Patent Publication Number: US-2023152559-A1

Title: Lens apparatus and image pickup apparatus

Description:
BACKGROUND 
     Technical Field 
     The disclosure relates to lens apparatuses and image pickup apparatuses. 
     Description of the Related Art 
     An image pickup apparatus that captures a stereoscopic image (video) is demanded in order to capture the video for content that provides a sense of reality, such as virtual reality. Japanese Patent Laid-Open No. (“JP”) 2020-8629 discloses a lens apparatus that can increase a baseline length with a compact configuration by forming optical images on a single image sensor by bending an optical path of each of two optical systems. JP 11-258518 discloses an observation optical system for magnification variation (zooming) by making variable an air gap in an objective lens. 
     In stereoscopic viewing with the lens apparatus disclosed in JP 2020-8629, a stereoscopic effect decreases for a distant object. In order to capture a stereoscopic image (video) having a natural stereoscopic effect for objects at various object distances, including the distant object, it is necessary to use a more telephoto magnification-varying optical system. The observation optical system disclosed in JP 11-258518 is not supposed to form two optical images on a single image sensor, and has difficulty in miniaturization while avoiding physical interference between optical elements. 
     SUMMARY 
     The disclosure provides a lens apparatus and an image pickup apparatus, each of which has a compact configuration and a long baseline length, and can acquire a stereoscopic image with a natural stereoscopic effect for a distant object. 
     A lens apparatus according to one aspect of the disclosure includes two optical systems. Each of the two optical systems includes, in order from an object side to an image side, a first lens unit having positive refractive power, a second lens unit having negative refractive power, a first reflective surface, a second reflective surface, and a rear lens unit having positive refractive power. At least a distance between the first lens unit and the second lens unit and a distance between the second lens unit and the first reflective surface are changed during magnification variation. The following inequality is satisfied: 
       0.05&lt; D out/ D in&lt;0.50 
     where Din is a distance between surface vertices of lenses disposed closest to the object side in each of the two optical systems, and Dout is a distance between surface vertices of lenses disposed closest to the image side in each of the two optical systems. An image pickup apparatus having the above lens apparatus also constitutes another aspect of the disclosure. 
     Further features of the disclosure 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 principal part of a lens apparatus according to Example 1. 
         FIG.  2    is a schematic diagram of an image circle according to Example 1. 
         FIG.  3    is a sectional view of the optical system according to Example 1. 
         FIGS.  4 A and  4 B  are schematic diagrams of barrels according to Example 1. 
         FIGS.  5 A and  5 B  are aberration diagrams of the optical system according to Example 1. 
         FIG.  6    is a sectional view of an optical system according to Example 2; 
         FIG.  7    is an optical path diagram of the optical system according to Example 2. 
         FIGS.  8 A and  8 B  are aberration diagrams of the optical system according to Example 2. 
         FIG.  9    is a sectional view of an optical system according to Example 3. 
         FIGS.  10 A and  10 B  are aberration diagrams of the optical system according to Example 3. 
         FIG.  11    is a sectional view of an optical system according to Example 4. 
         FIGS.  12 A and  12 B  are aberration diagrams of the optical system according to Example 4. 
         FIG.  13    is a schematic diagram of an image pickup apparatus having an optical system according to each example. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Referring now to the accompanying drawings, a detailed description will be given of embodiments according to the disclosure. 
     Referring now to  FIG.  1   , a description will be given of an imaging optical system (lens apparatus) according to Example 1.  FIG.  1    is a sectional view of principal part of an imaging optical system (lens apparatus)  100  according to this example. The imaging optical system  100  includes two optical systems  101  and  102 . The optical systems  101  and  102  are held by an unillustrated housing. Since the optical systems  101  and  102  are the same except for a reflecting direction of each reflecting member, which will be described below, the optical system  101  will be described as a representative in the following description. Hereinafter, in a case where the optical systems  101  and  102  are said to be the same, it means that the lens configurations and the like are the same except for the reflecting direction of each reflecting member. 
     The optical system  101  includes an intermediate unit LM that bends an optical path. The intermediate unit LM includes a first reflective surface R 1  and a second reflective surface R 2 . In this example, the intermediate unit LM has no refractive power. In this example, an optical axis AX 1  on an object side of the first reflective surface R 1  and an optical axis AX 2  on an image side of the second reflective surface R 2  are parallel to each other, but the optical axis AX 1  may be slightly internally rotated. The term “parallel” is not limited to a strictly parallel state, but includes a state that shifts from the parallel state by about ±5° (approximately parallel state). 
     In  FIG.  1   , IP denotes an image plane (paraxial imaging position). An image sensor such as a CCD sensor or a CMOS sensor or a film is disposed on the image plane IP. An image (optical image) is formed on the image plane IP by each of the optical systems  101  and  102 . That is, two optical images are formed on a single image sensor by the two optical systems  101  and  102  in the imaging optical system  100 . 
     Referring now to  FIG.  2   , a description will be given of two image circles (areas where optical images are formed, that is, effective image circle diameters) IC 1  and IC 2  formed on the image plane IP according to this example.  FIG.  2    is a schematic diagram of the image circles IC 1  and IC 2 . The image circle IC 1  is an image circle formed by the optical system  101 , and the image circle IC 2  is an image circle formed by the optical system  102 . Hence, in this example, two images having a parallax can be acquired by the single image sensor. 
     Referring now to  FIG.  3   , a description will be given of the optical system  101  according to this example.  FIG.  3    is a sectional view of the optical system  101  according to this example.  FIG.  3    illustrates the developed optical path bent by the first reflective surface R 1  and the second reflective surface R 2 . The optical system  101  includes, in order from the object side to the image side, a first lens unit L 1 , a second lens unit L 2 , a first reflective surface R 1 , a second reflective surface R 2 , and a rear lens unit LR. During magnification variation, at least a distance between the first lens unit L 1  and the second lens unit L 2  and a distance between the second lens unit L 2  and the first reflective surface R 1  vary. 
     The first lens unit L 1  has positive refractive power. In this example, the first lens unit L 1  is moved during magnification variation but may not be moved as in the following example. The second lens unit L 2  has negative refractive power and is moved during magnification variation. In this example, the first reflective surface R 1  is disposed at a position adjacent to the second lens unit L 2 . However, as will be described below, a lens unit having positive refractive power and an aperture stop (diaphragm) may be provided between the second lens unit L 2  and the first reflective surface R 1 . The rear lens unit LR has positive refractive power. The first reflective surface R 1  and the second reflective surface R 2  are disposed close to each other, and may be housed inside the same undivided barrel (integrated barrel). 
     In order to capture a stereoscopic image with a single image sensor, the image circles IC 1  and IC 2  of the optical systems  101  and  102  must be separated. In order to separate the image circles IC 1  and IC 2  at a desired angle of view, a field stop FD 1  may be provided on the object side of the first lens unit L 1 . Alternatively, a field stop FD 2  may be provided on the image side of the rear lens unit LR. That is, a field stop may be provided on at least one of a position closest to the object and a position closest to the image plane in the optical system  101 . 
     Referring now to  FIGS.  4 A and  4 B , a description will be given of barrels according to this example.  FIGS.  4 A and  4 B  are schematic diagrams of the barrels,  FIG.  4 A  illustrates a divided barrel between the two reflective surfaces by the aperture stop unit, and  FIG.  4 B  illustrates an integrated barrel between the two reflective surfaces.  FIG.  4 A  corresponds to the configuration disclosed in JP 2020-8629, and  FIG.  4 B  corresponds to this example. In JP 2020-8629, since an aperture stop is inserted between the two reflective surfaces R 1  and R 2  that bend the optical path, each reflective surface must be housed in a separate barrel. This is because the aperture stop unit generally has a diameter larger than that of the housing that holds the lens. Therefore, the configuration disclosed in JP 2020-8629 may cause a relative optical axis shift between the divided barrels, results in imaging displacement and rotation of the optical image, and deteriorates image quality. 
     On the other hand, this example has a purpose to make the configuration more telephoto than the configuration of JP 2020-8629 and the barrel displacement is more influential accordingly. Thus, this example provides no aperture stop between the two reflective surfaces and houses the two reflective surfaces in a single barrel. That is, this example holds the first reflective surface R 1  and the second reflective surface R 2  by the integrated barrel. This configuration can reduce relative displacement between the two reflective surfaces and improve the image quality. In this example, each of the first reflective surface R 1  and the second reflective surface R 2  is formed on a slope of a rectangular prism, but they may be formed on a set of two parallel surfaces of an integrated optical element, such as a simple plane mirror and a prism, as described below. 
     The first reflective surface R 1  and the second reflective surface R 2  may be inserted in a space and arranged between the second lens unit L 2  and the rear lens unit LR as in this example. This is because in a case where the reflective surface is disposed closer to the object side than the second lens unit L 2 , the diameters of the first lens unit L 1  and the first reflective surface R 1  become larger, and the imaging optical system  100  becomes larger. In order to dispose the reflective surface on the image side of the rear lens unit LR, it is necessary to secure a proper back focus and, in a case where the refractive power of the rear lens unit LR is relaxed for this purpose, the diameter of the lens of the rear lens unit LR becomes larger and the optical systems  101  and  102  interfere with each other. 
     The optical system  101  according to this example satisfies the following inequality due to bending of the optical path by the first reflective surface R 1  and the second reflective surface R 2 . This is similarly applied to an optical system according to each example described below. 
       0.05&lt; D out/ D in&lt;0.50  (1)
 
