Zoom lens and image pickup apparatus

Abstract

Provided is a zoom lens including, in order from object side: a positive first unit configured not to be moved for zooming; one or two negative second units configured to be moved for zooming; a stop configured to reduce an outer part of an off-axis light; two or three third units configured to be moved for zooming; and a fourth unit, in which focal lengths of the first unit and the second units, a distance on an optical axis from the stop to a vertex of a surface closest to the object side in the third units under a zoom state in which F-drop starts, and a distance on the optical axis from a vertex of a surface closest to the image side in the second units to the vertex of the surface closest to the object side in the third units under the zoom state are appropriately set.

Claims

1. A zoom lens comprising in order from an object side to an image side: a first lens unit having a positive refractive power and configured not to be moved for zooming; one or two second lens units having a negative refractive power and configured to be moved for zooming; a stop configured to reduce an outer part of an off-axial light; two or three third lens units configured to be moved for zooming; and a fourth lens unit, wherein conditional expressions
−13.0≤f1/f2≤−5.0; and
0.26≤Xi3/S23≤0.46 are satisfied where f1 represents a focal length of the first lens unit, f2 represents a focal length of the one or two second lens units, Xi3 represents a distance on an optical axis from the stop to a vertex of a surface closest to the object side in the two or three third lens units at a zoom state in which F-drop starts, and S23 represents a distance on the optical axis from a vertex of a surface closest to the image side in the one or two second lens units to the vertex of the surface closest to the object side in the two or three third lens units at the zoom state.

2. The zoom lens according to claim 1, wherein a conditional expression
0.1≤(β3t/β3w)/((β2t/β2w)≤0.9 is satisfied where β2w and β2t represent lateral magnifications of the one or two second lens units at a wide angle end and a telephoto end, respectively, and β3w and β3t represent lateral magnifications of the two or three third lens units at the wide angle end and the telephoto end, respectively.

3. The zoom lens according to claim 1, wherein a conditional expression
0.73≤x2i/s23≤0.95 is satisfied at a zoom state in which a focal length is expressed by
fw×√{square root over (Z)}, where fw represents a focal length of the zoom lens at a wide angle end, and Z represents a zoom ratio of the zoom lens, x2i represents a distance on the optical axis from the vertex on the surface closest to the image side in the one or two second lens units to the stop.

4. The zoom lens according to claim 1, wherein the stop is configured to be moved monotonously from the image side to the object side for zooming from a wide angle end to a telephoto end.

5. The zoom lens according to claim 1, wherein the stop is configured to be moved along with a lens unit closest to the object side of the two or three third lens units.

6. The zoom lens according to claim 1, further comprising a stop arranged on the image side of the stop and having a variable diameter of an aperture formed thereby.

7. The zoom lens according to claim 1, wherein the two or three third lens units have a positive refractive power.

8. The zoom lens according to claim 1, wherein the two or three third lens units include a lens unit having a negative refractive power.

9. The zoom lens according to claim 1, wherein the fourth lens unit has a positive refractive power and is arranged closest to the image side.

10. The zoom lens according to claim 1, wherein a conditional expression
45≤ft/fw≤130 is satisfied where fw represents a focal length of the zoom lens at a wide angle end, and ft represents a focal length of the zoom lens at a telephoto end.

11. An image pickup apparatus comprising: a zoom lens comprising in order from an object side to an image side: a first lens unit having a positive refractive power and configured not to be moved for zooming; one or two second lens units having a negative refractive power and configured to be moved for zooming; a stop configured to reduce an outer part of an off-axial light; two or three third lens units configured to be moved for zooming; and a fourth lens unit, wherein conditional expressions
−13.0≤f1/f2≤−5.0; and
0.26≤Xi3/S23≤0.46 are satisfied where f1 represents a focal length of the first lens unit, f2 represents a focal length of the one or two second lens units, Xi3 represents a distance on an optical axis from the stop to a vertex of a surface closest to the object side in the two or three third lens units at a zoom state in which F-drop starts, and S23 represents a distance on the optical axis from a vertex of a surface closest to the image side in the one or two second lens units to the vertex of the surface closest to the object side in the two or three third lens units at the zoom state; and an image pickup element configured to receive an image formed by the zoom lens.

12. The image pickup apparatus according to claim 11, wherein a conditional expression
56.0≤2ωw≤72.6 is satisfied where ωw represents a half angle of view of the zoom lens at a wide angle end.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows lens cross-sectional views in a state in which focus is at infinity at (a) a wide angle end, (b) an intermediate zoom position, (c) an F-drop point, and (d) a telephoto end according to Embodiment 1 (Numerical Embodiment 1) of the present invention.

(2) FIG. 2Aa shows longitudinal aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 1.

(3) FIG. 2Ab shows lateral aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 1.

(4) FIG. 2Ba shows longitudinal aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 1.

(5) FIG. 2Bb shows lateral aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 1.

(6) FIG. 2Ca shows longitudinal aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 1.

(7) FIG. 2Cb shows lateral aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 1.

(8) FIG. 2Da shows longitudinal aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 1.

(9) FIG. 2Db shows lateral aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 1.

(10) FIG. 3 shows lens cross-sectional views in the state in which focus is at infinity at (a) a wide angle end, (b) an intermediate zoom position, (c) an F-drop point, and (d) a telephoto end according to Embodiment 2 (Numerical Embodiment 2) of the present invention.

(11) FIG. 4Aa shows longitudinal aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 2.

(12) FIG. 4Ab shows lateral aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 2.

(13) FIG. 4Ba shows longitudinal aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 2.

(14) FIG. 4Bb shows lateral aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 2.

(15) FIG. 4Ca shows longitudinal aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 2.

(16) FIG. 4Cb shows lateral aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 2.

(17) FIG. 4Da shows longitudinal aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 2.

(18) FIG. 4Db shows lateral aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 2.

(19) FIG. 5 shows lens cross-sectional views in the state in which focus is at infinity at (a) a wide angle end, (b) an intermediate zoom position, (c) an F-drop point, and (d) a telephoto end according to Embodiment 3 (Numerical Embodiment 3) of the present invention.

(20) FIG. 6Aa shows longitudinal aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 3.

(21) FIG. 6Ab shows lateral aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 3.

(22) FIG. 6Ba shows longitudinal aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 3.

(23) FIG. 6Bb shows lateral aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 3.

(24) FIG. 6Ca shows longitudinal aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 3.

(25) FIG. 6Cb shows lateral aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 3.

(26) FIG. 6Da shows longitudinal aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 3.

(27) FIG. 6Db shows lateral aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 3.

(28) FIG. 7 shows lens cross-sectional views in the state in which focus is at infinity at (a) a wide angle end, (b) an intermediate zoom position, (c) an F-drop point, and (d) a telephoto end according to Embodiment 4 (Numerical Embodiment 4) of the present invention.

(29) FIG. 8Aa shows longitudinal aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 4.

(30) FIG. 8Ab shows lateral aberration diagrams in the state in which focus is at infinity at the wide angle end according to Numerical Embodiment 4.

(31) FIG. 8Ba shows longitudinal aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 4.

(32) FIG. 8Bb shows lateral aberration diagrams in the state in which focus is at infinity at the intermediate zoom position according to Numerical Embodiment 4.

(33) FIG. 8Ca shows longitudinal aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 4.

(34) FIG. 8Cb shows lateral aberration diagrams in the state in which focus is at infinity at the F-drop point according to Numerical Embodiment 4.

(35) FIG. 8Da shows longitudinal aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 4.

(36) FIG. 8Db shows lateral aberration diagrams in the state in which focus is at infinity at the telephoto end according to Numerical Embodiment 4.

(37) FIG. 9A is a schematic diagram for illustrating an operation of a movement mechanism according to an Embodiment of the present invention.

(38) FIG. 9B is a schematic diagram for illustrating an operation of the movement mechanism according to the Embodiment of the present invention.

(39) FIG. 9C is a schematic diagram for illustrating an operation of the movement mechanism according to the Embodiment of the present invention.

(40) FIG. 10 is a schematic diagram of a main part of an image pickup apparatus according to Embodiment 5 of the present invention.

DESCRIPTION OF THE EMBODIMENTS

(41) In the following, exemplary embodiments of the present invention are described with reference to the attached drawings.

(42) A zoom lens according to embodiments of the present invention includes, in order from an object side to an image side: a first lens unit having a positive refractive power, which is configured not to move for zooming; one or two second lens units having a negative refractive power, which is/are configured to move for zooming; a stop configured to reduce a part of outer light of an off-axis light; two or three third lens units having a positive refractive power, which are configured to move for zooming; and a fourth lens unit.

(43) In the zoom lens according embodiments of the present invention, the following conditional expressions are satisfied:
−13.0≤f1/f2≤−5.0  (1); and
0.26≤Xi3/S23≤0.46  (2),
where f1 represents a focal length of the first lens unit, f2 represents a focal length of the one or two second lens units, Xi3 represents a distance on an optical axis from the stop to a vertex of a surface closest to the object side in the two or three third lens units under a zoom state in which F-drop starts, and S23 represents a distance on the optical axis from a vertex of a surface closest to the image side in the one or two second lens units to the vertex of the surface closest to the object side in the two or three third lens units under the zoom state.

(44) The conditional expressions (1) and (2) are intended to define conditions for effectively cutting off-axis light flare in a zoom lens having a high magnification and a wide angle of view.

