manufacturing problem to bond the outer peripheral portion of the resin material with high accuracy to suppress deformations and the like. The optical system according to each example makes relatively stronger the refractive powers of the first lens L 12  and the second lens L 22  to correct higher-order aberrations, so that each lens tends to be larger and a thickness difference between the optical axis and the outer peripheral portion tends to be large. 
     Therefore, the optical system according to each example may satisfy the following inequality (8). 
       0.60&lt; Lar /( d 1+ d 2)&lt;2.00   (8)
 
     where Lar is a distance between the first lens L 12  and the second substrate L 21 , d 1  is a thickness of the first substrate L 11 , and d 2  is a thickness of the second substrate L 21 . If the value is lower than the lower limit in the inequality (8), each of the substrate  1  and the substrate  2  becomes so thick that a small optical system cannot be obtained. On the other hand, if the value is higher than the upper limit in the inequality (8), each of the first substrate L 11  and the second substrate L 21  becomes so thin that they are easy to deform and the manufacture becomes difficult. Alternatively, as the distance increases between the first lens L 12  and the second lens L 22  and the second lens L 22  becomes thicker, the spherical aberration, astigmatism, and the like increase. 
     The numerical range of the inequality (8) may be set to that in the following inequality (8a). 
       0.75&lt; Lar /( d 1+ d 2)&lt;1.80   (8a)
 
