JP5489323B2 - Wide angle zoom lens - Google Patents

Wide angle zoom lens Download PDF

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Publication number
JP5489323B2
JP5489323B2 JP2009097400A JP2009097400A JP5489323B2 JP 5489323 B2 JP5489323 B2 JP 5489323B2 JP 2009097400 A JP2009097400 A JP 2009097400A JP 2009097400 A JP2009097400 A JP 2009097400A JP 5489323 B2 JP5489323 B2 JP 5489323B2
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lens
group
wide
refractive power
positive
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JP2010249959A (en
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大勇 李
壮基 原田
浩史 山本
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Nikon Corp
Tamron Co Ltd
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Nikon Corp
Tamron Co Ltd
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Priority to JP2009097400A priority Critical patent/JP5489323B2/en
Priority to CN201010146463.0A priority patent/CN101859019B/en
Priority to CN201410030706.2A priority patent/CN103744170B/en
Priority to US12/662,355 priority patent/US8169718B2/en
Priority to CN201410031012.0A priority patent/CN103744171B/en
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Description

本発明は、広角ズームレンズ、さらに詳しくは、画角107°を超える一眼レフデジタルカメラ用の超広角で、ズーム比が2倍超える広角ズームレンズに関する。   The present invention relates to a wide-angle zoom lens, and more particularly to a wide-angle zoom lens for a single-lens reflex digital camera having an angle of view exceeding 107 ° and having a zoom ratio exceeding twice.

従来の一眼レフレックスカメラ用超広角ズームレンズとしては、物体側から像側へ順に、負の屈折力の第1レンズ群、正の屈折力の第2レンズ群、負の屈折力の第3レンズ群、正の屈折力の第4レンズ群を有し、広角端より望遠端へのズーミングに際し、前記第1レンズ群と第2レンズ群の間隔が減少し、前記第2レンズ群と第3レンズ群の間隔が増大し、前記第3レンズ群と第4レンズ群の間隔が減少するズームレンズであって、広角端におけるバックフォーカスをbfw、広角端における全系の焦点距離をfw、第2レンズ群と第4レンズ群の焦点距離を各々f2,f4とするとき、
2.9<bfw/fw<5.0
3.1<f4/fw<4.5
0.1<fw/f2<0.42
なる条件を満足することを特徴とするズームレンズが提案されている(例えば、特許文献1参照)。
As a conventional super wide-angle zoom lens for a single-lens reflex camera, in order from the object side to the image side, a first lens group having a negative refractive power, a second lens group having a positive refractive power, and a third lens having a negative refractive power And a fourth lens group having a positive refractive power, and during the zooming from the wide-angle end to the telephoto end, the distance between the first lens group and the second lens group decreases, and the second lens group and the third lens A zoom lens in which the distance between the groups is increased and the distance between the third lens group and the fourth lens group is decreased, wherein the back focus at the wide angle end is bfw, the focal length of the entire system at the wide angle end is fw, and the second lens When the focal lengths of the lens group and the fourth lens group are f2 and f4, respectively.
2.9 <bfw / fw <5.0
3.1 <f4 / fw <4.5
0.1 <fw / f2 <0.42
There has been proposed a zoom lens characterized by satisfying the following conditions (for example, see Patent Document 1).

特開2006−039531号広報JP 2006-039531 A

これらの従来の広角ズームレンズは、負、正、負、正の屈折力を持つレンズ群からなる4群ズームレンズタイプである。これらの従来の広角ズームレンズにおいては、広角端の画角が100°を超えると共に、2倍以上のズーム比を実現しようとしている。すなわち、特許文献1には、広角端の画角が105.8°程度、ズーム比1.95〜2.36程度が開示されている。   These conventional wide-angle zoom lenses are a four-group zoom lens type composed of lens groups having negative, positive, negative, and positive refractive powers. In these conventional wide-angle zoom lenses, the angle of view at the wide-angle end exceeds 100 °, and an attempt is made to realize a zoom ratio of 2 times or more. That is, Patent Document 1 discloses a field angle at the wide-angle end of about 105.8 ° and a zoom ratio of about 1.95 to 2.36.

特許文献1によって提案されている広角ズームレンズは、最も物体側のレンズは負の屈折力が強くなるように設定しており、広角端の画角が105°程度であり、前枠の有効径を小さく抑えることができる。等の利点を有しているが、しかしながら、第1群と絞りの距離は遠いので、広角端の画角はさらに大きくな広い画角と第1群の小型化を両立することが困難となる。   The wide-angle zoom lens proposed by Patent Document 1 is set so that the most object-side lens has a strong negative refractive power, the angle of view at the wide-angle end is about 105 °, and the effective diameter of the front frame Can be kept small. However, since the distance between the first lens group and the stop is long, it is difficult to achieve both a wider angle of view at the wide-angle end and a smaller size of the first lens group. .

(発明の目的)
本発明はこれらの従来例を鑑みなされたもので、広角端画角は110°を超えるズームレンズにおいて、第1群と第4群の小型化を実現した広角ズームレンズを提供することを目的とする。
(Object of invention)
The present invention has been made in view of these conventional examples, and an object of the present invention is to provide a wide-angle zoom lens in which the first group and the fourth group are miniaturized in a zoom lens having a wide-angle end angle of view exceeding 110 °. To do.