     where Din is a distance between surface vertices of lenses closest to the object in the two optical systems  101  and  102 , and Dout is a distance between surface vertices of lenses closest to the image plane in the two optical systems  101  and  102 . The distance Din is called a baseline length and affects the stereoscopic effect of a stereoscopic image. 
     Inequality (1) defines a ratio between the distance Din between the object-side lens surfaces of the two optical systems  101  and  102  and the distance Dout between the image-side lens surfaces. Satisfying inequality (1) can make the entire apparatus compact while ensuring a sufficient baseline length for stereoscopic viewing. In a case where the value is lower than the lower limit of inequality (1), the lenses of the two optical systems  101  and  102  on the image sides of the second reflective surfaces R 2  physically interfere with each other. Alternatively, the baseline length becomes too long and the parallax becomes excessive. In this case, the stereoscopic image becomes unsuitable for human viewing. On the other hand, in a case where the value is higher than the upper limit of inequality (1), the baseline length becomes too small and the parallax is small. In this case, it is difficult for a person to obtain a stereoscopic effect and thus this configuration is unsuitable for the purpose of imaging a stereoscopic video. The above configuration according to this example can provide a compact magnification-varying imaging optical system (lens apparatus) with a long baseline length and high image quality. 
     The numerical range of inequality (1) may be set to that of inequality (1a) or (1b) below for stereoscopic imaging with a more natural stereoscopic effect for human vision. 
       0.07&lt; D out/ D in&lt;0.47  (1a)
 
       0.13&lt; D out/ D in&lt;0.42  (1b)
 
     A description will now be given of a configuration that the imaging optical system  100  according to this example may satisfy. At least one of the two optical systems  101  and  102  may satisfy the configuration described below. The two optical systems  101  and  102  may have the same configuration, and thus both of the two optical systems  101  and  102  may satisfy the configurations described below. 
     In this example, an aperture stop SP is disposed between the second lens unit L 2  and the first reflective surface R 1 . In a case where the aperture stop SP is disposed on the object side of the second lens unit L 2 , an off-axis light beam in the rear lens unit LR becomes high, and the diameter of the lens here becomes large and it becomes difficult to avoid physical interference between the two optical systems  101  and  102 . In a case where the aperture stop SP is disposed on the image side of the second reflective surface R 2 , the diameter of the lens of the rear lens unit LR itself can be made small, but it becomes difficult to avoid physical interference between the aperture stop units in the two optical systems  101  and  102 . In addition, as described above, in a case where the aperture stop SP is disposed between the first reflective surface R 1  and the second reflective surface R 2 , the relative displacement (positional shift) of the reflective surfaces causes the image quality to deteriorate. Therefore, the aperture stop SP may be disposed between the second lens unit L 2  and the first reflective surface R 1 . 
     The first lens unit L 1  may include a single negative meniscus lens having a convex surface facing the object side and two positive lenses. Distortion and astigmatism can be suppressed by sharing the positive refractive power of the first lens unit L 1  between two or more positive lenses. One or more negative lenses can satisfactorily correct chromatic aberration. The second lens unit L 2  may include two negative lenses and one positive lens, and may include three negative lenses. Distortion and astigmatism can be suppressed by sharing the negative refractive power between two or more negative lenses. The positive lens can suppress chromatic aberration. 
     The rear lens unit LR may not be moved during magnification variation. On the image side of the second reflective surface R 2 , there is a problem of avoiding physical interference between the two optical systems  101  and  102  disposed in parallel. In a case where the rear lens unit LR is movable, a barrel for moving the rear lens unit LR is necessary in the barrel housing the optical system  101 . Such a multi-structured barrel has further difficulty in avoiding interference between the two optical systems  101  and  102 . Therefore, the rear lens unit LR may not be moved during magnification variation. 
     The optical system  101  according to this example may satisfy the following inequalities. This is similarly applicable to an optical system according to each example described below. 
       −1.60&lt; f 12 w/fw&lt;− 0.50  (2)
 
       0.25&lt; DRR/D in&lt;0.49  (3)
 
       0.50&lt; f 1/ fw&lt; 5.00  (4)
 
       −2.00&lt; f 2/ fw&lt;− 0.10  (5)
 
       0.50&lt; fR/fw&lt; 5.00  (6)
 
       1.00&lt; D out/Φout&lt;3.00  (7)
 
     Here, f12w is a combined focal length for the d-line (wavelength 587.6 nm) at the wide-angle ends of the first lens unit L 1  and the second lens unit L 2 . Hereinafter, unless otherwise specified, all focal lengths are based on the d-line. fw is a focal length at the wide-angle end of the entire optical system  101 . DRR is a distance along the optical axis between the first reflective surface R 1  and the second reflective surface R 2 . f1 is a focal length of the first lens unit L 1 . f2 is a focal length of the second lens unit L 2 . fR is a focal length of the rear lens unit LR. Φout is an effective diameter of a lens closest to the image plane in the optical system  101 . The effective diameter Φout is a diameter through which an effective light ray that contributes to imaging passes through that lens. 
     Inequality (2) defines a range regarding a relationship between the focal lengths of the first lens unit L 1  and the second lens unit L 2 . In a case where the value is lower than the lower limit of inequality (2), the refractive power of the first lens unit L 1  becomes too small, and the front lens diameter becomes large. On the other hand, in a case where the value is higher than the upper limit of inequality (2), the refractive powers of the first lens unit L 1  and the second lens unit L 2  become too strong and lateral chromatic aberration and astigmatism become significant. The numerical range of inequality (2) may be set to a range of inequality (2a) or (2b) below in order to achieve both the miniaturization and aberration correction in a well-balanced manner. 
       −1.55&lt; f 12 w/fw&lt;− 0.60  (2a)
 
       −1.51&lt; f 12 w/fw&lt;− 0.77  (2b)
 
     Inequality (3) defines a range regarding a relationship between the distance between the first reflective surface R 1  and the second reflective surface R 2  and the distance Din between the surface vertices of the lenses disposed closest to the object. In a case where the value is lower than the lower limit value of inequality (3), the baseline length becomes insufficient to provide a sufficient stereoscopic effect. On the other hand, in a case where the value is higher than the upper limit of inequality (3), the distance DRR between the two reflective surfaces becomes too long, and accordingly off-axis light beams pass through the outside of the lens in the rear lens unit LR. Therefore, the diameter of the lens in the rear lens unit LR becomes large, and it becomes difficult to arrange the two optical systems  101  and  102  in parallel. 
     The numerical range of inequality (3) may be set to that of inequality (3a) or (3b) below in order to achieve a better balance between the miniaturization and the stereoscopic effect. 
       0.26&lt; DRR/D in&lt;0.48  (3a)
 
       0.28&lt; DRR/D in&lt;0.47  (3b)
 
     Inequality (4) defines a range regarding the focal length of the first lens unit L 1 . In a case where the value is lower than the lower limit of inequality (4), the refractive power of the first lens unit L 1  becomes too strong and lateral chromatic aberration and astigmatism become significant. On the other hand, in a case where the value is higher than the upper limit of inequality (4), the refractive power of the first lens unit L 1  becomes too weak, the overall optical length becomes long, and it becomes difficult to reduce the size of the optical system. The numerical range of inequality (4) may be set to that of inequality (4a) or (4b) below in order to achieve both the aberration correction and miniaturization in a well-balanced manner. 
       0.80&lt; f 1/ fw&lt; 4.50  (4a)
 
       1.22&lt; f 1/ fw&lt; 3.57  (4b)
 