     A detailed description will now be given of the optical system according to each example. 
     EXAMPLE 1 
     Referring now to  FIGS. 1, 2A to 2D , a description will be given of the optical system  1   a  according to Example 1 (numerical example 1). As illustrated in  FIG. 1 , the optical system  1   a  includes a first unit L 1 , a second unit L 2 , and a third unit L 3 . The first unit L 1  includes a first substrate (front cover glass)  11 , and a first lens  12  disposed on the image side of it. The first lens  12  is a negative lens with a concave surface facing the image side, and the first lens  12  has a focal length of f1=−0.224 mm. The first lens  12  is formed on the surface on the image side of the first substrate  11  by using the wafer level process. The second unit L 2  includes a second substrate  21 , and a second lens  22  disposed on the object side of it. The second lens  22  is a positive lens with a convex surface facing the object side, and the second lens  22  has a focal length f2 of f2=0.287 mm. The second lens  22  is formed on the surface on the object side of the second substrate  21  by using the wafer level process. The third unit L 3  includes a third substrate (back cover glass)  31 , and a third lens  32  disposed on the object side of it. The third lens  32  is a positive lens with a convex surface facing the object side, and the third lens  32  has a focal length f3 of f3=0.508 mm. The third lens  32  is formed on the surface on the object side of the third substrate  31  by using the wafer level process. 
     In this example, the optical system  1   a  has a focal length f of f=0.238 mm. A distance d on the optical axis from the diaphragm SP to the third lens  32  is d=0.0657 mm. A distance L from the third lens  32  to the image plane IP is L=0.424 mm. The optical system  1   a  according to this example is designed to focus on an object at a position 10 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 2A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 2B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 2C , the distortion in this example is less than 40%. As illustrated in  FIG. 2D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   a  according to this example has proper aberrations. 
     EXAMPLE 2 
     Referring now to  FIGS. 3 and 4A to 4D , a description will be given of the optical system  1   b  according to Example 2 (numerical example 2). As illustrated in  FIG. 3 , the optical system  1   b  according to this example has the same basic configuration as that of the optical system  1   a  of Example 1. The first lens  12  has a focal length f1 of f1=−0.230 mm. The second lens  22  has a focal length f2 of f2=0.283 mm. The third lens  32  has a focal length f3 of f3=0.455 mm. The optical system  1   b  has a focal length f of f=0.235 mm. A distance d from the diaphragm SP to the third lens  32  is d=0.0865 mm. A distance L from the third lens  32  to the image plane IP is L=0.424 mm. The optical system  1   b  according to this example is designed to focus on an object at a position 10 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 4A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 4B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 4C , the distortion in this example is less than 40%. As illustrated in  FIG. 4D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   b  according to this example has proper aberrations. 
     EXAMPLE 3 
     Referring now to  FIGS. 5, 6A to 6D, and 17 , a description will be given of the optical system  1   c  according to Example 3 (numerical example 3). As illustrated in  FIG. 5 , the optical system  1   c  according to this example has the same basic configuration as that of the optical system  1   a  of Example 1. The first lens  12  has a focal length f1 of f1=−0.255 mm. The second lens  22  has a focal length f2 of f2=0.372 mm. The third lens  32  has a focal length f3 of f3=0.539 mm. 
     Referring now to  FIG. 17 , a description will be given of an optical system (wafer level lens)  20  as a comparative example.  FIG. 17  is a sectional view of the optical system  20  according to a comparative example. The optical system  20  includes a first unit L 10 , a second unit L 20 , and a third unit L 30 . The first unit L 10  includes a first substrate  211 , and a first lens  212  disposed on the image side of it. The first lens  212  is a negative lens with a concave surface facing the image side. The second unit L 20  includes a second substrate  221 , and a second lens  222  disposed on the object side of it. The second lens  222  is a positive lens with a convex surface facing the object side. The second unit L 20  includes a third substrate  231 , and a third lens  232  disposed on the image side of it. The third lens  232  is a positive lens with a convex surface facing the image side. The second unit L 20  includes a diaphragm SP between the second substrate  221  and the third substrate  231 . The third unit L 30  includes a fourth substrate (back cover glass)  261  and a fifth substrate (sensor cover glass)  241 . 
     On the other hand, the optical system  1   c  according to this example reduces the number of substrates by using the third substrate  31  required to form the third lens  32  as the back cover glass. Thus, this example can provide a small optical system having high optical performance in which the costs of materials and manufacturing process is reduced, by forming the final lens of the optical system  1   c  on the object side. 
     The optical system  1   c  has a focal length f of f=0.284 mm. A distance d from the diaphragm SP to the third lens  32  is d=0.0379 mm. A distance L from the third lens  32  to the image plane IP is L=0.624 mm. The optical system  1   c  according to this example is designed to focus on an object at a position 10 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 6A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 6B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 6C , the distortion in this example is less than 40%. As illustrated in  FIG. 6D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   c  according to this example has proper aberrations. 
     EXAMPLE 4 
     Referring now to  FIGS. 7 and 8A to 8D , a description will be given of the optical system  1   d  according to Example 4 (numerical example 4). As illustrated in  FIG. 7 , the optical system  1   d  according to this example has the same basic configuration as that of the optical system  1   a  of Example 1. In the optical system  1   d  according to this example, the third substrate  31  is used as the sensor cover glass, and the lens surface of the third lens  32  is formed on the object side of the third substrate  31 , and the third substrate  31  serves as the sensor cover glass and the back cover glass. The optical system  1   d  according to this example has a half angle of view of 59° and an F-number of 2.8, and is an extremely small, bright, and wide-angle optical system. The optical system  1   d  according to this example is designed to focus on an object at a position 5 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 8A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 8B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 8C , the distortion in this example is less than 40%. As illustrated in  FIG. 8D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   d  according to this example has proper aberrations. 