本発明は、
物体から順に、負の屈折力の第1レンズ群、正の屈折力の第2レンズ群、負の屈折力の第3レンズ群、正の屈折力の第4レンズ群からなり、各レンズ群を移動させて変倍を行い、
前記第1レンズ群は、負の屈折力の第1レンズ群の前群レンズ群及び負の屈折力の第1レンズ群の後群レンズ群によって構成し、無限遠物体から近距離へのフォーカシングを第1レンズ群の後群レンズ群を物体側へ移動させて行い、第2レンズ群は最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズの複数レンズで構成し、第4レンズ群は最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズで複数レンズ構成し、第4レンズ群内に少なくとも一面に非球面を有し、以下の条件式を満たすことを特徴とする広角ズームレンズ。
条件式 0.15 ≦ D1Sw/OVLw ≦ 0.3
但し、
D1Sw:被写体距離無限遠における広角端での第1レンズ群の最も像面側の面から
絞りまでの距離
OVLw:広角端でレンズ系の全長(最も物体側の面から最も像面側の面までの長さ)である。
The present invention
In order from an object, a first lens unit having a negative refractive power, a second lens unit having positive refractive power, a third lens unit having a negative refractive power, and a fourth lens unit having positive refractive power, the lens groups Move it to scale,
The first lens group includes a front lens group of the first lens group having a negative refractive power and a rear lens group of the first lens group having a negative refractive power, and performs focusing from an object at infinity to a short distance. The rear lens group of the first lens group is moved to the object side, and the second lens group is composed of a plurality of lenses, the lens having the most positive refractive power on the object side and the lens having the negative refractive power on the most image side. The fourth lens group includes a lens having a positive refractive power closest to the object side and a lens having a negative refractive power closest to the image side. The fourth lens group has at least one aspheric surface in the fourth lens group. A wide-angle zoom lens characterized by satisfying a conditional expression.
Conditional expression 0.15 ≤ D1Sw / OVLw ≤ 0.3
However,
D1Sw: From the surface closest to the image plane of the first lens unit at the wide-angle end at an infinite subject distance
Distance to aperture
OVLw: The total length of the lens system at the wide-angle end (the length from the most object-side surface to the most image-side surface).

(発明の条件式の説明)
広角端画角110°以上を確保すること、かつ第1群と第4群の有効径を小型化することの両立をはかるため、条件式を規定した。
条件式の下限を超えると、広角端で、第1群の小型化がし易いが、第4群の有効径が大きくなり、最大像高の主光線の結像面への入射角度が小さ過ぎることになる。条件式の下限を超えると、さらに、結像面への入射角度が浅くなり過ぎ、撮像素子の最適入射角度から外れる問題が発生する。
条件式の上限を超えると、第4群の小型化はし易いやすいが、第1群の小型化が困難となる。条件式の上限を超えると、さらに、球面収差、非点収差、ディストーション等が発生する。
条件式を 0.2 ≦ D1Sw/OVLw ≦ 0.25
とすると、本発明の効果をより確実なものとすることができる。
(Explanation of conditional expressions of the invention)
In order to achieve both the securing of a wide angle end angle of view of 110 ° or more and the reduction of the effective diameters of the first group and the fourth group, conditional expressions were defined.
If the lower limit of the conditional expression is exceeded, it is easy to reduce the size of the first group at the wide angle end, but the effective diameter of the fourth group becomes large, and the incident angle of the principal ray with the maximum image height on the imaging surface is too small. It will be. If the lower limit of the conditional expression is exceeded, the incident angle on the imaging surface becomes too shallow, and a problem arises that deviates from the optimum incident angle of the image sensor.
If the upper limit of the conditional expression is exceeded, it is easy to reduce the size of the fourth group, but it becomes difficult to reduce the size of the first group. If the upper limit of the conditional expression is exceeded, spherical aberration, astigmatism, distortion and the like are further generated.
Conditional expression 0.2 ≤ D1Sw / OVLw ≤ 0.25
Then, the effect of the present invention can be made more reliable.

(第2群構成)
第4群の有効径を小さく抑えるため、第2レンズ群は最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズで複数レンズ構成した。すなわち、図13(A)に示すように、前方(被写体側)に正パワーレンズ部100を配置し、後方(結像側)に負パワーレンズ部110を配置すると、該光学系の後方側領域において光線Lの高さが低くなり、後方側領域のレンズの外径を小さくすることができる。逆に、図13(B)に示すように、前方(被写体側)に負パワーレンズ部110を配置し、後方(結像側)に正パワーレンズ部100を配置すると、該光学系の後方側領域において光線Lの高さが高くなり、後方側領域のレンズの外径が大きくなってしまう。
(Second group configuration)
In order to keep the effective diameter of the fourth group small, the second lens group is composed of a lens having a positive refractive power on the most object side and a lens having a negative refractive power on the most image side. That is, as shown in FIG. 13A, when the positive power lens unit 100 is disposed on the front side (subject side) and the negative power lens unit 110 is disposed on the rear side (imaging side), the rear side region of the optical system. , The height of the light beam L is reduced, and the outer diameter of the lens in the rear region can be reduced. Conversely, as shown in FIG. 13B, when the negative power lens unit 110 is disposed in front (subject side) and the positive power lens unit 100 is disposed rearward (image forming side), the rear side of the optical system. In the region, the height of the light beam L is increased, and the outer diameter of the lens in the rear region is increased.

(第4群構成)
第4群の有効径を抑えることと色収差を補正するため、第4レンズ群は少なくとも2枚正レンズと2枚負レンズを有し、レンズの構成は、最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズで複数レンズ構成した。コマ収差と歪曲収差を補正するため、第4群の少なくとも一面を非球面とした。
(Group 4 configuration)
In order to suppress the effective diameter of the fourth group and correct chromatic aberration, the fourth lens group has at least two positive lenses and two negative lenses, and the lens configuration is a lens having the most positive refractive power on the object side. A plurality of lenses are constructed with lenses having the negative refractive power on the most image side. In order to correct coma and distortion, at least one surface of the fourth group is aspheric.