     Inequality (5) defines a range regarding the focal length of the second lens unit L 2 . In a case where the value is lower than the lower limit of inequality (5), the refractive power of the second lens unit L 2  becomes too strong and lateral chromatic aberration and astigmatism become significant. On the other hand, in a case where the value is higher than the upper limit of inequality (5), the refractive power of the second lens unit L 2  becomes too weak, and the overall optical length becomes long, making it difficult to reduce the size of the optical system. The numerical range of inequality (5) may be set to that of inequality (5a) or (5b) below in order to achieve both the aberration correction and miniaturization in a well-balanced manner. 
       −1.50&lt; f 2/ fw&lt;− 0.20  (5a)
 
       −0.95&lt; f 2/ fw&lt;− 0.39  (5b)
 
     Inequality (6) defines a range regarding the focal length of the rear lens unit LR. In a case where the value is lower than the lower limit of inequality (6), the refractive power of the rear lens unit LR becomes too strong, lateral chromatic aberration and astigmatism become significant, and a proper back focus cannot be secured. On the other hand, in a case where the value is higher than the upper limit of inequality (6), the refractive power of the rear lens unit LR becomes too weak, the overall optical length becomes long, and it becomes difficult to reduce the size of the optical system. The numerical range of inequality (6) may be set to that of inequality (6a) or (6b) below in order to achieve both the aberration correction and miniaturization in a well-balanced manner. 
       0.75&lt; fR/fw&lt; 3.50  (6a)
 
       1.03&lt; fR/fw&lt; 2.23  (6b)
 
     Inequality (7) defines a range regarding a relationship between the distance Dout between the surface vertices of the lenses closest to the image plane and the diameter of the lens closest to the image plane. In a case where the value is lower than the lower limit of inequality (7), the lenses in the rear lens units of the optical systems  101  and  102  physically interfere with each other. On the other hand, in a case where the value is higher than the upper limit of inequality (7), the diameter of the lens in the rear lens unit LR becomes too small, a light amount decreases, and high image quality cannot be obtained. The numerical range of inequality (7) may be set to that of inequality (7a) or (7b) below in order to achieve the physical interference and the maximization of the light amount in a well-balanced manner. 
       1.05&lt; D out/Φout&lt;2.40  (7a)
 
       1.10&lt; D out/Φout&lt;1.63  (7b)
 
       FIGS.  5 A and  5 B  are aberration diagrams of the optical system  101  according to this example in an in-focus state at infinity,  FIG.  5 A  illustrates aberration diagrams at the wide-angle end, and  FIG.  5 B  illustrates aberration diagrams at the telephoto end. In each aberration diagram, Fno denotes an F-number, and ω is half an angle of view (° ). In a spherical aberration diagram, a solid line represents spherical aberration for the d-line (wavelength of 587.6 nm), and an alternate long and two short dashes line represents spherical aberration for the g-line (wavelength of 435.8 nm). In the astigmatism diagram, a solid line S represents astigmatism on a sagittal image plane for the d-line, and a dashed line M represents astigmatism on a meridional image plane for the d-line. A distortion diagram illustrates distortion for the d-line. A chromatic aberration diagram illustrates lateral chromatic aberration for the g-line. These are similarly applicable to subsequent aberration diagrams. 
     Referring now to  FIGS.  6  to  12 B , a description will be given of optical systems  101   a ,  101   b , and  101   c  according to Examples 2 to 4.  FIG.  6    is a sectional view of the optical system  101   a  according to Example 2. In this example, as in Example 1, both the first reflective surface R 1  and the second reflective surface R 2  include a prism. However, in this example, unlike Example 1, the first reflective surface R 1  and the second reflective surface R 2  are formed on a single prism. That is, the first reflective surface R 1  and the second reflective surface R 2  according to this example are reflective surfaces of an integrally molded optical element (integrated prism). This configuration can more easily increase the degree of parallelism between the first reflective surface R 1  and the second reflective surface R 2 , have fewer manufacturing errors, and thus higher image quality than a configuration that uses different members for these two reflective surfaces. The integrated prism may have a parallelepiped shape made by extruding a parallelogram that is made by joining two right-angled prisms, in a direction orthogonal to the paper plane of the sectional view illustrated in  FIG.  6    or may have a polyhedral shape that is made smaller by cutting out a portion that is unnecessary for bending of the optical path. 
     This example is different from Example 1 in that the incident angle α of the on-axis principal ray in this example is 35° on the first reflective surface R 1  and the second reflective surface R 2  whereas the incident angle α of Example 1 is 45°, where the incident angle α is an angle between a line normal to the reflective surface and an incident light ray, as illustrated in  FIGS.  4 A and  4 B . In each example, the incident angle α (° ) is set to a range of 20&lt;α&lt;50. The incident angle α may be set to 20&lt;α&lt;46. Reflecting a light ray at a more acute angle on the reflective surface can reduce an apparent curvature difference between the meridional section and the sagittal section, thereby reduce an astigmatic difference, and have an effective configuration for high image quality, in a case where the reflective surface has curvature due to a manufacturing error. 
     In this example, a third lens unit L 3  having positive refractive power is disposed between the second lens unit L 2  and the first reflective surface R 1 . Therefore, the optical system  101   a  includes, in order from the object side, a first lens unit L 1  having positive refractive power, a second lens unit L 2  having negative refractive power, a third lens unit L 3  having positive refractive power, and a rear lens unit LR having positive refractive power. An afocal optical system that performs only magnification variation with the lens units L 1 , L 2 , and L 3  can collimate and guide an on-axis light flux to the first reflective surface R 1  and subsequent optical elements, and thereby it becomes easier to reduce an effective diameter after the optical path is bent. Therefore, it becomes easy to avoid interference between the two optical systems  101  and  102 . In this case, since there is little variation in aberration on the object side of the first reflective surface R 1  during magnification variation, aberration correction by the rear lens unit LR is facilitated. 
     The rear lens unit LR includes a rear A lens unit LRA, a rear B lens unit LRB, and a rear C lens unit LRC. The rear B lens unit LRB may be movable in a direction orthogonal to the optical axis for image stabilization. The rear A lens unit LRA is a lens unit on the object side of the rear B lens unit LRB. The rear C lens unit LRC is a lens unit on the image side of the rear B lens unit LRB. 
       FIG.  7    is an optical path diagram regarding the lens units L 1 , L 2 , and L 3  in the optical system  101   a . The optical path diagram of  FIG.  7    illustrates the on-axis angle of view and the most off-axis angle of view. The afocal here is not limited to a case where the marginal ray of the on-axis light beam is completely parallel to the optical axis, but may have an angle of about ±10°. 
     In this example, the third lens unit L 3  is movable during magnification variation but may not be moved during magnification variation in a case where the rear lens unit LR may compensate for the position of the image plane. Alternatively, a second N lens unit L 2 N having negative refractive power may be disposed between the second lens unit L 2  and the third lens unit L 3  to serve as a unit that compensates for the position of the image plane during magnification variation. The third lens unit L 3  may include one positive lens and one negative lens in order to satisfactorily correct chromatic aberration. 
     The configuration according to this example has four units that include a first lens unit L 1  having positive refractive power, a second lens unit L 2  having negative refractive power, a third lens unit L 3  having positive refractive power, a first reflective surface R 1 , a second reflective surface R 2 , and a rear lens unit LR having positive refractive power. This configuration can minimize the number of lens units, and provide the imaging optical system  100  as a compact and high-quality magnification-varying optical system. 
     In this example, the first lens unit L 1  is not moved during magnification variation. This configuration eliminates a shift of the optical axis of the first lens unit L 1  during magnification variation, and provides a configuration suitable for high image quality. 
     The optical system  101   a  may satisfy at least one of the following inequalities (8) to (12). This is similarly applicable to optical systems  101   b  and  101   c  according to Examples 3 and 4, which will be described below. 
       1.00&lt;| fRA/fRB|&lt; 2.00  (8)
 
       0.20&lt; f 3/ ft&lt; 1.00  (9)
 
       0.20&lt;3/min( D 3 R )&lt;1.40  (10)
 
       0.20&lt;min( D 3 R )/Max( D total)&lt;0.80  (11)
 
       0.60&lt; f 3/ fw&lt; 3.00  (12)
 