     EXAMPLE 5 
     Referring now to  FIGS. 9 and 10A to 10D , a description will be given of the optical system  1   e  according to Example 5 (numerical example 5). As illustrated in  FIG. 9 , the optical system  1   e  according to this example has the same basic configuration as that of the optical system  1   d  of Example 4. In the optical system  1   e  according to this example, the third substrate  31  is used as the sensor cover glass, and the lens surface of the third lens  32  is formed on the object side of the third substrate  31 , and the third substrate  31  serves as the sensor cover glass and the back cover glass. The optical system  1   e  according to this example has a half angle of view of 57° and an F-number of 2.8, and is an extremely small, bright, and wide-angle optical system. The optical system  1   e  according to this example is designed to focus on an object at a position 5 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 10A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 10B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 10  (C), the distortion in this example is less than 40%. As illustrated in  FIG. 10D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   e  according to this example has proper aberrations. The optical system  1   e  according to this example is an optical system having high manufacturing stability because of the short distance Lar between the first lens and the second substrate. 
     EXAMPLE 6 
     Referring now to  FIGS. 11 and 12A to 12D , a description will be given of the optical system  1   f  according to Example 6 (numerical example 6). As illustrated in  FIG. 11 , the optical system  1   f  according to this example has the same basic configuration as that of the optical system  1   d  of Example 4. In the optical system  1   f  according to this example, the third substrate  31  is used as the sensor cover glass, and the lens surface of the third lens  32  is formed on the object side of the third substrate  31 , and the third substrate  31  serves as the sensor cover glass and the back cover glass. The optical system  1   f  according to this example has a half angle of view of 61° and an F-number of 2.8, and is an extremely small, bright, and wide-angle optical system. The optical system  1   f  according to this example is designed to focus on an object at a position 5 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 12A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 12B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 12C , the distortion in this example is less than 40%. As illustrated in  FIG. 12D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   f  according to this example has proper aberrations. 
     EXAMPLE 7 
     Referring now to  FIGS. 13 and 14A to 14D , a description will be given of the optical system  1   g  according to Example 7 (numerical example 7). As illustrated in  FIG. 13 , the optical system  1   g  according to this example has the same basic configuration as that of the optical system  1   a  of Example 1. The optical system  1   g  according to this example has an image height of 0.82 mm, a half angle of view of 59°, and an F-number of 2.8, and is an extremely small, bright, and wide-angle optical system. The optical system  1   g  according to this example is designed to focus on an object at a position 50 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 14A , the spherical aberration in this example is less than 0.1 mm. As illustrated in  FIG. 14B , the astigmatism in this example is less than 0.1 mm. As illustrated in  FIG. 14C , the distortion in this example is less than 40%. As illustrated in  FIG. 14(D) , the lateral chromatic aberration in this example is less than 0.03 mm. As described above, the optical system  1   g  according to this example has proper aberrations. 
     EXAMPLE 8 
     Referring now to  FIGS. 15 and 16A to 16D , a description will be given of the optical system  1   h  according to Example 8 (numerical example 8). As illustrated in  FIG. 15 , the optical system  1   h  according to this example has the same basic configuration as that of the optical system  1   d  of Example 4. In Examples 1 to 7, the diaphragm SP is provided on the image side of the second substrate L 21 , but in the optical system  1   h  according to this example, the diaphragm SP is provided on the surface on the object side of the second substrate L 21 . The optical system  1   h  according to this example has a half angle of view of 60° and an F-number of 2.9, and is an extremely small, bright, and wide-angle optical system. The optical system  1   h  according to this example is designed to focus on an object at a position 5 mm from the surface closest to the object in the first unit L 1 . 
     As illustrated in  FIG. 16A , the spherical aberration in this example is less than 0.04 mm. As illustrated in  FIG. 16B , the astigmatism in this example is less than 0.04 mm. As illustrated in  FIG. 16C , the distortion in this example is less than 40%. As illustrated in  FIG. 16D , the lateral chromatic aberration in this example is less than 0.01 mm. Thus, the optical system  1   h  according to this example has proper aberrations. 
     A description will now be given of numerical examples 1 to 8 corresponding to Examples 1 to 8. In each numerical example, r denotes a radius of curvature (mm) of an i-th surface counted from the object side, d denotes an on-axis distance (mm) between an i-th surface and an (i+1)-th surface counted from the object side, and nd and vd are a refractive index and an Abbe number of an i-th optical element for the d-line. The Abbe number vd of a certain material is expressed by: 
         vd =( Nd− 1)/( NF−NC ) 
     where Nd, NF, and NC are refractive indexes for the d-line (587.6 nm), the F-line (486.1 nm), and the C-line (656.3 nm) in the Fraunhofer lines. 
     A focal length f (mm) is a value in focusing on an infinity object. BF denotes a backfocus and is a distance from the final surface of the optical system to the image plane. The overall length of the lens is a distance from the first surface to the image plane. An aspherical surface is represented by adding an asterisk * to the surface number. The aspherical shape is expressed as follows: 
     