本発明の広角ズームレンズにおいては、広角端画角は110°を超えるズームレンズにおいて、第1群と第4群の小型化を実現した広角ズームレンズを構成することができる。   In the wide-angle zoom lens of the present invention, it is possible to configure a wide-angle zoom lens in which the first group and the fourth group are miniaturized in a zoom lens having a wide-angle end field angle exceeding 110 °.

第1実施形態の広角ズームレンズの光学構成図である。It is an optical block diagram of the wide angle zoom lens of 1st Embodiment. 第1実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 4 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the first embodiment. 第1実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 3 is an aberration diagram illustrating spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the first embodiment. 第2実施形態の広角ズームレンズの光学構成図である。It is an optical block diagram of the wide angle zoom lens of 2nd Embodiment. 第2実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 6 is an aberration diagram showing spherical aberration, astigmatism, distortion and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the second embodiment. 第2実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 10 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the second embodiment. 第3実施形態の広角ズームレンズの光学構成図である。It is an optical block diagram of the wide-angle zoom lens of 3rd Embodiment. 第3実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 10 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the third embodiment. 第3実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 10 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the third embodiment. 第4実施形態の広角ズームレンズの光学構成図である。It is an optical block diagram of the wide-angle zoom lens of 4th Embodiment. 第4実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 10 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the wide-angle end of the wide-angle zoom lens according to the fourth embodiment. 第4実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を示す収差図である。FIG. 10 is an aberration diagram showing spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the wide-angle end of the wide-angle zoom lens according to the fourth embodiment. 本発明の第4レンズ群構成の原理説明図である。It is a principle explanatory view of the 4th lens group composition of the present invention.

以下に、本発明の広角ズームレンズの実施形態及びその収差状況を説明する。
(第1実施形態)
第1実施形態にかかる広角ズームレンズは、図1に示す構成を有する。各レンズ面の曲率半径R(mm)、各レンズ中心厚及びレンズの空気間隔D(mm)、各レンズのd線における屈折率Nd及びアッベ数ABVの値は、以下のとおりである。
In the following, embodiments of the wide-angle zoom lens of the present invention and aberrations thereof will be described.
(First embodiment)
The wide-angle zoom lens according to the first embodiment has the configuration shown in FIG. The values of the radius of curvature R (mm) of each lens surface, the center thickness of each lens and the air space D (mm) of each lens, the refractive index Nd of each lens d-line and the Abbe number ABV are as follows.

焦点距離:10.29〜15.5952〜23.3915
FNO:3.6〜4.15〜4.6
2ω:111.4〜85.4〜62.6

S R D Nd ABV
1 ASPH 90.9531 3.0000 1.74690 49.22
2 ASPH 13.3000 17.4155
3 -347.3422 1.1000 1.83944 42.72
4 27.7720 0.2500 1.51700 49.96
5 ASPH 32.9778 0.8225
6 20.1105 4.8835 1.70444 30.05
7 45.1356 D7
絞り 0.0000 1.6767
9 -70.4744 2.4522 1.69416 31.16
10 -14.1708 0.8000 1.88815 40.80
11 -37.7808 0.1500
12 33.1737 3.7557 1.59142 61.25
13 -14.2611 0.8000 1.81184 33.27
14 -28.6675 D14
15 -29.8948 0.8000 1.80831 46.50
16 23.7239 2.5836 1.93325 20.88
17 240.6296 D17
18 40.3874 4.8044 1.49845 81.61
19 -35.6422 0.1500
20 49.4590 0.8000 1.91048 31.31
21 17.3129 11.6398 1.49845 81.61
22 -14.5130 0.8000 1.91048 31.31
23 -20.5428 0.2000
24 ASPH -34.8009 0.2000 1.51700 49.96
25 -31.4677 1.3000 1.83930 37.34
26 -38.5550
Focal length: 10.29 ~ 15.5952 ~ 23.3915
FNO: 3.6-4.15-4.6
2ω: 111.4-85.4-62.6

SRD Nd ABV
1 ASPH 90.9531 3.0000 1.74690 49.22
2 ASPH 13.3000 17.4155
3 -347.3422 1.1000 1.83944 42.72
4 27.7720 0.2500 1.51700 49.96
5 ASPH 32.9778 0.8225
6 20.1105 4.8835 1.70444 30.05
7 45.1356 D7
Aperture 0.0000 1.6767
9 -70.4744 2.4522 1.69416 31.16
10 -14.1708 0.8000 1.88815 40.80
11 -37.7808 0.1500
12 33.1737 3.7557 1.59142 61.25
13 -14.2611 0.8000 1.81184 33.27
14 -28.6675 D14
15 -29.8948 0.8000 1.80831 46.50
16 23.7239 2.5836 1.93325 20.88
17 240.6296 D17
18 40.3874 4.8044 1.49845 81.61
19 -35.6422 0.1500
20 49.4590 0.8000 1.91048 31.31
21 17.3129 11.6398 1.49845 81.61
22 -14.5130 0.8000 1.91048 31.31
23 -20.5428 0.2000
24 ASPH -34.8009 0.2000 1.51700 49.96
25 -31.4677 1.3000 1.83930 37.34
26 -38.5550

焦点距離:10.2935 15.5952 23.3915
可変間隔
D7 21.974 11.228 4.641
D14 1.000 7.723 14.519
D17 10.742 5.812 0.900
Focal length: 10.2935 15.5952 23.3915
Variable interval
D7 21.974 11.228 4.641
D14 1.000 7.723 14.519
D17 10.742 5.812 0.900

ASPHは、非球面を示し、以下の式(式1)で示される。
(式1)

Figure 0005489323
z:非球面深さ
y:高さ
R:近軸曲率半径
K、A、B、C、D:非球面係数 ASPH indicates an aspherical surface and is represented by the following equation (Equation 1).
(Formula 1)
Figure 0005489323
z: aspheric depth y: height R: paraxial radius of curvature K, A, B, C, D: aspheric coefficient