     Here, fRA and fRB are focal lengths of the rear A lens unit LRA and the rear B lens unit LRB, respectively, in a case where the rear lens unit LR has an image stabilizing function. f3 is a focal length of the third lens unit L 3 . ft is a focal length at the telephoto end of the entire optical system  101 . D3R is a distance along the optical axis between the third lens unit L 3  and the rear lens unit LR. That is, the distance D3R is a sum (D 1 +DRR+D 2 ) of the distance D 1  along the optical axis between the optical surface closest to the image plane in the third lens unit L 3  and the first reflective surface R 1 , the distance DRR, and the distance D 2  along the optical axis between the second reflective surface R 2  and an optical surface closest to the object in the rear lens unit LR. min(D3R) is a minimum value of the distance D3R during magnification variation. Dtotal is a distance along the optical axis between the optical surface closest to the object and the optical surface closest to the image plane in the optical system  101 , and Max(Dtotal) is a maximum value of the distance Dtotal during magnification variation. The term “optical surface,” as used in this example, means a boundary surface through which a light ray passes during a use state and a surface extending with the same radius of curvature as the boundary surface. In particular, a reflective surface is also defined as the optical surface. In each example, a distance means an actual length. 
     Inequality (8) defines a range regarding a refractive power relationship between the movable unit and the non-movable unit in the rear lens unit LR in a case where the rear lens unit LR provides image stabilization. In this example, the rear B lens unit LRB in the rear lens unit LR is movable by a moving amount having a component in the direction orthogonal to the optical axis for image stabilization. Thereby, the image stabilization can be performed, and this configuration is suitable for high image quality. For the image stabilization, at least one of the rear A lens unit LRA and the rear C lens unit LRC may be provided. However, both the rear A lens unit LRA and the rear C lens unit LRC may be provided in order to prevent the moving amount of the rear B lens unit LRB for the image stabilization from being excessively large, to improve the image stabilizing sensitivity of the rear B lens unit LRB to some extent, and to satisfactorily correct aberrations. The image stabilizing sensitivity is a ratio |Δ 2 /Δ 1 | of a moving amount Δ 2  of an imaging point on the image plane to a moving amount Δ 1  in the direction orthogonal to the optical axis of the image stabilizing lens unit. 
     In a case where the value is higher than the upper limit of inequality (8), the negative refractive power becomes strong and the image stabilizing performance is improved, but the lens diameter in the rear lens unit LR becomes larger and it is difficult to avoid physical interference between the optical systems  101  and  102 . On the other hand, in a case where the value is lower than the lower limit of inequality (8), the negative refractive power becomes too weak and sufficient image stabilizing performance cannot be obtained. The numerical range of inequality (8) may be set to that of inequality (8a) or (8b) below in order to maximize the image stabilizing performance and avoid the physical interference described above. 
       1.10&lt;| fRA/fRB|&lt; 1.90  (8a)
 
       1.29&lt;| fRA/fRB|&lt; 1.70  (8b)
 
     Inequality (9) defines a range regarding the focal length of the third lens unit L 3 . In a case where the value is lower than the lower limit of inequality (9), the third lens unit L 3  makes higher an angle of an off-axis light beam and the lens diameter of the rear lens unit LR becomes large. On the other hand, in a case where the value is higher than the upper limit of inequality (9), the refractive power of the third lens unit L 3  becomes too weak, the distance between the second lens unit L 2  and the third lens unit L 3  becomes longer, and the diameter of the front lens increases. In addition, since the optical overall length becomes long, this is unsuitable for miniaturization. The numerical range of inequality (9) may be set to that of inequality (9a) or (9b) below in order to reduce the size of the entire optical system. 
       0.30&lt; f 3/ ft&lt; 0.80  (9a)
 
       0.45&lt; f 3/ ft&lt; 0.60  (9b)
 
     Inequality (10) defines a range regarding the focal length of the third lens unit L 3  and the distance between the third lens unit L 3  and the rear lens unit LR necessary to insert the reflecting member. In a case where the value is lower than the lower limit of inequality (10), the refractive power of the third lens unit L 3  becomes too strong, and it becomes difficult to correct coma and astigmatism. In a case where the value is higher than the upper limit of inequality (10), the overall optical length will be longer and unsuitable for miniaturization. The numerical range of inequality (10) may be set to that of inequality (10a) or (10b) below in order to achieve both the aberration correction and miniaturization of the optical system in a well-balanced manner. 
       0.30&lt; f 3/min( D 3 R )&lt;1.35  (10a)
 
       0.54&lt; f 3/min( D 3 R )&lt;1.30  (10b)
 
     Inequality (11) defines a range that may be satisfied over the entire magnification varying range by the distance D3R between the third lens unit L 3  and the rear lens unit LR, and the distance Dtotal along the optical axis from the most object-side optical surface to the most image-side optical surface in the optical system  101 . In a case where the value is lower than the lower limit of inequality (11), the distance between the third lens unit L 3  and the rear lens unit LR becomes too narrow and the baseline length necessary for natural stereoscopic vision cannot be obtained. On the other hand, in a case where the value is higher than the upper limit of inequality (11), the optical path bending portion becomes too long and large relative to the overall length of the optical system  101  and it becomes difficult to realize a compact optical system. The numerical range of inequality (11) may be set to that of inequality (11a) or (11b) below in order to achieve the stereoscopic effect and miniaturization of the optical system in a well-balanced manner. 
       0.25&lt;min( D 3 R )/Max( D total)&lt;0.70  (11a)
 
       0.31&lt;min( D 3 R )/Max( D total)&lt;0.57  (11b)
 
     Inequality (12) defines a range regarding the focal length of the third lens unit L 3 . In a case where the value is lower than the lower limit of inequality (12), the angle of the off-axis light flux in the third lens unit L 3  becomes too high and the lens diameter of the rear lens unit LR becomes large. On the other hand, in a case where the value is higher than the upper limit of inequality (12), the refractive power of the third lens unit L 3  becomes too weak, and both the distance between the second lens unit L 2  and the third lens unit L 3  and the diameter of the front lens increase. In addition, since the optical overall length becomes long, this is unsuitable for miniaturization. The numerical range of inequality (12) may be set to that of the following inequality (12a) or (12b) in order to reduce the size of the entire optical system. 
       0.80&lt; f 3/ fw&lt; 2.50  (12a)
 
       1.25&lt; f 3/ fw&lt; 1.67  (12b)
 
       FIGS.  8 A and  8 B  are aberration diagrams of the optical system  101   a  in this example in an in-focus state at infinity,  FIG.  8 A  illustrates aberration diagrams at the wide-angle end, and  FIG.  8 B  illustrates aberration diagrams at the telephoto end. 
     Referring now to  FIGS.  9 ,  10 A, and  10 B , a description will be given of the optical system  101   b  according to Example 3.  FIG.  9    is a sectional view of the optical system  101   b  according to this example. This example is different from the above examples in that the value of Dout/Din in inequality (1) is as small as 0.14, and this example can provide a stereoscopic image with an enhanced stereoscopic effect. In a case where the distance is made longer between the first reflective surface R 1  and the second reflective surface R 2 , a prism may be used for the reflective surface instead of a plane mirror because it facilitates aberration correction.  FIGS.  10 A and  10 B  are aberration diagrams of the optical system  101   b  according to this example in an in-focus state at infinity,  FIG.  10 A  illustrates aberration diagrams at the wide-angle end, and  FIG.  10 B  illustrates aberration diagrams at the telephoto end. 
     Referring now to  FIGS.  11 ,  12 A, and  12 B , a description will be given of the optical system  101   c  according to Example 4.  FIG.  11    is a sectional view of the optical system  101   c  according to this example. This example is different from each of the above examples in that the reflective surface includes a plane mirror. 
       FIGS.  12 A and  12 B  are aberration diagrams of the optical system  101   c  according to this example in an in-focus state at infinity,  FIG.  12 A  illustrates aberration diagrams at the wide-angle end, and  FIG.  12 B  illustrates aberration diagrams at the telephoto end. 
     Numerical examples 1 to 4 corresponding to Examples 1 to 4 will be illustrated below. In each numerical example, a surface number is the order of optical surfaces counted from the object side. r is a radius of curvature of an i-th (i is a natural number) optical surface (i-th surface) counted from the object side, and d is a distance between the i-th surface and an (i+1)-th surface. nd and νd are a refractive index and an Abbe number for the d-line of the lens, respectively. The Abbe number νd of a certain material is calculated as follows: 
       ν d =( 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 line, respectively. 
     In each numerical example, each of d, focal length (mm). F-number, and half angle of view (degrees) has a value in a case where the optical system according to each example is in-focus on an object at infinity (infinity object). BF (back focus) is a distance on the optical axis from the final lens surface (the lens surface closest to the image plane) to a paraxial image plane in terms of air equivalent length. An “overall lens length” is a length obtained by adding the back focus BF to a distance on the optical axis from the frontmost surface (lens surface on the most object side) to the final surface of the optical system. The lens unit includes one or more lenses. 
     Numerical Example 1 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                  1 
                 61.533 
                 1.00 
                 1.85478 
                 24.8 
                 36.92 
               