       
         
           
             
               
                 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 
                     
                   
                 
                 + 
               
             
             ⁢ 
             … 
           
         
       
     
     where x denotes a displacement amount from the surface apex in the optical axis direction, h denotes a height from the optical axis in the direction perpendicular to the optical axis, r denotes a paraxial radius of curvature, k denotes a conical constant, and Ai (i=4, 6, 8, . . . ) denotes an aspherical coefficient. 
     The indication of “e±Z” means “10±Z”. 
     NUMERICAL EXAMPLE1 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.10 
                 1.51680 
                 64.2 
               
               
                 2 
                 ∞ 
                 0.01 
                 1.51000 
                 57.5 
               
               
                  3* 
                 0.114 
                 0.17 
                   
                   
               
               
                  4* 
                 0.158 
                 0.10 
                 1.55000 
                 44.0 
               
               
                 5 
                 ∞ 
                 0.20 
                 1.51680 
                 64.2 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.07 
                   
                   
               
               
                  7* 
                 0.259 
                 0.05 
                 1.51000 
                 57.5 
               
               
                 8 
                 ∞ 
                 0.10 
                 1.51680 
                 64.2 
               
               
                 9 
                 ∞ 
                 0.30 
                 1.51680 
                 64.2 
               
               
                 10  
                 ∞ 
                 0.02 
                   
                   
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −1.40126e+000, A4 = 1.74465e+001, 
               
               
                 A6 = −6.09448e+001, A8 = 2.54898e+003, 
               
               
                 A10 = 1.11764e+005, A12 = −4.94130e+006 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −2.45619e−001, A4 = −2.46995e+001, 
               
               
                 A6 = −3.75404e+002, A8 = −7.60321e+003, 
               
               
                 A10 = 9.46804e+005, A12 = −5.15469e+007 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −1.67841e+001, A4 = 3.69380e+001, 
               
               
                 A6 = −1.45726e+003, A8 = 3.14333e+004, 
               
               
                 A10 = −4.22638e+004, A12 = −7.51083e+006 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.24 
               
               
                 Fno: 
                 2.88 
               
               
                 Half Angle of View: 
                 59.0 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.12 
               
               
                 BF: 
                 0.02 
               
               
                 Object Distance: 
                 10.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE2 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.10 
                 1.51680 
                 64.2 
               
               
                 2 
                 ∞ 
                 0.01 
                 1.51000 
                 57.5 
               
               
                  3* 
                 0.118 
                 0.14 
                   
                   
               
               
                  4* 
                 0.160 
                 0.10 
                 1.56318 
                 39.6 
               
               
                 5 
                 ∞ 
                 0.10 
                 1.51680 
                 64.2 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.09 
                   
                   
               
               
                  7* 
                 0.232 
                 0.06 
                 1.51000 
                 57.5 
               
               
                 8 
                 ∞ 
                 0.10 
                 1.51680 
                 64.2 
               
               
                 9 
                 ∞ 
                 0.30 
                 1.51680 
                 64.2 
               
               
                 10  
                 ∞ 
                 0.02 
                   
                   
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −8.11341e−001, A4 = −1.78031e+001, A6 = 1.00708e+003, 
               
               
                 A8 = 3.94833e+003, A10 = −2.85870e+006, A12 = 5.07388e+007 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −5.24295e+000, A4 = 1.20898e+002, A6 = −4.98544e+003, 
               
               
                 A8 = 1.15921e+005, A10 = −3.00410e+006, A12 = 3.92272e+007 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −1.80560e+001, A4 = 4.34353e+001, A6 = −1.72697e+003, 
               
               
                 A8 = −5.87235e+004, A10 = 7.12574e+006, A12 = −1.59311e+008 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.24 
               
               
                 Fno: 
                 2.88 
               
               
                 Half Angle of View: 
                 59.0 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.02 
               