(45) In the conditional expression (1), a ratio between the focal lengths of the first lens unit U1 and the second lens unit U2 defines a first aspect of the zoom lens according to embodiments of the present invention. When the conditional expression (1) is satisfied, a power ratio between the first lens unit U1 and the second lens unit U2 that is optimal for achieving a long focal length of the zoom lens at the telephoto end can be set, in particular. Further, based on the conditional expression (1), an appropriate range of the effective lens diameter of the second lens unit U2 can be defined with respect to specifications of the zoom lens assumed in embodiments of the present invention.

(46) When the ratio exceeds the upper limit of the conditional expression (1), it becomes difficult to correct aberrations on a telephoto side of the first lens unit U1. Further, a power required for varying magnification of the second lens unit U2 falls short, and it becomes difficult to achieve a high magnification of the zoom lens, and downsizing and reducing a weight of the second lens unit U2. When the ratio falls below the lower limit of the conditional expression (1), the power of the second lens unit U2 becomes relatively stronger, with the result that it becomes difficult to suppress variations in aberrations accompanying zooming, and to achieve both downsizing and reducing a weight of the first lens unit U1.

(47) It is more preferred to set the conditional expression (1) as follows:
−12.5≤f1/f2≤−6.0  (1a).

(48) It is more preferred to set the conditional expression (1a) as follows:
−12.0≤f1/f2≤−7.0  (1aa).

(49) It is more preferred to set the conditional expression (1aa) as follows:
−11.5≤f1/f2≤−8.0  (1aaa).

(50) In this example, the first lens unit U1 refers to the entire lens unit that is arranged closer on the object side than the second lens unit U2, and is at a constant distance from an image pickup surface during zooming. The first lens unit in embodiments of the present invention includes a mechanism configured to move a part or whole of the first lens unit during focusing. The above-mentioned focal length f1 of the first lens unit U1 refers to a focal length of the first lens unit U1 in the state in which focus is at infinity.

(51) Further, in the conditional expression (2), an appropriate range of arrangement of the flare cutting stop in the vicinity of an F-drop point in which a diameter of a ray passing through the second lens unit U2 and the third lens unit U3 is maximized while achieving a high magnification of the zoom lens. In the expression (2), Xi3 represents the distance on the optical axis from the flare cutting stop IF to the vertex of a frontmost surface (lens surface closest to the object side) of the third lens unit U3 at the so-called F-drop point, which is a zoom position at which a drop of an amount of light of an f-number starts, and S23 represents the distance on the optical axis from the vertex of a last surface (rearmost surface) of the second lens unit U2 to the vertex of the frontmost surface (lens surface closest to the object side) of the third lens unit U3 at the F-drop point. When the conditional expression (2) is satisfied, the flare cutting stop configured to effectively cut only an unnecessary off-axis light can be arranged appropriately without affecting an f-number ray, and comatic flare at the periphery of the image plane, which tends to occur when zooming is performed slightly toward the telephoto side from the wide angle end, can be suppressed appropriately.

(52) When the ratio exceeds the upper limit of the conditional expression (2), a sufficient stroke from the F-drop point to the telephoto end cannot be secured, and it becomes difficult to achieve a sufficiently high magnification of the zoom lens. Further, when a range exceeding the upper limit is to be achieved, a mechanism configured to steeply change a stop position as in Japanese Patent Application Laid-Open No. H06-186477 is separately required, to thereby complicate a zoom mechanism and hinder smooth zooming. When the ratio falls below the lower limit of the conditional expression (2), a position of the flare cutting stop is too close to the third lens unit U3, and the effect of cutting the off-axis light becomes disadvantageously relatively weaker.

(53) It is more preferred to set the conditional expression (2) as follows:
0.27≤Xi3/S23≤0.45  (2a).

(54) It is more preferred to set the conditional expression (2a) as follows:
0.28≤Xi3/S23≤0.44  (2aa).

(55) Further, in the zoom lens according to embodiments of the present invention, it is preferred to satisfy one or more of the following conditions.

(56) The following conditional expression is satisfied:
0.1≤(β3t/β3w)/(β2t/β2w)|≤0.9  (3),

(57) where β2w and β2t represent lateral magnifications of the one or two second lens units at a wide angle end and a telephoto end, respectively, and β3w and β3t represent lateral magnifications of the two or three third lens units at the wide angle end and the telephoto end, respectively.

(58) The conditional expression (3) is intended to define a condition for achieving an even higher magnification and effectively cutting off-axis light flare in the zoom lens according to embodiments of the present invention. When the conditional expression (3) is satisfied, shares of the second lens unit and the third lens unit for a magnification varying ratio can be appropriately assigned, which is advantageous in achieving high performance, downsizing, and reducing the weights.

(59) When the ratio exceeds the upper limit of the conditional expression (3), the second lens unit becomes relatively short in power and small in magnification varying share, which leads to an increase in effective diameter of the second lens unit, and a configuration that is disadvantageous in achieving a wide angle of the zoom lens. Further, the zoom stroke of the third lens unit, which is relatively heavy and large, is disadvantageously increased. When the ratio falls below the lower limit of the conditional expression (3), a relative magnification varying share of the third lens unit is reduced, which disadvantageously results in enlargement of a magnification varying portion of the zoom lens having a high magnification, and a situation in which the effect of effectively cutting flare cannot be exerted.

(60) It is more preferred to set the conditional expression (3) as follows:
0.12≤(β3t/β3w)/(β2t/β2w)|≤0.80  (3a).

(61) It is more preferred to set the conditional expression (3a) as follows:
0.15≤(β3t/β3w)/(β2t/β2w)|≤0.65  (3aa).

(62) Further, at a focal length expressed by:
fw×√{square root over (Z)},
where “fw” represents a focal length of the zoom lens at the wide angle end, and Z represents a magnification varying ratio from the wide angle end to the telephoto end, the following conditional expression is satisfied:
0.73≤x2i/s23≤0.95  (4),
where x2i represents a distance on the optical axis from the vertex of the last surface of the second lens unit to the flare cutting stop, and s23 represents a distance on the optical axis from the vertex of the last surface of the second lens unit to the vertex of the frontmost surface of the third lens unit.

(63) The conditional expression (4) is intended to define a condition regarding the position of the flare cutting stop for achieving both a high magnification and the flare cutting effect of the zoom lens according to embodiments of the present invention. In the conditional expression (4), x2i represents the distance on the optical axis from the vertex of the surface closest to the image side of the second lens unit to the flare cutting stop at the focal length of an intermediate zoom position fw×√{square root over (Z)}, where Z represents the magnification varying ratio of the entire lens system. In the conditional expression (4), s23 represents the distance on the optical axis from the vertex of the last surface of the second lens unit to the vertex of the frontmost surface of the third lens unit at the same position. A range in which it is most desired to exert the effect of cutting the lowermost ray by the flare cutting stop in embodiments of the present invention is a range from the wide angle end to the zoom position fw×√{square root over (Z)}. Through appropriate setting of arrangement of the flare cutting stop at this position, arrangement with which the effect of cutting the lowermost ray can be sufficiently exerted while ensuring a high magnification of the zoom lens is defined.

(64) When the ratio exceeds the upper limit of the conditional expression (4), the position of the flare cutting stop at the intermediate zoom position is close to the third lens unit, and the flare cutting effect cannot be sufficiently exerted. When the ratio falls below the lower limit of the conditional expression (4), it is required to separately install a mechanism configured to enable non-linear movement, a mechanism configured to avoid interference with the second lens unit, a unit configured to detect photographic conditions, and the like to a flare cutting stop holding portion in order to achieve a high magnification of the zoom lens. Therefore, complication of a mechanism and an increase in weight of the magnification varying portion are disadvantageously caused.

(65) It is more preferred to set the conditional expression (4) as follows:
0.74≤x2i/s23≤0.92  (4a).

(66) It is more preferred to set the conditional expression (4a) as follows:
0.75≤x2i/s23≤0.90(4aa).

(67) Further, an image pickup apparatus according to at least one embodiment of the present invention includes the zoom lens of each Embodiment and a solid image pickup element having a predetermined effective image pickup range, which is configured to receive an image formed by the zoom lens.

(68) In this example, it is preferred to satisfy the following conditional expressions:
45<ft/fw<130  (5); and
56.0<2ωw<72.6  (6),
where “ωw” represents a photographing half angle of view of the zoom lens at the wide angle end, “fw” represents a focal length of the entire system at the wide angle end, and “ft” represents a focal length of the entire system at the telephoto end.

(69) In the conditional expressions (5) and (6), ranges of the magnification of the zoom lens and the photographing angle of view at the wide angle end that are suitable for exerting the effects obtained by the present invention are defined, respectively. The phrase “photographing angle of view at the wide angle end” as used herein is a maximum photographing angle of view at the wide angle end with respect to an effective diagonal length of the image pickup element. The flare cutting stop described in embodiments of the present invention is configured to appropriately cut a lowermost ray flare component, which tends to be increased in the zoom lens having a high magnification and a wide angle of view, and is a technology that is effective in increasing optical performance at the intermediate zoom position in particular. In the conditional expressions (5) and (6), ranges of the magnification of the zoom lens and the angle of view at the wide angle end, to which embodiments of the present invention is effectively applied, are defined, respectively. When the magnification and the angle of view fall outside of the above-mentioned conditions, it is considered that a lens configuration and power arrangement of the zoom lens, and arrangement and a diameter of the flare cutting stop in achieving desired specifications are not appropriately set.