非球面係数
面1
K : -21.703831
A :0.137414E-04 B :-.284986E-07 C :0.473022E-10 D :-.418229E-13
E :0.157785E-16
面2
K : -0.864034
A :0.743621E-06 B :0.628016E-07 C :-.187456E-09 D :0.315824E-12
E :0.773230E-15
面5
K : 1.512115
A :0.292118E-04 B :-.127860E-06 C :0.842074E-09 D :-.326732E-11
E :0.634290E-14
面24
K : -0.150085
A :-.101962E-04 B :0.106224E-07 C :0.235188E-10 D :0.177170E-12
Aspheric coefficient surface 1
K: -21.703831
A: 0.137414E-04 B:-. 284986E-07 C: 0.473022E-10 D:-. 418229E-13
E: 0.157785E-16
Surface 2
K: -0.864034
A: 0.743621E-06 B: 0.628016E-07 C:-. 187456E-09 D: 0.315824E-12
E: 0.773230E-15
Surface 5
K: 1.512115
A: 0.292118E-04 B:-. 127860E-06 C: 0.842074E-09 D:-. 326732E-11
E: 0.634290E-14
Surface 24
K: -0.150085
A:-. 101962E-04 B: 0.106224E-07 C: 0.235188E-10 D: 0.177170E-12

第1実施形態の広角ズームレンズの各レンズの焦点距離は、以下のとおりである。
群の焦点距離
第1群: -15.253
第2群: 32.183
第3群: -38.7101
第4群: 32.558
Gr1a: -21.94
Gr1b: -104.94
The focal length of each lens of the wide-angle zoom lens of the first embodiment is as follows.
Group focal length Group 1: -15.253
Second group: 32.183
Group 3: -38.7101
Group 4: 32.558
Gr1a: -21.94
Gr1b: -104.94

広角端で
第2,3群合成焦点距離: 148.639
第2,3,4群合成焦点距離:31.483
第1,2,3群合成群焦点距離:-23.355
第1,2,3群合成群と4群の主点位置間間隔:83.074
レンズ全長:94.1
望遠端で
第2、3群の合成焦点距離:56.887
2nd and 3rd group focal length at wide angle end: 148.639
2nd, 3rd, 4th group composite focal length: 31.483
1st, 2nd and 3rd group composite focal length: -23.355
The distance between the principal points of the 1st, 2nd, 3rd group and 4th group: 83.074
Total lens length: 94.1
Combined focal length of groups 2 and 3 at telephoto end: 56.887

第1実施形態の広角ズームレンズの第11面の形状は、以下のとおりである。
有効径 法線角度

Figure 0005489323
The shape of the first surface of the wide-angle zoom lens of the first embodiment is as follows.
Effective diameter Normal angle
Figure 0005489323

第1実施形態の広角ズームレンズの条件式の値は、以下のとおりである。
条件式 D1Sw/OVLw=0.234
第2群の構成 (正負)(正負)
第4群の構成 正(負正負)負
The values of the conditional expressions of the wide angle zoom lens of the first embodiment are as follows.
Conditional expression D1Sw / OVLw = 0.234
Structure of the second group (positive / negative) (positive / negative)
Composition of the fourth group Positive (negative positive negative) negative

第1実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を図2を示す。第1実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を図3を示す。   FIG. 2 shows spherical aberration, astigmatism, distortion and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the first embodiment. FIG. 3 shows spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the first embodiment.

(第2実施形態)
第2実施形態の広角ズームレンズは、図4に示す構成を有する。各レンズ面の曲率半径R(mm)、各レンズ中心厚及びレンズの空気間隔D(mm)、各レンズのd線における、屈折率Nd及びアッベ数ABVは、以下のとおりである。
(Second Embodiment)
The wide-angle zoom lens of the second embodiment has the configuration shown in FIG. The radius of curvature R (mm) of each lens surface, the center thickness of each lens and the air space D (mm) of the lens, the refractive index Nd and the Abbe number ABV in the d-line of each lens are as follows.

焦点距離:10.29〜15.60〜23.39
FNO:3.6〜4.15〜4.6
2ω:111.36〜85.71〜62.88

S R D Nd ABV
1 ASPH 98.2835 3.0000 1.74330 49.22
2 ASPH 13.3000 17.0621
3 -375.8017 1.1000 1.83481 42.72
4 26.2992 0.2500 1.51460 49.96
5 ASPH 31.3128 0.8586
6 19.4744 4.2180 1.69895 30.05
7 44.8215 D7
8 0.0000 1.6811
9 -69.6742 2.4945 1.68893 31.16
10 -13.8558 0.8000 1.88300 40.80
11 -37.5514 0.1500
12 33.6029 3.7863 1.58913 61.25
13 -14.1772 0.8000 1.80610 33.27
14 -28.4616 D14
15 -31.0253 0.8000 1.80420 46.50
16 23.9527 2.5703 1.92286 20.88
17 237.9034 D17
18 41.0664 4.5125 1.49700 81.61
19 -35.8367 0.1500
20 49.9837 0.9000 1.90366 31.31
21 17.1665 11.7603 1.49700 81.61
22 -14.5000 1.1000 1.90366 31.31
23 -21.0822 0.2000
24 ASPH -50.4122 0.2000 1.51460 49.96
25 -44.1195 1.8000 1.83400 37.34
26 -53.8351
Focal length: 10.29-15.60-23.39
FNO: 3.6-4.15-4.6
2ω: 111.36 ~ 85.71 ~ 62.88