               
                 BF: 
                 0.02 
               
               
                 Object Distance: 
                 10.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE3 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.20 
                 1.51680 
                 64.2 
               
               
                 2 
                 ∞ 
                 0.01 
                 1.51000 
                 57.5 
               
               
                  3* 
                 0.130 
                 0.18 
                   
                   
               
               
                  4* 
                 0.205 
                 0.13 
                 1.55000 
                 44.0 
               
               
                 5 
                 ∞ 
                 0.20 
                 1.51680 
                 64.2 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.04 
                   
                   
               
               
                  7* 
                 0.286 
                 0.06 
                 1.53000 
                 56.0 
               
               
                 8 
                 ∞ 
                 0.20 
                 1.51680 
                 64.2 
               
               
                 9 
                 ∞ 
                 0.40 
                 1.51680 
                 64.2 
               
               
                 10  
                 ∞ 
                 0.02 
                   
                   
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −1.16949e+000, A4 = 2.17835e+001, A6 = 5.85940e+002, 
               
               
                 A8 = 1.97923e+004, A10 = −1.54923e+006, A12 = 3.88932e+007 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = 2.34627e−001, A4 = −8.16279e+000, A6 = −5.63709e+002, 
               
               
                 A8 = 1.06071e+004, A10 = 3.25696e+005, A12 = −2.41692e+007 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −3.76746e+001, A4 = 1.01499e+002, A6 = −8.41613e+003, 
               
               
                 A8 = 7.54769e+003, A10 = 4.76035e+007, A12 = −2.17281e+009 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.28 
               
               
                 Fno: 
                 2.88 
               
               
                 Half Angle of View: 
                 54.0 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.43 
               
               
                 BF 
                 0.02 
               
               
                 Object Distance 
                 10.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE4 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.62 
               
               
                 2 
                 ∞ 
                 0.045 
                 1.52290 
                 50.3 
                 0.48 
               
               
                  3* 
                 0.0846 
                 0.120 
                   
                   
                 0.28 
               
               
                  4* 
                 0.1231 
                 0.141 
                 1.52290 
                 50.3 
                 0.25 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.19 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.054 
                   
                   
                 0.12 
               
               
                  7* 
                 0.2286 
                 0.072 
                 1.52290 
                 50.3 
                 0.27 
               
               
                 8 
                 ∞ 
                 0.400 
                 1.51680 
                 64.2 
                 0.30 
               
               
                 9 
                 ∞ 
                 0.020 
                   
                   
                 0.55 
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −6.21168e+00, A4 = 6.25636e+02, A6 = −8.47952e+04, 
               
               
                 A8 = 7.80586e+06, A10 = −4.40616e+08, A12 = 1.38205e+10, 
               
               
                 A14 = −1.84957e+11 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −4.15041e+00, A4 = 2.01549e+02, A6 = −1.89467e+04, 
               
               
                 A8 = 1.87535e+06, A10 = −1.38040e+08, A12 = 5.97522e+09, 
               
               
                 A14 = −1.13123e+11 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −5.85227e+01, A4 = 2.60048e+02, A6 = −5.58127e+04, 
               
               
                 A8 = 7.10305e+06, A10 = −5.13511e+08, A12 = 1.94389e+10, 
               
               
                 A14 = −2.98356e+11 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.217 
               
               
                 Fno: 
                 2.83 
               
               
                 Half Angle of View: 
                 59.0 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.05 
               
               
                 BF: 
                 0.020 
               
               
                 Object Distance: 
                 5.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE5 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.62 
               
               
                 2 
                 ∞ 
                 0.045 
                 1.52290 
                 50.3 
                 0.49 
               
               
                  3* 
                 0.1087 
                 0.081 
                   
                   
                 0.29 
               
               
                  4* 
                 0.1272 
                 0.130 
                 1.52290 
                 50.3 
                 0.27 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.23 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.037 
                   
                   
                 0.13 
               
               
                  7* 
                 0.2355 
                 0.070 
                 1.52290 
                 50.3 
                 0.25 
               
               
                 8 
                 ∞ 
                 0.436 
                 1.51680 
                 64.2 
                 0.28 
               