(70) It is more preferred to set the conditional expression (5) as follows:
50<ft/fw<125  (5a).

(71) It is more preferred to set the conditional expression (5a) as follows:
55<ft/fw<115  (5aa).

(72) It is more preferred to set the conditional expression (5aa) as follows:
56<ft/fw<90  (5aaa).

(73) It is more preferred to set the conditional expression (6) as follows:
56.1<2ωw<70.8  (6a).

(74) It is more preferred to set the conditional expression (6a) as follows:
56.2<2ωw<68.0  (6aa).

(75) Now, a specific configuration of the zoom lens according to embodiments of the present invention is described by way of features of lens configurations of Numerical Embodiments 1 to 4 corresponding to Embodiments 1 to 4, respectively.

Embodiment 1

(76) FIG. 1 shows lens cross-sectional views of a zoom lens according to Embodiment 1 (Numerical Embodiment 1) of the present invention at (a) a wide angle end (14.3 mm), (b) an intermediate zoom position (focal length: 107.0 mm), (c) an F-drop point (552.2 mm), and (d) a telephoto end (800.8 mm). In the lens cross-sectional views, the left side is the object side (front side), and the right side is the image side (rear side).

(77) FIG. 2Aa, FIG. 2Ba, FIG. 2Ca, and FIG. 2Da are longitudinal aberration diagrams of the zoom lens according to Embodiment 1 at the wide angle end (14.3 mm), the intermediate zoom position (focal length: 107.0 mm), the F-drop point (552.2 mm), and the telephoto end (800.8 mm), respectively. FIG. 2Ab, FIG. 2Bb, FIG. 2Cb, and FIG. 2Db are lateral aberration diagrams of the zoom lens according to Embodiment 1 at the wide angle end (14.3 mm), the intermediate zoom position (focal length: 107.0 mm), the F-drop point (552.2 mm), and the telephoto end (800.8 mm), respectively. The figures are the lens cross-sectional views and the aberration diagrams in the state in which focus is on an object at infinity. Further, a value of a focal length is a value obtained by expressing a Numerical Embodiment, which is to be described later, in units of mm. The same equally applies to the subsequent Numerical Embodiments.

(78) In FIG. 1, the zoom lens according to Embodiment 1 includes, in order from the object side, a first lens unit U1 having a positive refractive power for focusing, a second lens unit U2 having a negative refractive power for varying magnification, which is configured to move from the object side to the image side for varying magnification from the wide angle end to the telephoto end, and a third lens unit U3. The third lens unit U3 consists of a first lens subunit U31 having a positive refractive power, which is configured move from the image side to the object side for varying magnification from the wide angle end to the telephoto end, and a second lens subunit U32 having a positive refractive power, which is configured to move from the image side to the object side for varying magnification. The zoom lens further includes a fourth lens unit U4 having a positive refractive power, which has an image forming action, on the image side of the third lens unit U3.

(79) The zoom lens according to embodiments of the present invention forms a zoom type of a so-called “multi-unit zoom system”, in which three or more lens units consisting of a front magnification varying lens unit and a rear magnification varying lens unit are configured to move, to easily achieve a high magnification and satisfactory optical performance.

(80) In the zoom lens according to embodiments of the present invention, a rear lens unit may include a lens unit that is removable from an optical path and is configured to shift the focal length of the entire system of the zoom lens. Further, an optical member forming a part of the fourth lens unit U4 may be moved along the optical axis to have a function of playing a role of adjusting a back focus.

(81) A flare cutting stop IF configured to cut only an unnecessary off-axis light without affecting an axial ray (f-number ray) is arranged between the second lens unit U2 and the third lens unit U3. The flare cutting stop may be adopted to have a form of being formed integrally with the third lens unit U3, and following the same locus as the third lens unit during varying magnification. Further, the flare cutting stop in Embodiment 1 has a constant aperture diameter over the entire zoom range, and does not require a mechanism configured to open and close a stop aperture and a zoom position detection unit for controlling a stop diameter, with the result that the flare cutting stop is easy to install at low cost.

(82) An aperture stop SP configured to determine the f-number is arranged between the third lens unit U3 and the fourth lens unit U4. Dummy glass DG corresponds to an optical filter or a color separation optical system in a camera, and is illustrated as a glass block in FIG. 1. When the zoom lens is used as an image pickup optical system for a broadcasting television camera, a video camera, or a digital still camera, an image plane IP corresponds to an image pickup surface of a solid-state image pickup element (photoelectric conversion element) or the like configured to receive light of an image formed by the zoom lens and to convert the light to electricity. When the zoom lens is used as an image pickup optical system for a film camera, the image plane IP corresponds to a film surface on which the image formed by the zoom lens is exposed.

(83) In each of the longitudinal aberration diagrams, spherical aberration is illustrated with respect to an e-line and a g-line by a solid line and a two-dot chain line, respectively. Further, astigmatism is illustrated on a meridional image plane by a broken line and on a sagittal image plane by a solid line. In addition, lateral chromatic aberration is illustrated with respect to the g-line by a two-dot chain line. A half angle of view is denoted by “ω” and an F number is denoted by Fno. In each of the longitudinal aberration diagrams, spherical aberration is illustrated in the unit of 0.4 mm, astigmatism in the unit of 0.4 mm, distortion in the unit of 10%, and a lateral chromatic aberration in the unit of 0.05 mm. In each Embodiment described below, each of the wide angle end and the telephoto end refers to a zooming position obtained when the second lens unit U2 for varying magnification is positioned at each of the ends of a range in which the lens unit may mechanically move along the optical axis.

(84) Next, correspondences with surface data of Numerical Embodiment 1 are described. The first lens unit U1 corresponds to the 1st surface to the 12th surface. The 1st surface to the 6th surface form a first lens subunit U11 having a negative refractive power (or substantially no power), which is configured not to move for focusing, and the 7th surface to the 12th surface correspond to a second lens subunit U12 having a positive refractive power, which is configured to move from the image pickup surface side to the object side during focusing from an infinity side to a proximity side. As the second lens subunit U12, a so-called “floating focus system” may be adopted, in which a part thereof takes a different locus when being driven for focusing, to thereby improve variations in aberrations during drive for focusing. The second lens unit U2 corresponds to the 13th surface to the 19th surface, and has a negative refractive power. The flare cutting stop IF configured to cut only the unnecessary off-axis light without affecting the f-number ray corresponds to the 20th surface. The first lens subunit U31 corresponds to the 21st surface to the 26th surface, and has a positive refractive power. The second lens subunit U32 corresponds to the 27th surface to the 31st surface, and has a positive refractive power. The aperture stop configured to determine the f-number corresponds to the 32nd surface. The fourth lens unit U4 corresponds to the 33rd surface to the 53rd surface, and has a positive refractive power. The 54th surface to the 56th surface form the dummy glass, which corresponds to the optical filter and the color separation optical system in the camera.

(85) Now, with reference to FIG. 9A, FIG. 9B, and FIG. 9C, operations of a movement mechanism of the zoom lens according to embodiments of the present invention and flare cutting by the flare cutting stop are outlined using the configuration of Embodiment 1 as an example. In FIG. 9A, FIG. 9B, and FIG. 9C, approximate positions of the movement mechanism of the zoom lens according to embodiments of the present invention at the wide angle end, the intermediate zoom position, and the telephoto end are illustrated, respectively. The second lens unit U2, the third lens unit U3, and the fourth lens unit U4 illustrated in the FIG. 9A, FIG. 9B, and FIG. 9C are connected from lens barrels configured to hold the lenses to a zoom cam structure, and are configured to move in an optical axis direction during zooming. The flare cutting stop IF in Numerical Embodiment 1 is formed integrally with a lens barrel configured to hold the first lens subunit U31, and is formed into a shape that does not affect an axial (f-number) ray. The flare cutting stop IF follows a locus of moving monotonously from the image plane side to the object side without being inverted during varying magnification from the wide angle end to the telephoto end. Further, the flare cutting stop IF has no mechanism configured to open and close an aperture portion, and has an invariable aperture diameter over the entire zoom range.

(86) Under a state at the wide angle end of FIG. 9A, the second lens unit U2 and the third lens unit U3 are arranged to be separated farthest from each other in the entire zoom range. When the axial ray and a most off-axis light from the second lens unit U2 to the third lens unit U3 are indicated by the one-dot chain line and the solid line, respectively, the axial (f-number) ray passes through an area of the second lens unit U2 near the optical axis in a state of a small ray width (pupil diameter), and then reaches the third lens unit U3 while being diverged. In contrast, the off-axis light passes through a portion of the second lens unit with a high effective diameter, and reaches the third lens unit U3 while being diverged. When a lowermost ray of the axial ray is represented by Rcl, and a lowermost ray of the off-axis light is represented by Ral, the lowermost ray Ral of the off-axis light passes through a position at a distance that is farther away from the optical axis at a position near the second lens unit U2, and the lowermost ray Rcl of the axial ray passes through a position at a distance that is farther away from the optical axis at a position near the third lens unit U3. Further, in the zoom lens according to embodiments of the present invention, a peripheral light amount ratio at the wide angle end is often determined by the effective diameter of the first lens unit U1 or the second lens unit U2, and there are few cases where it is required to cut the lowermost ray by the flare cutting stop at the wide angle end.