               
                  2 
                 41.300 
                 0.30 
                   
                   
                 36.00 
               
               
                  3 
                 43.262 
                 2.96 
                 1.69680 
                 55.5 
                 36.00 
               
               
                  4 
                 91.486 
                 0.10 
                   
                   
                 35.74 
               
               
                  5 
                 66.448 
                 3.23 
                 1.59522 
                 67.7 
                 35.52 
               
               
                  6 
                 −18590.409 
                 (Variable) 
                   
                   
                 35.21 
               
               
                  7 
                 17.356 
                 1.00 
                 1.80400 
                 46.5 
                 16.73 
               
               
                  8 
                 14.610 
                 2.32 
                   
                   
                 15.61 
               
               
                  9 
                 708.342 
                 1.00 
                 1.80400 
                 46.5 
                 15.53 
               
               
                 10 
                 13.667 
                 1.96 
                 1.80810 
                 22.8 
                 14.24 
               
               
                 11 
                 33.241 
                 3.45 
                   
                   
                 13.93 
               
               
                 12 
                 −20.964 
                 0.84 
                 1.88300 
                 40.8 
                 13.20 
               
               
                 13 
                 −32.689 
                 0.00 
                   
                   
                 13.31 
               
               
                 14 
                 67.508 
                 1.13 
                 1.90525 
                 35.0 
                 13.10 
               
               
                 15 
                 108.263 
                 (Variable) 
                   
                   
                 12.90 
               
               
                 16(Aperture Stop) 
                 ∞ 
                 1.32 
                   
                   
                 7.65 
               
               
                 17 
                 ∞ 
                 10.00  
                 1.51633 
                 64.1 
                 20.00 
               
               
                 18 
                 ∞ 
                 10.00  
                 1.51633 
                 64.1 
                 28.00 
               
               
                 19 
                 ∞ 
                 1.00 
                   
                   
                 20.00 
               
               
                 20 
                 ∞ 
                 10.00  
                 1.51633 
                 64.1 
                 20.00 
               
               
                 21 
                 ∞ 
                 10.00  
                 1.51633 
                 64.1 
                 28.00 
               
               
                 22 
                 ∞ 
                 (Variable) 
                   
                   
                 20.00 
               
               
                 23 
                 32.482 
                 2.44 
                 1.53775 
                 74.7 
                 14.62 
               
               
                 24 
                 −33.960 
                 0.10 
                   
                   
                 14.71 
               
               
                 25 
                 16.125 
                 3.15 
                 1.43875 
                 94.9 
                 14.52 
               
               
                 26 
                 −40.802 
                 1.03 
                 1.85478 
                 24.8 
                 14.25 
               
               
                 27 
                 97.774 
                 5.37 
                   
                   
                 13.90 
               
               
                 28 
                 26.279 
                 2.95 
                 1.72047 
                 34.7 
                 12.61 
               
               
                 29 
                 −14.430 
                 0.82 
                 1.69680 
                 55.5 
                 12.34 
               
               
                 30 
                 11.440 
                 2.59 
                   
                   
                 11.06 
               
               
                 31 
                 −14.957 
                 0.78 
                 1.88300 
                 40.8 
                 11.07 
               
               
                 32 
                 −19.637 
                 1.40 
                   
                   
                 11.51 
               
               
                 33 
                 53.143 
                 0.78 
                 1.91650 
                 31.6 
                 12.32 
               
               
                 34 
                 17.979 
                 2.05 
                 1.68893 
                 31.1 
                 12.38 
               
               
                 35 
                 −79.431 
                 (Variable) 
                   
                   
                 12.49 
               
               
                 Image Plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
               
                 ZOOM RATIO 2.78 
               
            
           
           
               
               
               
               
            
               
                   
                 WIDE- 
                   
                 TELE- 
               
               
                   
                 ANGLE 
                 MIDDLE 
                 PHOTO 
               
               
                   
               
               
                 Focal Length: 
                 28.80 
                 41.71 
                 79.99 
               
               
                 FNO 
                 5.60 
                 5.60 
                 5.59 
               
               
                 Half Angle of View (degrees) 
                 16.90 
                 11.85 
                 6.24 
               
               
                 Image Height 
                 8.75 
                 8.75 
                 8.75 
               
               
                 Overall lens length 
                 140.00 
                 153.36 
                 158.68 
               
               
                 BF 
                 33.27 
                 33.27 
                 33.27 
               
               
                 d 6 
                 1.00 
                 19.07 
                 38.36 
               
               
                 d15 
                 19.68 
                 14.97 
                 1.00 
               
               
                 d22 
                 1.00 
                 1.00 
                 1.00 
               
               
                 d35 
                 33.27 
                 33.27 
                 33.27 
               
               
                 Entrance Pupil Position 
                 2.9.98 
                 67.68 
                 116.41 
               
               
                 Exit Pupil Position 
                 −69.27 
                 −69.27 
                 −69.27 
               
               
                 Front Principal Point Position 
                 50.69 
                 92.42 
                 134.00 
               
               
                 Rear Principal Point Position 
                 4.47 
                 −8.45 
                 −46.73 
               
               
                   
               
            
           
           
               
            
               
                 Zoom Lens Unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                   
                   
                 Configu- 
                 Principal 
                 Principal 
               
               
                 Lens 
                 Starting 
                 Focal 
                 ration 
                 Point 
                 Point 
               
               
                 Unit 
                 Surface 
                 Length 
                 Length 
                 Position 
                 Position 
               
               
                   
               
               
                 L1 
                 1 
                 93.38 
                 7.59 
                 0.66 
                 −4.07 
               
               
                 L2 
                 7 
                 −24.77 
                 11.69 
                 5.17 
                 −3.90 
               
               
                 LM 
                 16 
                 ∞ 
                 0.32 
                 14.35 
                 −14.35 
               
               
                 LR 
                 23 
                 32.82 
                 23.46 
                 −10.57 
                 −23.42 
               
               
                   
               
            
           
           
               
            
               
                 Single Lens Data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Starting Surface 
                 Focal Length 
               
               
                   
               
               
                 1 
                 1 
                 −150.36 
               
               
                 2 
                 3 
                 114.89 
               
               
                 3 
                 5 
                 111.25 
               
               
                 4 
                 7 
                 −137.15 
               
               
                 5 
                 9 
                 −17.34 
               
               
                 6 
                 10 
                 27.49 
               
               
                 7 
                 12 
                 −68.49 
               
               
                 8 
                 14 
                 195.53 
               
               
                 9 
                 17 
                 0.00 
               
               
                 10 
                 18 
                 0.00 
               
               
                 11 
                 20 
                 0.00 
               
               
                 12 
                 21 
                 0.00 
               
               
                 13 
                 23 
                 31.17 
               
               
                 14 
                 25 
                 26.79 
               
               
                 15 
                 26 
                 −33.56 
               
               
                 16 
                 28 
                 13.33 
               
               
                 17 
                 29 
                 −9.04 
               
               
                 18 
                 31 
                 −77.08 
               
               
                 19 
                 33 
                 −29.97 
               
               
                 20 
                 34 
                 21.46 
               
               
                   
               
            
           
         
       
     
     Numerical Example 2 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                  1 
                 55.290 
                 1.00 
                 1.80810 
                 22.8 
                 32.98 
               
               
                  2 
                 36.349 
                 0.37 
                   
                   
                 32.10 
               
               
                  3 
                 38.952 
                 5.05 
                 1.59522 
                 67.7 
                 32.10 
               
               
                  4 
                 −161.885 
                 0.10 
                   
                   
                 31.86 
               
               
                  5 
                 25.530 
                 4.57 
                 1.43875 
                 94.7 
                 28.60 
               
               
                  6 
                 159.630 
                 (Variable) 
                   
                   
                 27.94 
               
               
                  7 
                 164.950 
                 1.00 
                 1.85026 
                 32.3 
                 15.72 
               
               
                  8 
                 13.433 
                 3.11 
                   
                   
                 13.77 
               
               
                  9 
                 −21.804 
                 1.00 
                 1.51633 
                 64.1 
                 13.73 
               
               
                 10 
                 17.581 
                 2.41 
                 1.80810 
                 22.8 
                 13.75 
               
               
                 11 
                 −75.114 
                 0.85 
                   
                   
                 13.65 
               
               
                 12 
                 −22.345 
                 0.84 
                 1.72916 
                 54.7 
                 13.62 
               