SRD Nd ABV
1 ASPH 98.2835 3.0000 1.74330 49.22
2 ASPH 13.3000 17.0621
3 -375.8017 1.1000 1.83481 42.72
4 26.2992 0.2500 1.51460 49.96
5 ASPH 31.3128 0.8586
6 19.4744 4.2180 1.69895 30.05
7 44.8215 D7
8 0.0000 1.6811
9 -69.6742 2.4945 1.68893 31.16
10 -13.8558 0.8000 1.88300 40.80
11 -37.5514 0.1500
12 33.6029 3.7863 1.58913 61.25
13 -14.1772 0.8000 1.80610 33.27
14 -28.4616 D14
15 -31.0253 0.8000 1.80420 46.50
16 23.9527 2.5703 1.92286 20.88
17 237.9034 D17
18 41.0664 4.5125 1.49700 81.61
19 -35.8367 0.1500
20 49.9837 0.9000 1.90366 31.31
21 17.1665 11.7603 1.49700 81.61
22 -14.5000 1.1000 1.90366 31.31
23 -21.0822 0.2000
24 ASPH -50.4122 0.2000 1.51460 49.96
25 -44.1195 1.8000 1.83400 37.34
26 -53.8351

焦点距離:10.29 15.60 23.40
可変間隔
D7 22.0922 11.2672 4.7266
D14 0.9588 7.5245 14.2504
D17 10.8553 5.8392 0.800
Focal length: 10.29 15.60 23.40
Variable interval
D7 22.0922 11.2672 4.7266
D14 0.9588 7.5245 14.2504
D17 10.8553 5.8392 0.800

非球面係数
面1
K : -30.868200
A :0.147706E-04 B :-.260370E-07 C :0.377473E-10 D :-.300023E-13
E :0.107463E-16
面2
K : -1.240297
A :0.207897E-04 B :0.298769E-07 C :0.267684E-09 D :-.163367E-11
E :0.372598E-14
面5
K : 2.187192
A :0.313924E-04 B :-.202309E-06 C :0.158321E-08 D :-.733956E-11
E :0.139279E-13
面24
K : -0.780042
A :-.942956E-05 B :0.141825E-07 C :0.244817E-10 D :0.194500E-12
Aspheric coefficient surface 1
K: -30.868200
A: 0.147706E-04 B:-. 260370E-07 C: 0.377473E-10 D:-. 300023E-13
E: 0.107463E-16
Surface 2
K: -1.240297
A: 0.207897E-04 B: 0.298769E-07 C: 0.267684E-09 D:-. 163367E-11
E: 0.372598E-14
Surface 5
K: 2.187192
A: 0.313924E-04 B:-. 202309E-06 C: 0.158321E-08 D:-. 733956E-11
E: 0.139279E-13
Surface 24
K: -0.780042
A:-. 942956E-05 B: 0.141825E-07 C: 0.244817E-10 D: 0.194500E-12

第2実施形態の広角ズームレンズの各レンズの焦点距離は、以下のとおりである。
群の焦点距離
第1群: -15.085
第2群: 32.5574
第3群: -40.0929
第4群: 33.0051
Gr1a: -21.0097
Gr1b: -102.427
The focal length of each lens of the wide-angle zoom lens of the second embodiment is as follows.
Group focal length Group 1: -15.085
Second group: 32.5574
Group 3: -40.0929
Group 4: 33.0051
Gr1a: -21.0097
Gr1b: -102.427

広角端で
第2,3群合成焦点距離: 140.206
第2,3,4群合成焦点距離:31.626
第1,2,3群合成群焦点距離:-24.033
第1,2,3群合成群と4群の主点位置間間隔:86.032
レンズ全長:94.1
望遠端で
第2、3群の合成焦点距離:57.754
2nd and 3rd group focal length at wide angle end: 140.206
2nd, 3rd, 4th group composite focal length: 31.626
1st, 2nd, 3rd group composite focal length: -24.033
Interval between principal points of the 1st, 2nd, 3rd group and 4th group: 86.032
Total lens length: 94.1
Combined focal length of groups 2 and 3 at the telephoto end: 57.754

第2実施形態の広角ズームレンズの第11面の形状は、以下のとおりである。
有効径 法線角度

Figure 0005489323
The shape of the first surface of the wide-angle zoom lens of the second embodiment is as follows.
Effective diameter Normal angle
Figure 0005489323

第2実施形態の広角ズームレンズの条件式の値は、以下のとおりである。
条件式 D1Sw/OVLw=0.235
第2群の構成 (正負)(正負)
第4群の構成 正(負正負)負
The values of the conditional expressions of the wide angle zoom lens of the second embodiment are as follows.
Conditional expression D1Sw / OVLw = 0.235
Structure of the second group (positive / negative) (positive / negative)
Composition of the fourth group Positive (negative positive negative) negative

第2実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を図5を示す。第2実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を図6を示す。   FIG. 5 shows spherical aberration, astigmatism, distortion and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the second embodiment. FIG. 6 shows spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the second embodiment.

(第3実施形態)
第1実施形態にかかる広角ズームレンズは、図7に示す構成を有する。各レンズ面の曲率半径R(mm)、各レンズ中心厚及びレンズの空気間隔D(mm)、各レンズのd線における屈折率Nd及びアッベ数ABVの値は、以下のとおりである。
(Third embodiment)
The wide-angle zoom lens according to the first embodiment has the configuration shown in FIG. The values of the radius of curvature R (mm) of each lens surface, the center thickness of each lens and the air space D (mm) of each lens, the refractive index Nd of each lens d-line and the Abbe number ABV are as follows.