               
                 9 
                 ∞ 
                 0.020 
                   
                   
                 0.54 
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −7.43588e+00, A4 = 4.87017e+02, A6 = −6.30018e+04, 
               
               
                 A8 = 5.88716e+06, A10 = −3.17706e+08, A12 = 8.90173e+09, 
               
               
                 A14 = −9.27729e+10 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −1.29842e+00, A4 = 3.07945e+01, A6 = −2.42278e+03, 
               
               
                 A8 = 4.47425e+05, A10 = −3.15142e+07, A12 = 1.04795e+09, 
               
               
                 A14 = −1.02518e+10 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −4.78137e+01, A4 = 2.30855e+02, A6 = −4.83783e+04, 
               
               
                 A8 = 6.29551e+06, A10 = −4.66358e+08, A12 = 1.79953e+10, 
               
               
                 A14 = −2.79997e+11 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.277 
               
               
                 Fno: 
                 2.79 
               
               
                 Half Angle of View: 
                 57.0 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.02 
               
               
                 BF 
                 0.02 
               
               
                 Object Distance 
                 5.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE6 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.65 
               
               
                 2 
                 ∞ 
                 0.045 
                 1.51500 
                 54.0 
                 0.51 
               
               
                  3* 
                 0.1149 
                 0.140 
                   
                   
                 0.31 
               
               
                  4* 
                 0.1755 
                 0.096 
                 1.51500 
                 54.0 
                 0.23 
               
               
                 5 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.19 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.098 
                   
                   
                 0.12 
               
               
                  7* 
                 0.1943 
                 0.105 
                 1.51500 
                 54.0 
                 0.38 
               
               
                 8 
                 ∞ 
                 0.414 
                 1.51680 
                 64.2 
                 0.40 
               
               
                 9 
                 ∞ 
                 0.020 
                   
                   
                 0.55 
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −8.38246e+00, A4 = 4.47212e+02, A6 = −4.82082e+04, 
               
               
                 A8 = 3.54964e+06, A10 = −1.58303e+08, A12 = 3.76729e+09, 
               
               
                 A14 = −3.72323e+10 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −1.35880e+00, A4 = 1.56995e+02, A6 = −4.30232e+04, 
               
               
                 A8 = 6.73782e+06, A10 = −5.77854e+08, A12 = 2.48373e+10, 
               
               
                 A14 = −4.33446e+11 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −2.10248e+01, A4 = 1.20066e+02, A6 = −1.10557e+04, 
               
               
                 A8 = 6.07621e+05, A10 = −1.93372e+07, A12 = 3.27476e+08, 
               
               
                 A14 = −2.27986e+09 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.226 
               
               
                 Fno: 
                 2.84 
               
               
                 Half Angle of View: 
                 61.1 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.12 
               
               
                 BF: 
                 0.02 
               
               
                 Object Distance: 
                 5.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE7 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.240 
                 1.51680 
                 64.2 
                 2.35 
               
               
                 2 
                 ∞ 
                 0.176 
                 1.52290 
                 50.3 
                 2.02 
               
               
                  3* 
                 0.2457 
                 0.341 
                   
                   
                 1.20 
               
               
                  4* 
                 0.2957 
                 0.418 
                 1.52290 
                 50.3 
                 0.91 
               
               
                 5 
                 ∞ 
                 0.300 
                 1.51680 
                 64.2 
                 0.74 
               
               
                 6 (Diaphragm) 
                 ∞ 
                 0.122 
                   
                   
                 0.27 
               
               
                  7* 
                 0.7245 
                 0.135 
                 1.52290 
                 50.3 
                 0.83 
               
               
                 8 
                 ∞ 
                 0.300 
                 1.51680 
                 64.2 
                 0.88 
               
               
                 9 
                 ∞ 
                 0.553 
                 1.51680 
                 64.2 
                 1.14 
               
               
                 10  
                 ∞ 
                 0.020 
                   
                   
                 1.62 
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −1.82995e+00, A4 = 1.95941e+00, A6 = −9.41015e+00, 
               