(87) Next, for the intermediate zoom position of FIG. 9B, a zoom range expressed by the focal lengths is assumed as the intermediate zoom position in embodiments of the present invention:
fw×5√{square root over (Z)} to fw×√{square root over (Z)},
where “fw” represents a focal length at the wide angle end, and Z represents a zoom magnification from the wide angle end to the telephoto end of the zoom lens.

(88) At the intermediate zoom position of FIG. 9B, the axial ray and the off-axis light both have larger ray widths than at the wide angle end, but in the vicinity of the third lens unit U3, the off-axis light Ral has a larger area (hatched portion of FIG. 9B) of passing through a position away from the optical axis than the axial ray Rcl. The hatched portion is a ray portion that can be cut without affecting the f-number, and is a portion in which comatic flare occurs as a variation accompanying zooming from the wide angle end. Therefore, through cutting of the off-axis light in a range in which the peripheral light amount ratio with respect to a light amount at the center of the image plane does not cause a problem in terms of quality, optical performance in the periphery of the image plane can be increased. This area exists continuously up to almost the F-drop point, and hence it is effective to arrange the flare cutting stop, which is determined based on the diameter of the f-number ray, at an appropriate position to cut an unnecessary off-axis light as much as possible.

(89) At the telephoto end of FIG. 9C, the lowermost ray Ral of the off-axis light passes through the inside of the lowermost ray Rcl of the axial ray, and hence in a region from the F-drop point to the telephoto end, flare cutting cannot be achieved without affecting the f-number.

(90) To address this problem, in the four-unit zoom lens of a so-called “transfer type” described in Japanese Patent Application Laid-Open No. H06-186477, an effective diameter of the third lens unit U3 is defined by an f-number condition, and there is a tendency that a large amount of excess off-axis light enters to cause a large amount of off-axial comatic flare. Therefore, it is required to arrange the flare cutting stop at a position that is as close to the front as possible from the wide angle end to the F-drop point, and a complicated configuration by means of a magnet, for example, is required to reduce unnecessary space for varying magnification after the F-drop point.

(91) In contrast, when the multi-unit zoom system as in FIG. 9A, FIG. 9B, and FIG. 9C is used, the third lens unit and the fourth lens unit of a five-lens zoom lens can be arranged on the object side and on the image plane side, respectively, while maintaining a principal point position of the third lens unit U3 of the four-unit zoom lens, which results in the effect that effective diameters of the third and fourth lens units can be reduced while maintaining the f-number. With this effect, the axial ray and the off-axis light can be lowered with respect to the four-unit zoom lens, and downsizing and reducing the weight of moving lens units are achieved, which are very advantageous factors. However, when a variation in optical performance accompanying zooming is to be improved, the power of the second lens unit can be relatively mitigated in the multi-unit zoom system. As a result, the effective diameter of the second lens unit U2 is increased to result in a problem in which a diameter of the off-axis light from the wide angle end to the intermediate zoom range is mainly increased in accordance therewith. To address this problem, embodiments of the present invention may be applied to effectively cut off-axial comatic flare. The arrangement of the second lens unit U2 and the third lens unit U3 and the way the rays pass through those lens units, which are configured to move for varying magnification, are changed from the four-unit zoom lens described in Japanese Patent Application Laid-Open No. H06-186477, with the result that the conditional expression related to the configuration of the flare cutting stop is changed.

(92) To give a specific comparative example for consideration, in Japanese Patent Application Laid-Open No. H06-186477, it is specified that a value corresponding to Xi3/S23 of the conditional expression (2) in embodiments of the present invention is from 0.459 to 0.918. As an index of the effect of cutting the lowermost ray by the flare cutting stop, a ratio between ray heights of a principal ray and a lowermost ray of the most off-axis light at the zoom position of FIG. 9B is considered, for example. According to a reproduction experiment based on patent data of Japanese Patent Application Laid-Open No. H06-186477, an embodiment in which about 15% of a lowermost ray component was cut by the flare cutting stop is found. In contrast, according to Embodiments of the present invention, a value corresponding to Xi3/S23 of the conditional expression (2) is from 0.271 to 0.456, which is outside the range of Embodiments of Japanese Patent Application Laid-Open No. H06-186477, but up to about 20% of a lowermost ray component can be cut by the flare cutting stop. As a result, it was confirmed that the effect of the flare cutting stop that was equivalent to or larger than in the related art was exerted also in an area of a numerical range that is different from that of the four-unit zoom lens in the related art while achieving high specifications, high performance, downsizing, and reducing the weight through employment of the multi-unit zoom lens. It should be noted, however, that the above-mentioned experiment is merely an example of verifying the effect of embodiments of the present invention, and it can be understood that a method of evaluating and a required proportion of the lowermost ray cutting vary depending on differences in required specifications and performance. This equally applies to all Embodiments.

(93) Numerical Embodiment 1, which corresponds to Embodiment 1, is described. In all Numerical Embodiments without limiting to Numerical Embodiment 1, the order of a surface (optical surface) from the object side is represented by “i”, a curvature radius of the i-th surface from the object side is represented by “ri”, and an interval between the i-th surface and the (i+1)-th surface from the object side (on the optical axis) is represented by “di”. Moreover, a refractive index, an Abbe number, and a partial dispersion ratio with respect to a medium (optical member) between the i-th surface and the (i+1)-th surface are represented by “ndi”, “vdi”, and θgFi, respectively, and an air-equivalent back focus is represented by BF. When an X axis is set in the optical axis direction, an H axis is set in a direction perpendicular to the optical axis, a direction of travel of light is defined as positive, a paraxial curvature radius is represented by R, a conic constant is represented by “k”, and aspherical coefficients are represented by A3 to A16, the aspherical shape is expressed by the expression below. Moreover, “e-Z” means “×10−Z”.

(94) $X=\frac{H^2/R}{1+\sqrt{1-\left(1+k\right){\left(H/R\right)}^2}}+A4H^4+A6H^6+A8H^8+A{10}^{10}+A12H^{12}+A14H^{14}+A16H^{16}+A3H^3+A5H^5+A7H^7+A9H^9+A11H^{11}+A13H^{13}+A15H^{15}$

(95) Values corresponding to the conditional expressions in Embodiment 1 are shown in Table 1. In Embodiment 1, the expressions (1) to (6) are satisfied as appropriate to achieve the zoom lens having a wide angle of view, a high zoom ratio, a small size, a light weight, and high optical performance over the entire zoom range. Although it is required that the zoom lens according to embodiments of the present invention satisfy the expressions (1) and (2), the zoom lens is not always required to satisfy the expressions (3) to (6). However, when at least one of the expressions (3) to (6) is satisfied, even better effects may be provided. The same holds true for the Embodiments 2 to 4.

Embodiment 2

(96) FIG. 3 shows lens cross-sectional views of a zoom lens according to Embodiment 2 (Numerical Embodiment 2) of the present invention in the state in which focus is on an object at infinity at (a) a wide angle end (focal length: 10.00 mm), (b) an intermediate zoom position (focal length: 89.44 mm), (c) an F-drop point (focal length: 342.87 mm), and (d) a telephoto end (focal length: 800.00 mm).

(97) FIG. 4Aa, FIG. 4Ba, FIG. 4Ca, and FIG. 4Da are longitudinal aberration diagrams of the zoom lens according to Embodiment 2 (Numerical Embodiment 2) of the present invention in the state in which focus is on the object at infinity at the wide angle end (focal length: 10.00 mm), the intermediate zoom position (focal length: 89.44 mm), the F-drop point (focal length: 342.87 mm), and the telephoto end (focal length: 800.00 mm), respectively. FIG. 4Ab, FIG. 4Bb, FIG. 4Cb, and FIG. 4Db are lateral aberration diagrams of the zoom lens according to Embodiment 2 (Numerical Embodiment 2) of the present invention in the state in which focus is on the object at infinity ay the wide angle end (focal length: 10.00 mm), the intermediate zoom position (focal length: 89.44 mm), the F-drop point (focal length: 342.87 mm), and the telephoto end (focal length: 800.00 mm), respectively.

(98) Next, correspondences with surface data of Numerical Embodiment 2 are described. The first lens unit U1 corresponds to the 1st surface to the 14th surface. The 1st surface to the 8th surface form a first lens subunit U11 having a negative refractive power (or substantially no power), which is configured not to move during focusing, and the 9th surface to the 14th surface correspond to a second lens subunit U12 having a positive refractive power, which is configured to move from the image pickup surface side to the object side during focusing from an infinity side to a proximity side. As the second lens subunit U12, a so-called “floating focus system” may be adopted, in which a part thereof takes a different locus when being driven for focusing, to thereby improve variations in aberrations during drive for focusing. The second lens unit U2 corresponds to the 15th surface to the 21st surface, and has a negative refractive power. The flare cutting stop IF configured to cut only the unnecessary off-axis light without affecting the f-number ray corresponds to the 22nd surface. The first lens subunit U31 corresponds to the 23rd surface to the 29th surface, and has a positive refractive power. The second lens subunit U32 corresponds to the 30th surface to the 31st surface, and has a positive refractive power. The aperture stop configured to determine the f-number corresponds to the 32nd surface. The fourth lens unit U4 corresponds to the 33rd surface to the 48th surface, and has a positive refractive power. The 49th surface to the 51st surface form the dummy glass, which corresponds to the optical filter and the color separation optical system in the camera.