焦点距離:10.29〜15.60〜23.39
FNO:3.6〜4.15〜4.6
2ω:111.38〜85.4〜62.63
S R D Nd ABV
1 ASPH 91.2892 3.0000 1.74330 49.22
2 ASPH 13.3000 17.1746
3 -550.1946 1.1000 1.83481 42.72
4 26.8414 0.2500 1.51460 49.96
5 ASPH 31.7796 0.8380
6 19.6685 4.8948 1.69895 30.05
7 43.3886 D7
8 0.0000 1.6759
9 -70.7449 2.4534 1.68893 31.16
10 -14.1775 0.8000 1.88300 40.80
11 -37.9248 0.1500
12 33.1085 3.7574 1.58913 61.25
13 -14.2673 0.7937 1.80610 33.27
14 -28.7457 D14
15 -29.9856 0.8000 1.80420 46.50
16 23.8293 2.5887 1.92286 20.88
17 241.4124 D17
18 40.5319 4.7504 1.49700 81.61
19 -35.4136 0.1500
20 49.8255 0.9000 1.90366 31.31
21 17.3000 11.4746 1.49700 81.61
22 -14.5000 0.9000 1.90366 31.31
23 -20.5448 0.2000
24 ASPH -34.3632 0.2000 1.51460 49.96
25 -31.0708 1.3000 1.83400 37.34
26 -37.8865
Focal length: 10.29-15.60-23.39
FNO: 3.6-4.15-4.6
2ω: 111.38 ~ 85.4 ~ 62.63
SRD Nd ABV
1 ASPH 91.2892 3.0000 1.74330 49.22
2 ASPH 13.3000 17.1746
3 -550.1946 1.1000 1.83481 42.72
4 26.8414 0.2500 1.51460 49.96
5 ASPH 31.7796 0.8380
6 19.6685 4.8948 1.69895 30.05
7 43.3886 D7
8 0.0000 1.6759
9 -70.7449 2.4534 1.68893 31.16
10 -14.1775 0.8000 1.88300 40.80
11 -37.9248 0.1500
12 33.1085 3.7574 1.58913 61.25
13 -14.2673 0.7937 1.80610 33.27
14 -28.7457 D14
15 -29.9856 0.8000 1.80420 46.50
16 23.8293 2.5887 1.92286 20.88
17 241.4124 D17
18 40.5319 4.7504 1.49700 81.61
19 -35.4136 0.1500
20 49.8255 0.9000 1.90366 31.31
21 17.3000 11.4746 1.49700 81.61
22 -14.5000 0.9000 1.90366 31.31
23 -20.5448 0.2000
24 ASPH -34.3632 0.2000 1.51460 49.96
25 -31.0708 1.3000 1.83400 37.34
26 -37.8865

焦点距離:10.29 15.60 23.40
可変間隔
D7 22.252 11.5339 4.8871
D14 1.000 7.8478 14.5915
D17 10.6954 5.7013 0.800
Focal length: 10.29 15.60 23.40
Variable interval
D7 22.252 11.5339 4.8871
D14 1.000 7.8478 14.5915
D17 10.6954 5.7013 0.800

非球面係数
面1
K : -23.358778
A :0.138306E-04 B :-.284728E-07 C :0.473046E-10 D :-.418342E-13
E :0.157340E-16
面2
K : -0.865462
A :0.617175E-06 B :0.624054E-07 C :-.184300E-09 D :0.328276E-12
E :0.773908E-15
面5
K : 1.536049
A :0.293177E-04 B :-.126814E-06 C :0.844851E-09 D :-.324948E-11
E :0.634290E-14
面24
K : -0.133768 KC : 100
A :-.102523E-04 B :0.105589E-07 C :0.225709E-10 D :0.159981E-12
Aspheric coefficient surface 1
K: -23.358778
A: 0.138306E-04 B:-. 284728E-07 C: 0.473046E-10 D:-. 418342E-13
E: 0.157340E-16
Surface 2
K: -0.865462
A: 0.617175E-06 B: 0.624054E-07 C:-. 184300E-09 D: 0.328276E-12
E: 0.773908E-15
Surface 5
K: 1.536049
A: 0.293177E-04 B:-. 126814E-06 C: 0.844851E-09 D:-. 324948E-11
E: 0.634290E-14
Surface 24
K: -0.133768 KC: 100
A:-. 102523E-04 B: 0.105589E-07 C: 0.225709E-10 D: 0.159981E-12

第3実施形態の広角ズームレンズの各レンズの焦点距離は、以下のとおりである。
群の焦点距離
第1群: -15.297
第2群: 32.268
第3群: -38.818
第4群: 32.560
Gr1a: -21.294
Gr1b: -106.239
The focal length of each lens of the wide-angle zoom lens according to the third embodiment is as follows.
Group focal length Group 1: -15.297
Second group: 32.268
Group 3: -38.818
Group 4: 32.560
Gr1a: -21.294
Gr1b: -106.239

広角端で
第2,3群合成焦点距離: 148.971
第2,3,4群合成焦点距離:31.486
第1,2,3群合成群焦点距離:-23.429
第1,2,3群合成群と4群の主点位置間間隔:83.241
レンズ全長:94.0988
望遠端で
第2、3群の合成焦点距離:56.936
2nd and 3rd group focal length at wide angle end: 148.971
2nd, 3rd and 4th lens groups: 31.486
1st, 2nd, 3rd group composite focal length: -23.429
The distance between the principal points of the 1st, 2nd, 3rd group and 4th group: 83.241
Total lens length: 94.0988
Combined focal length of groups 2 and 3 at the telephoto end: 56.936

第3実施形態の広角ズームレンズの第11面の形状は、以下のとおりである。
有効径 法線角度

Figure 0005489323
The shape of the first surface of the wide-angle zoom lens of the third embodiment is as follows.
Effective diameter Normal angle
Figure 0005489323

第3実施形態の広角ズームレンズの条件式の値は、以下のとおりである。
条件式 D1Sw/OVLw=0.236
第2群の構成 (正負)(正負)
第4群の構成 正(負正負)負
The values of the conditional expressions of the wide angle zoom lens of the third embodiment are as follows.
Conditional expression D1Sw / OVLw = 0.236
Structure of the second group (positive / negative) (positive / negative)
Composition of the fourth group Positive (negative positive negative) negative

第3実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を図8を示す。第1実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を図9を示す。   FIG. 8 shows spherical aberration, astigmatism, distortion and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the third embodiment. FIG. 9 shows spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the first embodiment.