               
                 13 
                 −70.712 
                 (Variable) 
                   
                   
                 13.70 
               
               
                 14 
                 54.947 
                 2.74 
                 1.73400 
                 51.5 
                 12.90 
               
               
                 15 
                 −13.889 
                 1.01 
                 1.89190 
                 37.1 
                 12.79 
               
               
                 16 
                 −35.761 
                 (Variable) 
                   
                   
                 12.73 
               
               
                 17(Aperture Stop) 
                 ∞ 
                 1.32 
                   
                   
                 12.07 
               
               
                 18 
                 ∞ 
                 12.00  
                 1.51633 
                 64.1 
                 23.00 
               
               
                 19 
                 ∞ 
                 20.00  
                 1.51633 
                 64.1 
                 25.00 
               
               
                 20 
                 ∞ 
                 12.00  
                 1.51633 
                 64.1 
                 25.00 
               
               
                 21 
                 ∞ 
                 (Variable) 
                   
                   
                 23.00 
               
               
                 22 
                 26.982 
                 2.42 
                 1.53775 
                 74.7 
                 14.03 
               
               
                 23 
                 −35.836 
                 0.10 
                   
                   
                 14.06 
               
               
                 24 
                 27.834 
                 2.65 
                 1.43875 
                 94.7 
                 13.80 
               
               
                 25 
                 −23.912 
                 1.03 
                 1.85478 
                 24.8 
                 13.58 
               
               
                 26 
                 3121.471 
                 (Variable) 
                   
                   
                 13.45 
               
               
                 27 
                 41.313 
                 2.59 
                 1.74000 
                 28.3 
                 13.33 
               
               
                 28 
                 −17.992 
                 0.82 
                 1.70154 
                 41.2 
                 13.16 
               
               
                 79 
                 14.792 
                 2.34 
                   
                   
                 12.36 
               
               
                 30 
                 −22.095 
                 0.78 
                 1.69680 
                 55.5 
                 12.39 
               
               
                 31 
                 −83.146 
                 (Variable) 
                   
                   
                 12.93 
               
               
                 32 
                 40.512 
                 0.78 
                 1.91650 
                 31.6 
                 14.27 
               
               
                 33 
                 26.938 
                 2.04 
                 1.79360 
                 37.1 
                 14.38 
               
               
                 34 
                 −71.942 
                 (Variable) 
                   
                   
                 14.49 
               
               
                 Image Plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
               
                 ZOOM RATIO 2.78 
               
            
           
           
               
               
               
               
            
               
                   
                 WIDE- 
                   
                 TELE- 
               
               
                   
                 ANGLE 
                 MIDDLE 
                 PHOTO 
               
               
                   
               
               
                 Focal Length: 
                 28.80 
                 41.08 
                 80.00 
               
               
                 FNO 
                 3.98 
                 3.98 
                 4.00 
               
               
                 Half Angle of View (degrees) 
                 16.90 
                 12.02 
                 6.24 
               
               
                 Image Height 
                 8.75 
                 8.75 
                 8.75 
               
               
                 Overall lens length 
                 135.00 
                 135.00 
                 134.99 
               
               
                 BF 
                 27.91 
                 28.23 
                 28.90 
               
               
                 d 6 
                 0.93 
                 6.56 
                 13.43 
               
               
                 d13 
                 14.46 
                 10.45 
                 1.00 
               
               
                 d16 
                 3.45 
                 1.81 
                 4.37 
               
               
                 d21 
                 0.30 
                 0.30 
                 0.50 
               
               
                 d26 
                 0.97 
                 1.32 
                 0.47 
               
               
                 d31 
                 2.06 
                 1.39 
                 1.39 
               
               
                 d34 
                 27.91 
                 28.23 
                 28.90 
               
               
                 Entrance Pupil Position 
                 28.49 
                 45.47 
                 81.51 
               
               
                 Exit Pupil Position 
                 −84.09 
                 −76.87 
                 −77.86 
               
               
                 Front Principal Point Position 
                 49.89 
                 70.50 
                 101.56 
               
               
                 Rear Principal Point Position 
                 −0.89 
                 −12.85 
                 −51.10 
               
               
                   
               
            
           
           
               
            
               
                 Zoom Lens Unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                   
                   
                 Configu- 
                 Principal 
                 Principal 
               
               
                 Lens 
                 Starting 
                 Focal 
                 ration 
                 Point 
                 Point 
               
               
                 Unit 
                 Surface 
                 Length 
                 Length 
                 Position 
                 Position 
               
               
                   
               
               
                 L1 
                 1 
                 39.12 
                 11.09 
                 2.72 
                 −4.69 
               
               
                 L2 
                 7 
                 −12.32 
                 9.20 
                 1.59 
                 −5.06 
               
               
                 L3 
                 14 
                 37.57 
                 3.75 
                 1.32 
                 −0.84 
               
               
                 LM 
                 17 
                 ∞ 
                 5.32 
                 15.17 
                 −15.17 
               
               
                 LRA 
                 22 
                 29.20 
                 6.21 
                 −0.31 
                 −4.25 
               
               
                 LRB 
                 27 
                 −20.32 
                 6.53 
                 3.86 
                 −1.03 
               
               
                 LRC 
                 32 
                 34.72 
                 2.83 
                 0.53 
                 −1.04 
               
               
                   
               
            
           
           
               
            
               
                 Single Lens Data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Starting Surface 
                 Focal Length 
               
               
                   
               
               
                 1 
                 1 
                 −134.48 
               
               
                 2 
                 3 
                 53.25 
               
               
                 3 
                 5 
                 68.55 
               
               
                 4 
                 7 
                 −17.25 
               
               
                 5 
                 9 
                 −18.69 
               
               
                 6 
                 10 
                 17.84 
               
               
                 7 
                 12 
                 −45.13 
               
               
                 8 
                 14 
                 15.36 
               
               
                 9 
                 15 
                 −26.03 
               
               
                 10 
                 18 
                 0.00 
               
               
                 11 
                 19 
                 0.00 
               
               
                 12 
                 20 
                 0.00 
               
               
                 13 
                 22 
                 29.02 
               
               
                 14 
                 24 
                 29.78 
               
               
                 15 
                 25 
                 −27.76 
               
               
                 16 
                 27 
                 17.26 
               
               
                 17 
                 28 
                 −11.45 
               
               
                 18 
                 30 
                 −43.41 
               
               
                 19 
                 32 
                 −90.21 
               
               
                 20 
                 33 
                 24.92 
               
               
                   
               
            
           
         
       
     
     Numerical Example 3 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                  1 
                 ∞ 
                 1.00 
                   
                   
                 34.20 
               
               
                  2 
                 50.774 
                 1.00 
                 1.80810 
                 22.8 
                 33.36 
               
               
                  3 
                 35.103 
                 3.13 
                   
                   
                 32.44 
               
               
                  4 
                 50.401 
                 4.04 
                 1.59522 
                 67.7 
                 32.52 
               
               
                  5 
                 −238.185 
                 0.10 
                   
                   
                 32.34 
               
               
                  6 
                 28.709 
                 5.40 
                 1.43875 
                 94.7 
                 30.13 
               
               
                  7 
                 −335.318 
                 (Variable) 
                   
                   
                 29.59 
               
               
                  8 
                 891.959 
                 1.00 
                 1.85026 
                 32.3 
                 16.60 
               
               
                  9 
                 15.061 
                 3.45 
                   
                   
                 14.78 
               
               
                 10 
                 −19.903 
                 1.00 
                 1.51633 
                 64.1 
                 14.75 
               
               
                 11 
                 20.707 
                 2.50 
                 1.80810 
                 22.8 
                 15.19 
               
               
                 12 
                 −80.461 
                 0.78 
                   
                   
                 15.17 
               
               
                 13 
                 −28.235 
                 0.84 
                 1.72916 
                 54.7 
                 15.15 
               
               
                 14 
                 −46.634 
                 (Variable) 
                   
                   
                 15.29 
               
               
                 15 
                 71.305 
                 2.88 
                 1.73400 
                 51.5 
                 14.39 
               
               
                 16 
                 −15.739 
                 1.00 
                 1.89190 
                 37.1 
                 14.30 
               
               
                 17 
                 −39.124 
                 (Variable) 
                   
                   
                 14.27 
               
               
                 18(Aperture Stop) 
                 ∞ 
                 1.32 
                   
                   
                 13.45 
               
               
                 19 
                 ∞ 
                 7.00 
                 1.51633 
                 64.1 
                 13.27 
               