               
                 A8 = 1.22664e A10 = −1.03796e+01, A12 = 2.50580e+01, 
               
               
                 A14 = −1.99537e+01 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −2.78973e+00, A4 = 7.70474e+00, A6 = −7.05350e+01, 
               
               
                 A8 = 6.41973e+02, A10 = −4.32391e+03, A12 = 1.49156e+04, 
               
               
                 A14 = −1.96470e+04 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −4.43879e+01, A4 = 3.13426e+00, A6 = −4.10059e+01, 
               
               
                 A8 = 3.38398e+02, A10 = −1.58008e+03, A12 = 3.73365e+03, 
               
               
                 A14 = −3.53936e+03 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.565 
               
               
                 Fno: 
                 2.75 
               
               
                 Half Angle of View: 
                 59.0 
               
               
                 Image Height: 
                 0.82 
               
               
                 Overall Lens Length: 
                 2.60 
               
               
                 BF: 
                 0.020 
               
               
                 Object Distance: 
                 50.0 
               
               
                   
               
            
           
         
       
     
     NUMERICAL EXAMPLE8 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Effective 
               
               
                 Surface No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                 1 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.59 
               
               
                 2 
                 ∞ 
                 0.045 
                 1.52290 
                 50.3 
                 0.45 
               
               
                  3* 
                 0.0984 
                 0.125 
                   
                   
                 0.27 
               
               
                  4* 
                 0.1397 
                 0.138 
                 1.52290 
                 50.3 
                 0.19 
               
               
                 5 (Diaphragm) 
                 ∞ 
                 0.100 
                 1.51680 
                 64.2 
                 0.11 
               
               
                 6 
                 ∞ 
                 0.033 
                   
                   
                 0.19 
               
               
                  7* 
                 0.2093 
                 0.071 
                 1.52290 
                 50.3 
                 0.28 
               
               
                 8 
                 ∞ 
                 0.400 
                 1.51680 
                 64.2 
                 0.30 
               
               
                 9 
                 ∞ 
                 0.020 
                   
                   
                 0.55 
               
               
                 Image Plane 
                 ∞ 
                   
                   
                   
                   
               
            
           
           
               
            
               
                 ASPHERIC DATA 
               
               
                 3rd Surface 
               
               
                   
               
               
                 K = −1.23301e+01, A4 = 7.56038e+02, A6 = −1.22104e+05, 
               
               
                 A8 = 1.32431e+07, A10 = −8.55926e+08, A12 = 2.91280e+10, 
               
               
                 A14 = −4.02217e+11 
               
               
                   
               
               
                 4th Surface 
               
               
                   
               
               
                 K = −3.52848e+00, A4 = 1.55637e+02, A6 = −1.82661e+04, 
               
               
                 A8 = 3.72846e+06, A10 = −6.48173e+08, A12 = 5.88096e+10, 
               
               
                 A14 = −2.17851e+12 
               
               
                   
               
               
                 7th Surface 
               
               
                   
               
               
                 K = −4.99166e+01, A4 = 2.46197e+02, A6 = −4.89127e+04, 
               
               
                 A8 = 5.57700e+06, A10 = −3.64668e+08, A12 = 1.25259e+10, 
               
               
                 A14 = −1.75004e+11 
               
               
                   
               
            
           
           
               
               
            
               
                 Focal Length: 
                 0.215 
               
               
                 Fno: 
                 2.91 
               
               
                 Half Angle of View: 
                 59.7 
               
               
                 Image Height: 
                 0.28 
               
               
                 Overall Lens Length: 
                 1.03 
               
               
                 BF: 
                 0.020 
               
               
                 Object Distance: 
                 5.0 
               
               
                   
               
            
           
         
       
     
     Table 1 summarizes numerical values regarding the inequalities (1) to (8) in each numerical example. 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Numerical Example 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Inequality 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 f 
                 0.238 
                 0.235 
                 0.284 
                 0.217 
                 0.277 
                 0.226 
                 0.565 
                 0.215 
               