(99) Values corresponding to the conditional expressions in Embodiment 2 are shown in Table 1. In Embodiment 2, the expressions (1) to (6) are satisfied as appropriate to achieve the zoom lens having a wide angle of view, a high zoom ratio, a small size, a light weight, and high optical performance over the entire zoom range. In Embodiment 2, in particular, the structure configured to avoid interference with the flare cutting stop as illustrated in FIG. 9A, FIG. 9B, and FIG. 9C is provided to utilize an interval between the second lens unit U2 and the third lens unit U3 for varying magnification without waste. With this configuration, zooming at a high magnification with a magnification varying ratio of 80× from the wide angle end to the telephoto end is achieved with the structure that is low in cost and easily implemented without complicating the structure of the magnification varying lens unit.

Embodiment 3

(100) FIG. 5 shows lens cross-sectional views of a zoom lens according to Embodiment 3 (Numerical Embodiment 3) of the present invention in the state in which focus is on an object at infinity at (a) a wide angle end (focal length: 10.20 mm), (b) an intermediate zoom position (focal length: 88.33 mm), (c) an F-drop point (focal length: 327.86 mm), and (d) a telephoto end (focal length: 765.00 mm).

(101) FIG. 6Aa, FIG. 6Ba, FIG. 6Ca, and FIG. 6Da are longitudinal aberration diagrams of the zoom lens according to Embodiment 3 (Numerical Embodiment 3) of the present invention in the state in which focus is on the object at infinity at the wide angle end (focal length: 10.20 mm), the intermediate zoom position (focal length: 88.33 mm), the F-drop point (focal length: 327.86 mm), and the telephoto end (focal length: 765.00 mm), respectively. FIG. 6Ab, FIG. 6Bb, FIG. 6Cb, and FIG. 6Db are lateral aberration diagrams of the zoom lens according to Embodiment 3 (Numerical Embodiment 3) of the present invention in the state in which focus is on the object at infinity at the wide angle end (focal length: 10.20 mm), the intermediate zoom position (focal length: 88.33 mm), the F-drop point (focal length: 327.86 mm), and the telephoto end (focal length: 765.00 mm), respectively.

(102) Next, correspondences with surface data of Numerical Embodiment 3 are described. The first lens unit U1 corresponds to the 1st surface to the 14th surface. The 1st surface to the 8th surface form a first lens subunit U11 having a negative refractive power (or substantially no power), which is configured not to move during focusing, and the 9th surface to the 14th surface correspond to a second lens subunit U12 having a positive refractive power, which is configured to move from the image pickup surface side to the object side during focusing from an infinity side to a proximity side. As the second lens subunit U12, a so-called “floating focus system” may be adopted, in which a part thereof takes a different locus when being driven for focusing, to thereby improve variations in aberrations during drive for focusing. The second lens unit U2 corresponds to the 15th surface to the 21st surface, and has a negative refractive power. The flare cutting stop IF configured to cut only the unnecessary off-axis light without affecting the f-number ray corresponds to the 22nd surface. The first lens subunit U31 corresponds to the 23rd surface to the 24th surface, has a positive refractive power, and is configured to move integrally with the flare cutting stop IF during varying magnification. The second lens subunit U32 corresponds to the 25th surface to the 29th surface, and has a negative refractive power. A third lens subunit U33 corresponds to the 30th surface to the 31st surface, and has a positive refractive power. The aperture stop configured to determine the f-number corresponds to the 32nd surface. The fourth lens unit U4 corresponds to the 33rd surface to the 48th surface, and has a positive refractive power. The 49th surface to the 51st surface form the dummy glass, which corresponds to the optical filter and the color separation optical system in the camera.

(103) Values corresponding to the conditional expressions in Embodiment 3 are shown in Table 1. In Embodiment 3, the expressions (1) to (6) are satisfied as appropriate to achieve the zoom lens having a wide angle of view, a high zoom ratio, a small size, a light weight, and high optical performance over the entire zoom range. In Embodiment 3, in particular, the second lens subunit U32 has a negative refractive power, but is adapted to the conditional expressions for exerting the effects of embodiments of the present invention without any problem. Here, Embodiment 3 is close to a form obtained by dividing the third lens unit U3 of Embodiment 2, and hence when applying the conditional expression (3) to a lens unit composed of the first lens subunit U31 and the second lens subunit U32 of Embodiment 3 as the third lens unit, (|(β3t/β3w)/(β2t/β2w)|) is 0.534, which satisfies the conditional expression (3). Also in Embodiment 3, the structure configured to avoid interference between the second lens unit U2 and the flare cutting stop as illustrated in FIG. 9A, FIG. 9B, and FIG. 9C is provided as in Embodiment 2 to utilize an interval between the second lens unit U2 and the first lens subunit U31 for varying magnification without waste. With this configuration, zooming at a high magnification with a magnification varying ratio of 75× from the wide angle end to the telephoto end is achieved with the structure that is low in cost and easily implemented without complicating the structure of the magnification varying lens unit.

Embodiment 4

(104) FIG. 7 shows lens cross-sectional views of a zoom lens according to Embodiment 4 (Numerical Embodiment 4) of the present invention in the state in which focus is on an object at infinity at (a) a wide angle end (focal length: 14.30 mm), (b) an intermediate zoom position (focal length: 107.30 mm), (c) an F-drop point (focal length: 555.00 mm), and (d) a telephoto end (focal length: 805.09 mm).

(105) FIG. 8Aa, FIG. 8Ba, FIG. 8Ca, and FIG. 8Da are longitudinal aberration diagrams of the zoom lens according to Embodiment 4 (Numerical Embodiment 4) of the present invention in the state in which focus is on the object at infinity at the wide angle end (focal length: 14.30 mm), the intermediate zoom position (focal length: 107.30 mm), the F-drop point (focal length: 555.00 mm), and the telephoto end (focal length: 805.09 mm), respectively. FIG. 8Ab, FIG. 8Bb, FIG. 8Cb, and FIG. 8Db are lateral aberration diagrams of the zoom lens according to Embodiment 4 (Numerical Embodiment 4) of the present invention in the state in which focus is on the object at infinity at the wide angle end (focal length: 14.30 mm), the intermediate zoom position (focal length: 107.30 mm), the F-drop point (focal length: 555.00 mm), and the telephoto end (focal length: 805.09 mm), respectively.

(106) Next, correspondences with surface data of Numerical Embodiment 4 are described. The first lens unit U1 corresponds to the 1st surface to the 12th surface. The 1st surface to the 6th surface form a first lens subunit U11 having a negative refractive power (or substantially no power), which is configured not to move during focusing, and the 7th surface to the 12th surface correspond to a second lens subunit U12 having a positive refractive power, which is configured to move from the image pickup surface side to the object side during focusing from an infinity side to a proximity side. As the second lens subunit U12, a so-called “floating focus system” may be adopted, in which a part thereof takes a different locus when being driven for focusing, to thereby improve variations in aberrations during drive for focusing. The second lens unit U2 corresponds to the 13th surface to the 19th surface, and has a negative refractive power. In Numerical Embodiment 4, the second lens unit U2 is divided into, in order from the object side, a first lens subunit U21 having a negative refractive power and a second lens subunit U22 having a negative refractive power to have slightly different loci at the intermediate zoom position. This configuration results in a form with which aberrations at the intermediate zoom position can be corrected more advantageously in particular. Values relating to the refractive power and the position of the second lens unit U2 in the conditional expressions of the present invention are calculated on the assumption that the first lens subunit U21 and the second lens subunit U22 are regarded as one lens unit. The flare cutting stop IF configured to cut only the unnecessary off-axis light without affecting the f-number ray corresponds to the 20th surface. The first lens subunit U31 corresponds to the 21st surface to the 26th surface, has a positive refractive power, and is configured to move integrally with the flare cutting stop IF during varying magnification. The second lens subunit U32 corresponds to the 27th surface to the 31st surface, and has a positive refractive power. The aperture stop configured to determine the f-number corresponds to the 32nd surface. The fourth lens unit U4 corresponds to the 33rd surface to the 53rd surface, and has a positive refractive power. The 54th surface to the 56th surface form the dummy glass, which corresponds to the optical filter and the color separation optical system in the camera.

(107) Values corresponding to the conditional expressions in Embodiment are shown in Table 1. In Embodiment 4, the expressions (1) to (6) are satisfied as appropriate to achieve the zoom lens having a wide angle of view, a high zoom ratio, a small size, a light weight, and high optical performance over the entire zoom range. In Embodiment 4, in particular, a form in which the second lens unit U2 is divided into two lens subunits is adopted for advantages in further correcting aberrations, but when the two lens subunits are regarded as one lens unit in view of the role of sharing magnification varying, is adapted to the conditional expressions for exerting the effects of embodiments of the present invention without any problem. Embodiment 4 achieves zooming at a high magnification with a magnification varying ratio of 56.3× from the wide angle end to the telephoto end with the structure that is low in cost and easily implemented.