               
                 20 
                 ∞ 
                 −55.00  
                   
                   
                 18.76 
               
               
                 21 
                 ∞ 
                 7.00 
                   
                   
                 19.10 
               
               
                 22 
                 ∞ 
                 (Variable) 
                   
                   
                 16.49 
               
               
                 23 
                 27.814 
                 3.10 
                 1.53775 
                 74.7 
                 17.08 
               
               
                 24 
                 −38.441 
                 0.10 
                   
                   
                 17.07 
               
               
                 25 
                 29.313 
                 3.26 
                 1.43875 
                 94.7 
                 16.44 
               
               
                 26 
                 −25.951 
                 1.03 
                 1.85478 
                 24.8 
                 16.14 
               
               
                 27 
                 1712.494 
                 (Variable) 
                   
                   
                 15.84 
               
               
                 28 
                 40.391 
                 2.97 
                 1.74000 
                 28.3 
                 15.36 
               
               
                 29 
                 −20.626 
                 0.82 
                 1.70154 
                 41.2 
                 15.12 
               
               
                 30 
                 14.724 
                 3.01 
                   
                   
                 13.83 
               
               
                 31 
                 −21.090 
                 0.78 
                 1.69680 
                 55.5 
                 13.85 
               
               
                 32 
                 −86.303 
                 (Variable) 
                   
                   
                 14.48 
               
               
                 33 
                 39.734 
                 0.78 
                 1.91650 
                 31.6 
                 16.61 
               
               
                 34 
                 40.004 
                 1.95 
                 1.79360 
                 37.1 
                 16.65 
               
               
                 35 
                 −92.532 
                 1.00 
                   
                   
                 16.72 
               
               
                 36 
                 ∞ 
                 (Variable) 
                   
                   
                 16.76 
               
               
                 Image Plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
               
                 ZOOM RATIO 2.78 
               
            
           
           
               
               
               
               
            
               
                   
                 WIDE- 
                   
                 TELE- 
               
               
                   
                 ANGLE 
                 MIDDLE 
                 PHOTO 
               
               
                   
               
               
                 Focal Length: 
                 28.80 
                 35.08 
                 80.00 
               
               
                 FNO 
                 3.99 
                 3.95 
                 4.00 
               
               
                 Half Angle of View (degrees) 
                 16.90 
                 14.01 
                 6.24 
               
               
                 Image Height 
                 8.75 
                 8.75 
                 8.75 
               
               
                 Overall lens length 
                 165.90 
                 165.91 
                 165.89 
               
               
                 BF 
                 24.33 
                 25.30 
                 26.09 
               
               
                 d 7 
                 0.13 
                 3.68 
                 14.21 
               
               
                 d14 
                 18.18 
                 14.44 
                 1.10 
               
               
                 d17 
                 1.52 
                 1.72 
                 4.45 
               
               
                 d22 
                 0.46 
                 0.30 
                 0.30 
               
               
                 d27 
                 1.33 
                 1.82 
                 1.11 
               
               
                 d32 
                 2.70 
                 1.39 
                 1.39 
               
               
                 d36 
                 24.33 
                 25.30 
                 26.09 
               
               
                 Entrance Pupil Position 
                 29.32 
                 37.47 
                 77.59 
               
               
                 Exit Pupil Position 
                 −248.12 
                 −183.77 
                 −180.41 
               
               
                 Front Principal Point Position 
                 55.08 
                 66.67 
                 126.59 
               
               
                 Rear Principal Point Position 
                 −4.47 
                 −9.78 
                 −53.91 
               
               
                   
               
            
           
           
               
            
               
                 Zoom Lens Unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                   
                   
                 Configu- 
                 Principal 
                 Principal 
               
               
                 Lens 
                 Starting 
                 Focal 
                 ration 
                 Point 
                 Point 
               
               
                 Unit 
                 Surface 
                 Length 
                 Length 
                 Position 
                 Position 
               
               
                   
               
               
                 L1 
                 1 
                 41.63 
                 14.67 
                 7.45 
                 −3.60 
               
               
                 L2 
                 8 
                 −14.55 
                 9.57 
                 1.00 
                 −6.26 
               
               
                 L3 
                 15 
                 43.79 
                 3.88 
                 1.47 
                 −0.76 
               
               
                 LM 
                 18 
                 ∞ 
                 −39.68 
                 23.41 
                 −23.41 
               
               
                 LRA 
                 23 
                 30.25 
                 7.50 
                 −0.32 
                 −5.07 
               
               
                 LRB 
                 28 
                 −19.53 
                 7.58 
                 4.57 
                 −1.24 
               
               
                 LRC 
                 33 
                 35.30 
                 3.74 
                 0.41 
                 −2.10 
               
               
                   
               
            
           
           
               
            
               
                 Single Lens Data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Starting Surface 
                 Focal Length 
               
               
                   
               
               
                 1 
                 1 
                 −144.87 
               
               
                 2 
                 4 
                 70.25 
               
               
                 3 
                 6 
                 60.55 
               
               
                 4 
                 8 
                 −18.03 
               
               
                 5 
                 10 
                 −19.49 
               
               
                 6 
                 11 
                 20.61 
               
               
                 7 
                 13 
                 −100.07 
               
               
                 8 
                 15 
                 17.82 
               
               
                 9 
                 16 
                 −30.13 
               
               
                 10 
                 19 
                 0.00 
               
               
                 11 
                 20 
                 0.00 
               
               
                 12 
                 21 
                 0.00 
               
               
                 13 
                 23 
                 30.51 
               
               
                 14 
                 25 
                 31.95 
               
               
                 15 
                 26 
                 −29.90 
               
               
                 16 
                 28 
                 18.84 
               
               
                 17 
                 29 
                 −12.13 
               
               
                 18 
                 31 
                 −40.25 
               
               
                 19 
                 33 
                 2689.60 
               
               
                 20 
                 34 
                 35.42 
               
               
                   
               
            
           
         
       
     
     Numerical Example 4 
       
     
       
         
           
               
             
               
                   
               
               
                 UNIT: mm 
               
               
                   
               
             
            
               
                 Surface Data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 Diameter 
               
               
                   
               
               
                  1 
                 ∞ 
                 0.10 
                   
                   
                 34.00 
               
               
                  2 
                 50.402 
                 1.92 
                 1.80810 
                 22.8 
                 33.35 
               
               
                  3 
                 35.017 
                 4.14 
                   
                   
                 32.08 
               
               
                  4 
                 61.018 
                 3.60 
                 1.59522 
                 67.7 
                 32.15 
               
               
                  5 
                 −198.013 
                 0.10 
                   
                   
                 32.00 
               
               
                  6 
                 27.196 
                 5.68 
                 1.43875 
                 94.7 
                 29.92 
               
               
                  7 
                 −272.077 
                 (Variable) 
                   
                   
                 29.40 
               
               
                  8 
                 −355.440 
                 1.00 
                 1.85026 
                 32.3 
                 16.42 
               
               
                  9 
                 15.895 
                 3.19 
                   
                   
                 14.72 
               
               
                 10 
                 −22.643 
                 1.00 
                 1.51633 
                 64.1 
                 14.69 
               
               
                 11 
                 20.214 
                 2.59 
                 1.80810 
                 22.8 
                 15.01 
               
               
                 12 
                 −80.071 
                 0.76 
                   
                   
                 14.97 
               
               
                 13 
                 −29.267 
                 0.84 
                 1.72916 
                 54.7 
                 14.93 
               
               
                 14 
                 −57.323 
                 (Variable) 
                   
                   
                 15.03 
               
               
                 15 
                 60.994 
                 3.23 
                 1.73400 
                 51.5 
                 13.88 
               
               
                 16 
                 −15.526 
                 0.97 
                 1.89190 
                 37.1 
                 13.72 
               
               
                 17 
                 −41.517 
                 (Variable) 
                   
                   
                 13.64 
               
               
                 18(Aperture Stop) 
                 ∞ 
                 11.32  
                   
                   
                 13.36 
               
               
                 19 
                 ∞ 
                 15.00  
                   
                   
                 12.96 
               
               
                 20 
                 ∞ 
                 (Variable) 
                   
                   
                 12.42 
               
               
                 21 
                 27.859 
                 2.49 
                 1.53775 
                 74.7 
                 13.96 
               
               
                 22 
                 −38.892 
                 0.10 
                   
                   
                 13.98 
               
               
                 23 
                 25.863 
                 2.81 
                 1.43875 
                 94.7 
                 13.70 
               
               
                 24 
                 −27.911 
                 1.03 
                 1.85478 
                 24.8 
                 13.41 
               