(第4実施形態)
第4実施形態にかかる広角ズームレンズは、図10に示す構成を有する。各レンズ面の曲率半径R(mm)、各レンズ中心厚及びレンズの空気間隔D(mm)、各レンズのd線における屈折率Nd及びアッベ数ABVの値は、以下のとおりである。
(Fourth embodiment)
The wide-angle zoom lens according to the fourth embodiment has the configuration shown in FIG. The values of the radius of curvature R (mm) of each lens surface, the center thickness of each lens and the air space D (mm) of each lens, the refractive index Nd of each lens d-line and the Abbe number ABV are as follows.

焦点距離:10.295〜15.598〜23.393
FNO:3.6〜4.15〜4.6
2ω:111.42〜85.5〜62.84

S R D Nd ABV
1 ASPH 72.8710 3.0000 1.74330 49.22
2 ASPH 12.9000 16.2015
3 770.1839 1.1000 1.88300 40.80
4 26.0522 0.3000 1.53610 41.21
5 ASPH 30.6791 1.1966
6 20.4544 4.7353 1.69895 30.05
7 43.9685 D7
8 0.0000 1.5074
9 -68.4574 2.5124 1.68893 31.16
10 -12.6110 1.7924 1.88300 40.80
11 -37.3079 0.1500
12 34.8661 3.7882 1.58913 61.25
13 -13.8945 0.8000 1.80610 33.27
14 -26.8129 D14
15 -30.4122 0.8000 1.77250 49.62
16 20.1071 2.8524 1.84666 23.78
17 292.4999 D17
18 45.2832 4.3580 1.49700 81.61
19 -36.2850 0.1500
20 48.9769 0.9000 1.90366 31.31
21 17.4000 12.2843 1.49700 81.61
22 -14.3000 1.1000 1.90366 31.31
23 -20.2760 0.2000
24 ASPH -37.3436 0.3500 1.51460 49.96
25 -32.4182 1.5000 1.58144 40.89
26 -44.7821
Focal length: 10.295-15.598-23.393
FNO: 3.6-4.15-4.6
2ω: 111.42〜85.5〜62.84

SRD Nd ABV
1 ASPH 72.8710 3.0000 1.74330 49.22
2 ASPH 12.9000 16.2015
3 770.1839 1.1000 1.88300 40.80
4 26.0522 0.3000 1.53610 41.21
5 ASPH 30.6791 1.1966
6 20.4544 4.7353 1.69895 30.05
7 43.9685 D7
8 0.0000 1.5074
9 -68.4574 2.5124 1.68893 31.16
10 -12.6110 1.7924 1.88300 40.80
11 -37.3079 0.1500
12 34.8661 3.7882 1.58913 61.25
13 -13.8945 0.8000 1.80610 33.27
14 -26.8129 D14
15 -30.4122 0.8000 1.77250 49.62
16 20.1071 2.8524 1.84666 23.78
17 292.4999 D17
18 45.2832 4.3580 1.49700 81.61
19 -36.2850 0.1500
20 48.9769 0.9000 1.90366 31.31
21 17.4000 12.2843 1.49700 81.61
22 -14.3000 1.1000 1.90366 31.31
23 -20.2760 0.2000
24 ASPH -37.3436 0.3500 1.51460 49.96
25 -32.4182 1.5000 1.58144 40.89
26 -44.7821

焦点距離:10.295 15.598 23.393
可変間隔
D7 21.1006 10.4692 3.7599
D14 0.8270 7.7520 14.2056
D17 11.0939 5.8381 0.800
Focal length: 10.295 15.598 23.393
Variable interval
D7 21.1006 10.4692 3.7599
D14 0.8270 7.7520 14.2056
D17 11.0939 5.8381 0.800

非球面係数
面1
K : -4.855874
A :0.147578E-04 B :-.354016E-07 C :0.454072E-10 D :-.116025E-13
E :0.227158E-16 F :-.308920E-19 G :-.677424E-22 H :-.335578E-25
J :0.137873E-27
面2
K : -1.110553
A :0.277891E-04 B :0.404370E-07 C :0.612679E-10 D :0.362235E-12
E :-.110342E-13 F :0.528104E-17 G :0.320816E-18 H :0.145731E-21
J :-.347259E-23
面5
K : 0.335030
A :0.226449E-04 B :-.966072E-07 C :0.176373E-09 D :0.114032E-12
E :0.138279E-14
面24
K : -0.608663
A :-.983362E-05 B :0.214587E-07 C :-.114789E-09 D :0.130510E-11
E :-.267583E-14
Aspheric coefficient surface 1
K: -4.855874
A: 0.147578E-04 B:-. 354016E-07 C: 0.454072E-10 D:-. 116025E-13
E: 0.227158E-16 F:-. 308920E-19 G:-. 677424E-22 H:-. 335578E-25
J: 0.137873E-27
Surface 2
K: -1.110553
A: 0.277891E-04 B: 0.404370E-07 C: 0.612679E-10 D: 0.362235E-12
E:-. 110342E-13 F: 0.528104E-17 G: 0.320816E-18 H: 0.145731E-21
J:-. 347259E-23
Surface 5
K: 0.335030
A: 0.226449E-04 B:-. 966072E-07 C: 0.176373E-09 D: 0.114032E-12
E: 0.138279E-14
Surface 24
K: -0.608663
A:-. 983362E-05 B: 0.214587E-07 C:-. 114789E-09 D: 0.130510E-11
E:-. 267583E-14