Embodiment 5

(108) FIG. 10 is a schematic diagram of an image pickup apparatus (television camera system) using the zoom lens according to any one of Embodiments 1 to 4 as a photographing optical system. A zoom lens 101, which is the zoom lens according to any one of Embodiments 1 to 4, is removable from a camera 201. The zoom lens 101 is attached to the camera 201 to form an image pickup apparatus 301. The zoom lens 101 includes a first lens unit F, a magnification varying portion V, and a rear lens unit R for forming an image. The first lens unit F includes a lens unit for focusing. The magnification varying portion V includes a front magnification varying lens unit VF configured to move on the optical axis during varying magnification, the flare cutting stop IF, and a rear magnification varying lens unit VR. An aperture stop is denoted by SP. Drive mechanisms 102 and 103, such as helicoids or cams, are configured to drive the first lens unit F and the magnification varying portion V in the optical axis direction, respectively. Motors (drive units) 105 to 107 are configured to electrically drive the drive mechanisms 102 and 103 and an aperture stop SP, respectively. Detectors 109 to 111, such as encoders, potentiometers, or photosensors, are configured to detect positions on the optical axis of the first lens unit F and the magnification varying portion V, and a stop diameter of the aperture stop SP. The camera 201 includes a glass block 202, which corresponds to an optical filter or a color separation optical system in the camera 201, and a solid image pickup element (photoelectric conversion element) 203, such as a CCD sensor or a CMOS sensor, configured to receive an object image formed by the zoom lens 101. Further, CPUs 204 and 113 are configured to control various kinds of driving of the camera 201 and the zoom lens 101, respectively.

(109) As described above, when the zoom lens according to embodiments of the present invention is applied to a television camera, the image pickup apparatus having high optical performance can be achieved.

Numerical Embodiment 1

(110) TABLE-US-00001 Unit: mm Surface data Surface Effective Focal number r d nd νd θgF diameter length  1 −2,942.18811 6.00000 1.834810 42.74 0.5648 203.750 −358.417  2 335.45859 1.80000 192.610  3 335.06633 23.70767 1.433870 95.10 0.5373 191.868 588.078  4 −1,057.92901 0.20000 190.148  5 525.29863 14.68252 1.433870 95.10 0.5373 193.025 995.955  6 −2,449.90453 25.25075 193.154  7 377.04224 20.53079 1.433870 95.10 0.5373 193.717 681.715  8 −1,365.49684 0.25000 193.047  9 306.95406 16.15620 1.433870 95.10 0.5373 187.894 856.440 10 1,716.23164 1.49946 186.359 11 188.24393 16.19337 1.438750 94.66 0.5340 175.691 776.951 12 408.07756 (Variable) 173.184 13 −532.82374 2.20000 2.003300 28.27 0.5980 44.984 −35.106 14 38.13165 11.72245 38.642 15 −44.54614 1.45000 1.743198 49.34 0.5531 37.438 −36.767 16 72.56546 9.77415 1.892860 20.36 0.6393 38.715 32.645 17 −46.48441 1.62858 39.806 18 −41.75805 2.00000 1.882997 40.76 0.5667 39.744 −65.283 19 −152.60813 (Variable) 42.316 20 (Flare Cutting 26.00000 60.360 Stop) 21 152.33559 11.49260 1.729157 54.68 0.5444 82.983 133.769 22 −265.71450 6.61910 83.273 23 139.88768 13.50202 1.438750 94.66 0.5340 83.569 205.022 24 −246.30392 0.49825 82.934 25 264.09410 2.60000 1.854780 24.80 0.6122 79.988 −179.267 26 97.10593 (Variable) 77.223 27 86.50601 15.38886 1.496999 81.54 0.5375 77.479 129.181 28 −236.96933 0.50000 76.571 29 415.87662 2.50000 1.805181 25.42 0.6161 73.248 −258.974 30 139.36202 7.84908 1.603112 60.64 0.5415 70.931 195.306 31 −764.20052 (Variable) 69.699 32 (Stop) 4.84000 34.039 33 −138.18307 1.40000 1.717004 47.92 0.5605 31.464 −48.078 34 46.43091 0.47326 30.197 35 33.96796 4.50685 1.854780 24.80 0.6122 30.253 57.662 36 100.46819 2.99046 29.383 37 −259.50169 1.40000 1.891900 37.13 0.5780 28.555 −68.817 38 81.27385 20.1700 27.879 39 −1,353.89742 4.17772 1.487490 70.23 0.5300 25.682 83.062 40 −39.48578 1.19320 25.530 41 −52.65530 1.60000 1.882997 40.76 0.5667 24.659 −16.067 42 19.85501 9.52924 1.639799 34.46 0.5922 24.591 22.854 43 −46.23969 14.9900 25.412 44 −144.86408 7.20624 1.516330 64.14 0.5353 26.359 59.225 45 −25.75718 0.69246 27.232 46 −78.44236 1.80000 2.001000 29.13 0.5997 26.128 −15.418 47 19.63195 12.22279 1.808095 22.76 0.6307 26.257 20.196 48 −74.15936 0.19847 27.560 49 1,100.38435 8.06667 1.548141 45.79 0.5686 27.708 39.371 50 −22.07117 1.80000 1.854780 24.80 0.6122 27.864 −35.607 51 −81.32000 11.65158 29.492 52 −55.36979 8.12203 1.487490 70.23 0.5300 32.076 100.553 53 −27.30240 9.49982 33.752 54 ∞ 63.04000 1.608590 46.44 0.5664 70.000 55 ∞ 8.70000 1.516330 64.15 0.5352 70.000 56 ∞ 10.99810 70.000 Image ∞ plane Aspherical surface data Thirteenth surface K = 1.99852e+000 A4 = 1.15677e−006 A6 = −2.75064e−008 A8 = −3.06848e−010 A10 = 9.10515e−013 A12 = 3.28486e−015 A14 = 1.35261e−018 A16 = 5.54400e−022 A3 = 2.74335e−007 A5 = 9.95673 e−008 A7 = 4.02226e−009 A9 = 6.12079e−012 A11 = −8.52506e−014 A13 = −6.85632e−017 A15 = −3.84859e−020 Twenty-second surface K = 1 .21093e+001 A4 = 2.82183e−007 A6 = −5.59441e−011 A8 = −2.00796e−014 A10 = 9.78964e−017 A12 = −6.30815e−020 A14 = 1.70834e−023 A16 = −4.73901e−027 A3 = −2.90901e−008 A5 = 1.58196e−009 A7 = 1.10620e−012 A9 = −1.50730e−015 A11 = 5.86871e−020 A13 = 1.04584e−022 A15 = 1.44467e−025 Thirty-first surface K = −2.23400e+002 A4 = 2.77687e−007 A6 = 4.69555e−010 A8 = 1.39733e−013 A10 = −2.98156e−016 A12 = 4.58582e−019 A14 = −2.25443e−022 A16 = 5.80568e−026 A3 = 1.70768e−007 A5 = −5.73181e−009 A7 = −1.36230e−011 A9 = 7.92918e−015 A11 = −8.14405e−018 A13 = 2.06016e−021 A15 = −8.57551e−025 Various data Zoom ratio 56.00 Focal length 14.30 107.04 552.17 800.80 F−number 2.95 2.95 2.95 4.28 Half angle 32.90 4.94 0.96 0.66 of view Total lens 727.27 727.27 727.27 727.27 length d12 3.47 136.28 184.78 188.97 d19 263.33 89.82 31.05 13.68 d26 4.21 17.44 3.79 6.78 d31 2.99 30.47 54.38 64.58 Entrance pupil 133.62 741.83 3,367.79 4,979.68 position Exit pupil 473.66 473.66 473.66 473.66 position Front principal 148.37 873.63 4,578.95 7,166.52 point position Rear principal −3.30 −96.04 −541.17 −789.80 point position Zoom lens unit data Front Rear Lens principal principal First Focal structure point point Unit surface length length position position 1 1 251.50 126.27 72.69 −19.27 2 13 −24.07 28.78 3.62 −16.98 31 20 134.62 60.71 20.97 −27.55 32 27 112.37 26.24 4.27 −13.07 4 32 72.20 119.03 88.04 126.80 Single lens data Lens First surface Focal length 1 1 −358.42 2 3 588.08 3 5 995.95 4 7 681.71 5 9 856.44 6 11 776.95 7 13 −35.11 8 15 −36.77 9 16 32.64 10 18 −65.28 11 21 133.77 12 23 205.02 13 25 −179.27 14 27 129.18 15 29 −258.97 16 30 195.31 17 33 −48.08 18 35 57.66 19 37 −68.82 20 39 83.06 21 41 −16.07 22 42 22.85 23 44 59.22 24 46 −15.42 25 47 20.20 26 49 39.37 27 50 −35.61 28 52 100.55 29 54 0.00 30 55 0.00