               
                 25 
                 771.990 
                 (Variable) 
                   
                   
                 13.21 
               
               
                 26 
                 38.655 
                 2.80 
                 1.74000 
                 28.3 
                 12.90 
               
               
                 27 
                 −19.882 
                 0.82 
                 1.70154 
                 41.2 
                 12.60 
               
               
                 28 
                 13.777 
                 3.68 
                   
                   
                 11.76 
               
               
                 29 
                 −20.635 
                 0.78 
                 1.69680 
                 55.5 
                 12.06 
               
               
                 30 
                 −69.361 
                 (Variable) 
                   
                   
                 12.57 
               
               
                 31 
                 40.925 
                 0.78 
                 1.91650 
                 31.6 
                 13.71 
               
               
                 32 
                 38.915 
                 1.54 
                 1.79360 
                 37.1 
                 13.78 
               
               
                 33 
                 −134.889 
                 (Variable) 
                   
                   
                 13.87 
               
               
                 Image Plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Various Data 
               
               
                 ZOOM RATIO 2.78 
               
            
           
           
               
               
               
               
            
               
                   
                 WIDE- 
                   
                 TELE- 
               
               
                   
                 ANGLE 
                 MIDDLE 
                 PHOTO 
               
               
                   
               
               
                 Focal Length: 
                 28.80 
                 41.37 
                 80.00 
               
               
                 FNO 
                 3.97 
                 3.94 
                 4.00 
               
               
                 Half Angle of View (degrees) 
                 16.90 
                 11.94 
                 6.24 
               
               
                 Image Height 
                 8.75 
                 8.75 
                 8.75 
               
               
                 Overall lens length 
                 129.86 
                 129.86 
                 129.85 
               
               
                 BF 
                 26.18 
                 25.45 
                 27.41 
               
               
                 d 7 
                 0.20 
                 6.54 
                 14.11 
               
               
                 d14 
                 18.94 
                 12.70 
                 1.27 
               
               
                 d17 
                 2.12 
                 2.02 
                 5.87 
               
               
                 d20 
                 7.59 
                 7.34 
                 6.24 
               
               
                 d25 
                 1.09 
                 2.14 
                 1.28 
               
               
                 d30 
                 1.47 
                 1.39 
                 1.39 
               
               
                 d33 
                 26.18 
                 25.45 
                 27.41 
               
               
                 Entrance Pupil Position 
                 30.50 
                 46.85 
                 80.47 
               
               
                 Exit Pupil Position 
                 −66.14 
                 −64.92 
                 −61.63 
               
               
                 Front Principal Point Position 
                 50.31 
                 69.29 
                 88.59 
               
               
                 Rear Principal Point Position 
                 −2.62 
                 −15.92 
                 −52.59 
               
               
                   
               
            
           
           
               
            
               
                 Zoom Lens Unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                   
                   
                 Configu- 
                 Principal 
                 Principal 
               
               
                 Lens 
                 Starting 
                 Focal 
                 ration 
                 Point 
                 Point 
               
               
                 Unit 
                 Surface 
                 Length 
                 Length 
                 Position 
                 Position 
               
               
                   
               
               
                 L1 
                 1 
                 41.89 
                 15.55 
                 8.06 
                 −3.59 
               
               
                 L2 
                 8 
                 −14.75 
                 9.37 
                 0.96 
                 −6.02 
               
               
                 L3 
                 15 
                 43.35 
                 4.20 
                 1.40 
                 −1.02 
               
               
                 LM 
                 18 
                 ∞ 
                 26.32 
                 13.16 
                 −13.16 
               
               
                 LRA 
                 21 
                 28.43 
                 6.42 
                 −0.18 
                 −4.27 
               
               
                 LRB 
                 26 
                 −18.97 
                 8.08 
                 4.62 
                 −1.72 
               
               
                 LRC 
                 31 
                 40.00 
                 2.33 
                 0.25 
                 −1.03 
               
               
                   
               
            
           
           
               
            
               
                 Single Lens Data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Starting Surface 
                 Focal Length 
               
               
                   
               
               
                 1 
                 1 
                 −150.36 
               
               
                 2 
                 4 
                 78.77 
               
               
                 3 
                 6 
                 56.68 
               
               
                 4 
                 8 
                 −17.87 
               
               
                 5 
                 10 
                 −20.52 
               
               
                 6 
                 11 
                 20.21 
               
               
                 7 
                 13 
                 −83.05 
               
               
                 8 
                 15 
                 17.17 
               
               
                 9 
                 16 
                 −28.30 
               
               
                 10 
                 21 
                 30.58 
               
               
                 11 
                 23 
                 31.09 
               
               
                 12 
                 24 
                 −31.49 
               
               
                 13 
                 26 
                 18.11 
               
               
                 14 
                 27 
                 −11.48 
               
               
                 15 
                 29 
                 −42.43 
               
               
                 16 
                 31 
                 −1062.67 
               
               
                 17 
                 32 
                 38.21 
               
               
                   
               
            
           
         
       
     
     Table 1 illustrates the lower and upper limits of inequalities (1) to (12) and numerical values in each example. Since Example 1 does not include the third lens unit L 3 , the rear A lens unit LRA, and the rear B lens unit LRB, a hyphen (−) is illustrated in inequalities (8) to (12). 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Inequality 
                 Lower Limit 
                 Upper Limit 
                 Ex. 1 
                 Ex. 2 
                 Ex. 3 
                 Ex. 4 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 0.05 
                 0.50 
                 0.31 
                 0.36 
                 0.14 
                 0.38 
               
               
                 2 
                 −1.60 
                 −0.50 
                 −1.38 
                 −0.85 
                 −0.94 
                 −0.96 
               
               
                 3 
                 0.25 
                 0.49 
                 0.35 
                 0.41 
                 0.43 
                 0.31 
               
               
                 4 
                 0.50 
                 5.00 
                 3.24 
                 1.36 
                 1.45 
                 1.45 
               
               
                 5 
                 −2.00 
                 −0.10 
                 −0.86 
                 −0.43 
                 −0.51 
                 −0.51 
               
               
                 6 
                 0.50 
                 5.00 
                 1.14 
                 1.69 
                 1.88 
                 2.03 
               
               
                 7 
                 1.00 
                 3.00 
                 1.48 
                 1.28 
                 1.11 
                 1.33 
               
               
                 8 
                 1.00 
                 2.00 
                 — 
                 1.44 
                 1.55 
                 1.50 
               
               
                 9 
                 0.20 
                 1.00 
                 — 
                 0.50 
                 0.55 
                 0.54 
               
               
                 10 
                 0.20 
                 1.40 
                 — 
                 0.90 
                 0.61 
                 1.20 
               
               
                 11 
                 0.20 
                 0.80 
                 — 
                 0.42 
                 0.52 
                 0.35 
               
               
                 12 
                 0.60 
                 3.00 
                 — 
                 1.39 
                 1.52 
                 1.51 
               
               
                   
               
            
           
         
       
     
     Referring now to  FIG.  13   , a description will be given of an image pickup apparatus (digital still camera)  200  using the optical system  101  ( 101   a ,  101   b ,  101   c ) according to each example as an imaging optical system  220 .  FIG.  13    is a schematic diagram of an image pickup apparatus  200  having the optical system according to each example. The image pickup apparatus  200  includes a camera body  250  having an image sensor  260  and a lens apparatus  210  having an imaging optical system  220  corresponding to the optical system according to any one of Examples 1 to 4. The lens apparatus  210  and the camera body  250  may be integrated with each other, or may be detachable from each other. The reason why only a single optical system is illustrated in  FIG.  13    is that two optical systems are arranged side by side in the depth direction. Since the image pickup apparatus  200  includes the lens apparatus  210  as a magnification-varying telephoto lens, stereoscopic imaging is available with a long baseline length with a compact configuration. The optical system according to each example is applicable not only to the digital still camera illustrated in  FIG.  13   , but also to various image pickup apparatuses such as broadcast cameras, film-based cameras, surveillance cameras, and the like. 
     Each example can provide a lens apparatus and an image pickup apparatus, each of which has a compact configuration and a long baseline length, and can acquire a stereoscopic image with a natural stereoscopic effect for a distant object. Each example can reduce relative displacement between the two reflective surfaces that bend the optical paths, and improve the image quality. 
     While the disclosure has been described with reference to exemplary examples, it is to be understood that the disclosure is not limited to the disclosed exemplary examples. 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. 2021-187560, filed on Nov. 18, 2021, which is hereby incorporated by reference herein in its entirety.