               
                 f1 
                 −0.224 
                 −0.230 
                 −0.255 
                 −0.162 
                 −0.208 
                 −0.223 
                 −0.470 
                 −0.188 
               
               
                 f2 
                 0.287 
                 0.283 
                 0.372 
                 0.235 
                 0.243 
                 0.341 
                 0.566 
                 0.267 
               
               
                 f3 
                 0.508 
                 0.455 
                 0.539 
                 0.437 
                 0.450 
                 0.377 
                 1.386 
                 0.400 
               
               
                 d 
                 0.0657 
                 0.0865 
                 0.0379 
                 0.0538 
                 0.0366 
                 0.0981 
                 0.1219 
                 0.1327 
               
               
                 L 
                 0.424 
                 0.424 
                 0.624 
                 0.420 
                 0.456 
                 0.434 
                 0.873 
                 0.420 
               
               
                 d1 
                 0.100 
                 0.100 
                 0.200 
                 0.100 
                 0.100 
                 0.100 
                 0.240 
                 0.100 
               
               
                 d2 
                 0.200 
                 0.100 
                 0.200 
                 0.100 
                 0.100 
                 0.100 
                 0.300 
                 0.100 
               
               
                 Lar 
                 0.269 
                 0.240 
                 0.306 
                 0.261 
                 0.211 
                 0.236 
                 0.759 
                 0.263 
               
               
                 f2/f 
                 1.204 
                 1.206 
                 1.310 
                 1.086 
                 0.877 
                 1.510 
                 1.002 
                 1.240 
               
               
                 f3/f1 
                 −2.272 
                 −1.976 
                 −2.111 
                 −2.700 
                 −2.167 
                 −1.691 
                 −2.949 
                 −2.127 
               
               
                 d/f 
                 0.276 
                 0.368 
                 0.133 
                 0.248 
                 0.132 
                 0.435 
                 0.216 
                 0.616 
               
               
                 L/f 
                 1.778 
                 1.804 
                 2.195 
                 1.937 
                 1.644 
                 1.924 
                 1.546 
                 1.949 
               
               
                 (f2 − f1)/f3 
                 1.005 
                 1.129 
                 1.165 
                 0.909 
                 1.001 
                 1.495 
                 0.747 
                 1.137 
               
               
                 f3/f 
                 2.130 
                 1.936 
                 1.896 
                 2.016 
                 1.623 
                 1.672 
                 2.454 
                 1.858 
               
               
                 d/f3 
                 0.129 
                 0.190 
                 0.070 
                 0.123 
                 0.081 
                 0.260 
                 0.088 
                 0.332 
               
               
                 Lar/(d1 + d2) 
                 0.896 
                 1.200 
                 0.765 
                 1.306 
                 1.054 
                 1.180 
                 1.405 
                 1.316 
               
               
                   
               
            
           
         
       
     
     The optical system according to each example is suitable for an imaging optical system used for a built-in camera of an electronic apparatus such as a mobile phone, a smartphone, or a wearable terminal, and an objective optical system for an endoscope, or the like. 
     EXAMPLE 9 
     Referring now to  FIG. 18 , a description will be given of an electronic apparatus according to Example 9 of the present invention.  FIG. 18  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 8, and an image sensor  73  that receives image light formed by the optical system  72 . As described above, applying the optical system according to each example to an image pickup apparatus such as a smartphone can realize a small image pickup apparatus having high optical performance. 
     EXAMPLE 10 
     Referring now to  FIG. 19 , a description will be given of an image pickup apparatus according to Example 10 of the present invention.  FIG. 19  is a schematic view of principal part of an 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 any of the optical systems according to Examples 1 to 8, 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, applying the optical system of each of the examples to the image pickup apparatus of the endoscope can realize a small image pickup apparatus having high optical performance. 
     Each example can a small and inexpensive optical system having high optical performance, and an image pickup apparatus 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. 2021-003690, filed on Jan. 13, 2021, and No. 2021-175257, filed on Oct. 27, 2021 which are hereby incorporated by reference herein in their entirety.