Numerical Embodiment 2

(111) TABLE-US-00002 Surface data Surface Effective Focal number R d nd νd θgF diameter length  1 1,997.02113 6.00000 1.788001 47.37 0.5559 195.890 −452.598  2 303.49132 1.94485 189.686  3 317.22604 19.16858 1.433870 95.10 0.5373 190.331 698.448  4 −7,044.93390 0.20000 190.807  5 673.24372 6.00000 1.834000 37.16 0.5776 192.066 −1,014.711  6 374.48011 0.79177 191.559  7 345.92209 19.79827 1.433870 95.10 0.5373 192.306 687.598  8 −2,170.21310 28.23869 192.619  9 339.68529 21.07732 1.433870 95.10 0.5373 195.887 648.526 10 −1,632.16760 0.25000 195.399 11 246.79128 21.92714 1.433870 95.10 0.5373 190.025 593.790 12 5,400.98293 1.20000 188.476 13 187.53643 11.51644 1.496999 81.54 0.5375 175.349 938.175 14 306.70190 (Variable) 173.642 15 930.09210 2.35000 1.882997 40.76 0.5667 53.860 −58.233 16 48.93704 8.62302 46.980 17 −228.62144 1.45000 1.772499 49.60 0.5520 45.855 −37.375 18 33.31892 13.01460 1.784696 26.29 0.6135 43.011 34.566 19 −126.76144 3.63452 43.106 20 −47.00906 2.00000 1.696797 55.53 0.5434 43.046 −59.719 21 383.02728 (Variable) 45.323 22 (Flare Cutting 25.00000 62.791 Stop) 23 359.47102 10.40779 1.603112 60.64 0.5415 79.418 159.320 24 −130.40784 0.88057 80.339 25 229.25254 11.10721 1.496999 81.54 0.5375 82.087 205.850 26 −182.74509 9.50174 82.045 27 −206.21310 2.50000 1.717362 29.52 0.6047 79.378 −106.306 28 123.17797 7.78057 1.496999 81.54 0.5375 79.607 284.767 29 912.13699 (Variable) 79.861 30 247.96165 14.10652 1.618000 63.33 0.5441 81.677 126.414 31 −112.19096 (Variable) 81.715 32 (Stop) 4.90749 33.163 33 −72.13544 1.80000 1.816000 46.62 0.5568 31.566 −39.850 34 60.43089 5.13557 1.808095 22.76 0.6307 31.230 59.455 35 −237.28216 7.55722 31.078 36 −28.78125 1.49977 1.816000 46.62 0.5568 30.264 −24.953 37 72.49578 10.08032 1.548141 45.79 0.5686 33.567 38.544 38 −28.55262 16.01453 34.877 39 194.31854 9.07524 1.531717 48.84 0.5631 38.230 68.490 40 −44.35136 1.49161 38.328 41 −104.49421 1.50000 1.882997 40.76 0.5667 36.109 −38.029 42 50.24421 8.69548 1.518229 58.90 0.5457 35.505 45.865 43 −42.76309 0.49453 35.604 44 151.55145 6.51018 1.496999 81.54 0.5375 33.452 59.851 45 −36.61436 1.50000 1.882997 40.76 0.5667 32.872 −44.960 46 −449.26887 1.00055 32.614 47 79.39231 5.73260 1.522494 59.84 0.5440 32.142 83.887 48 −96.27308 10.00000 31.452 49 ∞ 33.00000 1.608590 46.44 0.5664 40.000 50 ∞ 13.20000 1.516330 64.14 0.5353 40.000 51 ∞ 14.52000 50.000 Image ∞ plane Aspherical surface data Fifteenth surface K = −2.51552e+003 A4 = 1.29148e−006 A6 = −5.23984e−010 A8 = 3.22417e−013 Twenty-third surface K = 4.42423e+000 A4 = −3.50816e−007 A6 = 4.78501e−012 A8 = −2.62170e−015 Various data Zoom ratio 80.00 Focal length 10.00 89.44 342.87 800.00 F−number 1.80 1.80 1.83 4.20 Half angle 28.81 3.52 0.92 0.39 of view Total lens 697.94 697.94 697.94 697.94 length d14 2.99 139.53 167.98 176.93 d21 274.47 99.82 31.50 −15.54 d29 1.47 4.67 5.34 7.40 d31 14.83 49.75 88.93 124.97 Entrance pupil 157.062 1,033.44 3,371.19 10,682.26 position Exit pupil 11,703.09 11,703.09 11,703.09 11,703.09 position Front principal 167.07 1,123.56 3,724.12 11,536.76 point position Rear principal 4.52 −74.92 −328.35 −785.26 point position Zoom lens unit data Front Rear Lens principal principal First Focal structure point point Unit surface length length position position 1 1 246.00 138.11 81.41 −19.51 2 15 −28.50 31.07 8.71 −11.29 31 22 162.05 67.18 15.80 −37.04 32 30 126.41 14.11 6.09 −2.75 4 32 60.40 139.20 60.72 7.63 Single lens data Lens First surface Focal length 1 1 −452.60 2 3 698.45 3 5 −1,014.71 4 7 687.60 5 9 648.53 6 11 593.79 7 13 938.17 8 15 −58.23 9 17 −37.37 10 18 34.57 11 20 −59.72 12 23 159.32 13 25 205.85 14 27 −106.31 15 28 284.77 16 30 126.41 17 34 −39.85 18 35 59.45 19 37 −24.95 20 38 38.54 21 40 68.49 22 42 −38.03 23 43 45.87 24 45 59.85 25 46 −44.96 26 48 83.89 27 50 0.00 28 51 0.00

Numerical Embodiment 3

(112) TABLE-US-00003 Unit: mm Surface Effective Focal number r d nd νd θgF diameter length  1 1,997.02113 6.00000 1.788001 47.37 0.5559 191.702 −434.145  2 292.93504 1.94485 182.157  3 306.27157 19.16858 1.433870 95.10 0.5373 182.775 709.381  4 40,647.76021 0.20000 183.428  5 644.82819 6.00000 1.834000 37.16 0.5776 184.630 −1,043.409  6 369.80177 0.79177 184.233  7 340.12243 19.79827 1.433870 95.10 0.5373 184.977 663.014  8 −1,862.37637 28.23869 185.367  9 344.48142 21.07732 1.433870 95.10 0.5373 188.697 631.883 10 −1,334.37205 0.25000 188.150 11 238.37882 21.92714 1.433870 95.10 0.5373 183.035 568.371 12 6,480.80392 1.20000 181.276 13 186.26080 11.51644 1.496999 81.54 0.5375 169.039 982.666 14 294.36889 (Variable) 166.664 15 902.31264 2.35000 1.882997 40.76 0.5667 52.994 −59.961 16 50.22465 8.42696 46.500 17 −206.37092 1.45000 1.772499 49.60 0.5520 45.377 −37.051 18 33.51906 12.77912 1.784696 26.29 0.6135 42.303 34.802 19 −128.75037 3.69367 42.418 20 −47.50344 2.00000 1.696797 55.53 0.5434 42.318 −60.277 21 383.02728 (Variable) 44.481 22 (Flare Cutting 15.00000 62.791 Stop) 23 362.55588 10.16936 1.603112 60.64 0.5415 77.257 156.579 24 −127.01769 (Variable) 78.203 25 264.91299 10.45745 1.496999 81.54 0.5375 80.475 215.010 26 −177.62551 10.00285 80.483 27 −213.23223 2.50000 1.717362 29.52 0.6047 77.926 −106.127 28 120.47636 8.98229 1.496999 81.54 0.5375 78.226 271.870 29 1,058.69990 (Variable) 78.646 30 254.51562 14.10652 1.618000 63.33 0.5441 79.859 122.586 31 −106.14322 (Variable) 79.928 32 (Stop) 4.90749 33.149 33 −72.13544 1.80000 1.816000 46.62 0.5568 31.533 −39.850 34 60.43089 5.13557 1.808095 22.76 0.6307 31.182 59.455 35 −237.28216 7.55722 31.023 36 −28.78125 1.49977 1.816000 46.62 0.5568 30.185 −24.953 37 72.49578 10.08032 1.548141 45.79 0.5686 33.439 38.544 38 −28.55262 16.01453 34.771 39 194.31854 9.07524 1.531717 48.84 0.5631 37.986 68.490 40 −44.35136 1.49161 38.073 41 −104.49421 1.50000 1.882997 40.76 0.5667 35.871 −38.029 42 50.24421 8.69548 1.518229 58.90 0.5457 35.263 45.865 43 −42.76309 0.49453 35.364 44 151.55145 6.51018 1.496999 81.54 0.5375 33.231 59.851 45 −36.61436 1.50000 1.882997 40.76 0.5667 32.624 −44.960 46 −449.26887 1.00055 32.357 47 79.39231 5.73260 1.522494 59.84 0.5440 31.878 83.887 48 −96.27308 10.00000 31.171 49 ∞ 33.00000 1.608590 46.44 0.5664 40.000 50 ∞ 13.20000 1.516330 64.14 0.5353 40.000 51 ∞ 14.00000 50.000 Image ∞ plane Aspherical surface data Fifteenth surface K = −2.66393e+003 A4 = 1.23749e−006 A6 = −5.73970e−010 A8 = 3.72435e−013 Twenty-third surface K = 6.47133e+000 A4 = −3.95205e−007 A6 = 2.42444e−012 A8 = −2.35458e−015 Various data Zoom ratio 75.00 Focal length 10.20 88.33 327.86 765.00 F−number 1.80 1.80 1.94 4.20 Half angle 28.26 3.55 0.96 0.41 of view Total lens 690.36 690.36 690.36 690.36 length BF 14.00 14.00 14.00 14.00 d14 3.03 136.43 164.78 173.91 d21 277.58 107.00 40.42 −7.68 d24 1.00 4.26 5.01 4.24 d29 1.45 1.66 2.71 7.52 d31 14.07 47.77 84.21 119.14 Entrance pupil 157.01 998.27 3,156.40 9,859.86 position Exit pupil 11,703.09 11,703.09 11,703.09 11,703.09 position Front principal 167.25 1,087.54 3,494.71 10,678.34 point position Rear principal 3.77 −74.60 −315.05 −754.02 point position Zoom lens unit data Front Rear Lens principal principal First Focal structure point point Unit surface length length position position 1 1 242.80 138.11 81.68 −18.91 2 15 −28.73 30.70 8.74 −11.09 31 22 156.58 25.17 19.73 −1.66 32 25 −1,370.11 31.94 113.83 82.28 33 30 122.59 14.11 6.24 −2.60 4 32 60.40 139.20 60.72 7.63 Single lens data Lens First surface Focal length 1 1 −434.15 2 3 709.38 3 5 −1,043.41 4 7 663.01 5 9 631.88 6 11 568.37 7 13 982.67 8 15 −59.96 9 17 −37.05 10 18 34.80 11 20 −60.28 12 23 156.58 13 25 215.01 14 27 −106.13 15 28 271.87 16 30 122.59 17 33 −39.85 18 34 59.45 19 36 −24.95 20 37 38.54 21 39 68.49 22 41 −38.03 23 42 45.87 24 44 59.85 25 45 −44.96 26 47 83.89 27 49 0.00 28 50 0.00

Numerical Embodiment 4

(113) TABLE-US-00004 Unit: mm Surface Effective Focal number r d nd νd θgF diameter length 1 −2,942.18811 6.00000 1.834810 42.74 0.5648 217.338 −358.417 2 335.45859 1.80000 205.268 3 335.06633 23.70767 1.433870 95.10 0.5373 204.608 588.078 4 −1,057.92901 0.20000 203.310 5 525.29863 14.68252 1.433870 95.10 0.5373 194.016 995.955 6 −2,449.90453 25.25075 194.142 7 377.04224 20.53079 1.433870 95.10 0.5373 194.714 681.715 8 −1,365.49684 0.25000 194.066 9 306.95406 16.15620 1.433870 95.10 0.5373 188.834 856.440 10 1,716.23164 1.49946 187.339 11 188.24393 16.19337 1.438750 94.66 0.5340 176.515 776.951 12 408.07756 (Variable) 174.075 13 −532.82374 2.20000 2.003300 28.27 0.5980 45.965 −35.598 14 38.70473 11.72245 39.358 15 −44.02487 1.45000 1.743198 49.34 0.5531 38.272 −36.949 16 74.97068 9.77415 1.892860 20.36 0.6393 39.450 33.422 17 −47.40353 (Variable) 40.531 18 −41.60635 2.00000 1.882997 40.76 0.5667 40.435 −67.527 19 −138.92605 (Variable) 43.138 20 (Flare Cutting 23.00000 63.353 Stop) 21 144.13786 11.49260 1.729157 54.68 0.5444 82.058 129.132 22 −265.71450 6.61910 82.314 23 156.77329 13.50202 1.438750 94.66 0.5340 82.423 222.075 24 −252.33271 0.49825 81.676 25 263.81666 2.60000 1.854780 24.80 0.6122 79.054 −167.484 26 92.94563 (Variable) 76.338 27 84.17766 15.38886 1.496999 81.54 0.5375 76.936 126.593 28 −236.69003 0.50000 76.160 29 381.41978 2.50000 1.805181 25.42 0.6161 73.073 −300.006 30 148.29386 7.84908 1.603112 60.64 0.5415 71.042 205.783 31 −764.20052 (Variable) 69.767 32 (Stop) 4.84000 32.930 33 −128.97009 1.40000 1.717004 47.92 0.5605 30.504 −48.412 34 48.03452 0.46927 29.399 35 34.19077 4.49157 1.854780 24.80 0.6122 29.468 55.493 36 112.28150 3.00681 28.626 37 −212.76669 1.40000 1.891900 37.13 0.5780 27.741 −63.929 38 78.81799 18.42000 27.097 39 −516.38868 4.15431 1.487490 70.23 0.5300 25.535 83.729 40 −38.04634 1.21516 25.439 41 −52.28324 1.60000 1.882997 40.76 0.5667 24.584 −16.155 42 20.06016 9.53057 1.639799 34.46 0.5922 24.625 22.915 43 −45.48049 14.90110 25.500 44 −161.46817 7.07021 1.516330 64.14 0.5353 26.161 58.695 45 −25.97910 0.68287 26.929 46 −74.12050 1.80000 2.001000 29.13 0.5997 25.951 −15.374 47 19.86030 10.53753 1.808095 22.76 0.6307 26.222 20.184 48 −73.70705 0.20030 27.252 49 803.00743 8.16674 1.548141 45.79 0.5686 27.454 38.874 50 −21.92635 1.80000 1.854780 24.80 0.6122 27.672 −35.784 51 −78.51014 11.41542 29.352 52 −55.33406 8.00662 1.487490 70.23 0.5300 32.053 99.245 53 −27.08806 10.70540 33.719 54 ∞ 63.04000 1.608590 46.44 0.5664 70.000 55 ∞ 8.70000 1.516330 64.15 0.5352 70.000 56 ∞ 12.93000 70.000 Image ∞ plane Aspherical surface data Thirteenth surface K = 1.99852e+000 A4 = 1.15677e−006 A6 = −2.75064e−008 A8 = −3.06848e−010 A10 = 9.10515e−013 A12 = 3.28486e−015 A14 = 1.35261e−018 A16 = 5.54400e−022 A3 = 2.74335e−007 A5 = 9.95673 e−008 A7 = 4.02226e−009 A9 = 6.12079e−012 A11 = −8.52506e−014 A13 = −6.85632e−017 A15 = −3.84859e−020 Twenty-second surface K = 1.21093e+001 A4 = 2.82183e−007 A6 = −5.59441e−011 A8 = −2.00796e−014 A10 = 9.78964e−017 A12 = −6.30815e−020 A14 = 1.70834e−023 A16 = −4.73901e−027 A3 = −2.90901e−008 A5 = 1.58196e−009 A7 = 1.10620e−012 A9 = −1.50730e−015 A11 = 5.86871e−020 A13 = 1.04584e−022 A15 = 1.44467e−025 Thirty-first surface K = −2.23400e+002 A4 = 2.77687e−007 A6 = 4.69555e−010 A8 = 1 .39733e−013 A10 = −2.98156e−016 A12 = 4.58582e−019 A14 = −2.25443e−022 A16 = 5.80568e−026 A3 = 1.70768e−007 A5 = −5.73181e−009 A7 = −1.36230e−011 A9 = 7.92918e−015 A11 = −8.14405e−018 A13 = 2.06016e−021 A15 = −8.57551e−025 Various data Zoom ratio 56.30 Focal length 14.30 107.30 555.00 805.09 F−number 2.95 2.95 2.95 4.28 Half angle 32.90 4.93 0.95 0.66 of view Total lens 728.48 728.48 728.48 728.48 length BF 12.93 12.93 12.93 12.93 d12 6.61 136.28 184.15 188.26 d17 2.11 4.89 3.34 3.05 d19 261.93 85.90 29.61 12.81 d26 7.53 20.05 4.00 5.24 d31 2.45 33.51 59.53 71.27 Entrance pupil 138.95 753.72 3,450.77 5,157.20 position Exit pupil 519.25 519.25 519.25 519.25 position Front principal 153.65 883.75 4,614.13 7,242.45 point position Rear principal −1.37 −94.37 −542.07 −792.16 point position Zoom lens unit data Front Rear Lens principal principal First Focal structure point point Unit surface length length position position   1 1 251.50 126.27 72.69 −19.27   2 13 −24.18 29.26 3.76 −17.17 (21 13 −58.94 25.15 −9.89 −36.49) (22 18 −67.53 2.00 −0.46 −1.53)  31 20 142.07 57.71 15.57 −29.49  32 27 107.51 26.24 4.41 −12.95   4 32 73.30 87.52 123.65 115.11 Single lens data Lens First surface Focal length 1 1 −358.42 2 3 588.08 3 5 995.95 4 7 681.71 5 9 856.44 6 11 776.95 7 13 −35.60 8 15 −36.95 9 16 33.42 10 18 −67.53 11 21 129.13 12 23 222.07 13 25 −167.48 14 27 126.59 15 29 −300.01 16 30 205.78 17 33 −48.41 18 35 55.49 19 37 −63.93 20 39 83.73 21 41 −16.16 22 42 22.91 23 44 58.69 24 46 −15.37 25 47 20.18 26 49 38.87 27 50 −35.78 28 52 99.25 29 54 0.00 30 55 0.00

(114) TABLE-US-00005 TABLE 1 Embodi- Embodi- Embodi- Embodi- Conditional Expression ment 1 ment 2 ment 3 ment 4 (1) f1/f2 −10.448 −8.632 −8.451 −10.476 (2) Xi3/S23 0.456 0.442 0.270 0.437 (3) |(β3t/β3w)/ 0.331 0.539 0.202 0.356 (β2t/β2w)| (4) x2i/s23 0.776 0.800 0.877 0.789 (5) ft/fw 56.0 80.0 75.0 56.3 (6) 2ωw 65.8 57.6 56.5 65.8 f1 251.50 246.00 242.80 251.50 f2 −24.07 −28.50 −28.73 −24.18 Xi3 26.00 25.00 15.00 23.00 S23 57.05 56.50 55.42 29.61 β3t −1.11 −2.16 2.82 −1.21 β3w −0.26 −0.26 −0.97 −0.27 β2t −1.55 −2.31 −2.30 −1.51 β2w −0.12 −0.15 −0.16 −0.12 x2i 89.82 99.82 107.00 85.90 s23 115.82 124.82 122.00 108.90 ft 800.80 800.00 765.00 805.09 fw 14.30 10.00 10.20 14.30

(115) While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.

(116) This application claims the benefit of Japanese Patent Application No. 2018-214834, filed Nov. 15, 2018, which is hereby incorporated by reference herein in its entirety.