第4実施形態の広角ズームレンズの各レンズの焦点距離は、以下のとおりである。
群の焦点距離
第1群: -15.199
第2群: 32.3369
第3群: -40.4942
第4群: 33.2409
Gr1a: -21.5478
Gr1b: -95.6574
The focal length of each lens of the wide-angle zoom lens of the fourth embodiment is as follows.
Group focal length Group 1: -15.199
Second group: 32.3369
Group 3: -40.4942
Group 4: 33.2409
Gr1a: -21.5478
Gr1b: -95.6574

広角端で
第2,3群合成焦点距離: 143.052
第2,3,4群合成焦点距離:31.312
第1,2,3群合成群焦点距離:-24.561
第1,2,3群合成群と4群の主点位置間間隔:87.987
レンズ全長:94.6
望遠端で
第2、3群の合成焦点距離:58.115
At the wide-angle end, 2nd and 3rd group combined focal length: 143.052
2nd, 3rd and 4th lens groups: 31.312
1st, 2nd, 3rd group composite focal length: -24.561
The distance between the principal points of the 1st, 2nd, 3rd group and 4th group: 87.987
Total lens length: 94.6
Combined focal length of groups 2 and 3 at telephoto end: 58.115

第4実施形態の広角ズームレンズの第11面の形状は、以下のとおりである。
有効径 法線角度

Figure 0005489323
The shape of the first surface of the wide-angle zoom lens of the fourth embodiment is as follows.
Effective diameter Normal angle
Figure 0005489323

第4実施形態の広角ズームレンズの条件式の値は、以下のとおりである。
条件式 D1Sw/OVLw=0.223
第2群の構成 (正負)(正負)
第4群の構成 正(負正負)負
The values of the conditional expressions of the wide-angle zoom lens of the fourth embodiment are as follows.
Conditional expression D1Sw / OVLw = 0.223
Structure of the second group (positive / negative) (positive / negative)
Composition of the fourth group Positive (negative positive negative) negative

第4実施形態の広角ズームレンズの広角端の球面収差、非点収差、歪曲収差及び倍率色収差を図11を示す。第1実施形態の広角ズームレンズの望遠端の球面収差、非点収差、歪曲収差及び倍率色収差を図12を示す。   FIG. 11 shows spherical aberration, astigmatism, distortion and lateral chromatic aberration at the wide angle end of the wide angle zoom lens according to the fourth embodiment. FIG. 12 shows spherical aberration, astigmatism, distortion, and lateral chromatic aberration at the telephoto end of the wide-angle zoom lens according to the first embodiment.

特許文献1の第1実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.409
第2群の構成 (負正)正
第4群の構成 正(負正)
The values of the conditional expressions in the first embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.409
Group 2 configuration (negative positive) Positive Group 4 configuration positive (negative positive)

特許文献1の第2実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.366
第2群の構成 (負正)正
第4群の構成 正(負正)
The values of the conditional expressions in the second embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.366
Group 2 configuration (negative positive) Positive Group 4 configuration positive (negative positive)

特許文献1の第3実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.348
第2群の構成 (負正)正
第4群の構成 正(負正)
The values of the conditional expressions in the third embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.348
Group 2 configuration (negative positive) Positive Group 4 configuration positive (negative positive)

特許文献1の第4実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.371
第2群の構成 (負正)正
第4群の構成 正(負正)
The values of the conditional expressions in the fourth embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.371
Group 2 configuration (negative positive) Positive Group 4 configuration positive (negative positive)

特許文献1の第5実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.325
第2群の構成 (負正)正
第4群の構成 (正負正)負正
The values of the conditional expressions in the fifth embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.325
Second group configuration (negative positive) Positive Fourth group configuration (positive negative) Negative positive

特許文献1の第6実施形態の条件式の値は以下のとおりである。
条件式 D1Sw/OVLw=0.325
第2群の構成 (負正)正
第4群の構成 正(負正)
The values of the conditional expressions in the sixth embodiment of Patent Document 1 are as follows.
Conditional expression D1Sw / OVLw = 0.325
Group 2 configuration (negative positive) Positive Group 4 configuration positive (negative positive)

Gr1A 第1レンズ群の前群
Gr1B 第1レンズ群の後群
Gr1A Front group of the first lens group Gr1B Rear group of the first lens group

Claims (1)

物体から順に、負の屈折力の第1レンズ群、正の屈折力の第2レンズ群、負の屈折力の第3レンズ群、正の屈折力の第4レンズ群からなり、各レンズ群を移動させて変倍を行い、
前記第1レンズ群は、負の屈折力の第1レンズ群の前群レンズ群及び負の屈折力の第1レンズ群の後群レンズ群によって構成し、無限遠物体から近距離へのフォーカシングを第1レンズ群の後群レンズ群を物体側へ移動させて行い、第2レンズ群は最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズの複数レンズで構成し、第4レンズ群は最も物体側が正の屈折力を持つレンズと最も像側が負の屈折力を持つレンズで複数レンズ構成し、第4レンズ群内に少なくとも一面に非球面を有し、以下の条件式を満たすことを特徴とする広角ズームレンズ。
条件式 0.15 ≦ D1Sw/OVLw ≦ 0.3
但し、
D1Sw:被写体距離無限遠における広角端での第1レンズ群の最も像面側の面から
絞りまでの距離
OVLw:広角端でレンズ系の全長(最も物体側の面から最も像面側の面までの長さ)
In order from an object, a first lens unit having a negative refractive power, a second lens unit having positive refractive power, a third lens unit having a negative refractive power, and a fourth lens unit having positive refractive power, the lens groups Move it to scale,
The first lens group includes a front lens group of the first lens group having a negative refractive power and a rear lens group of the first lens group having a negative refractive power, and performs focusing from an object at infinity to a short distance. The rear lens group of the first lens group is moved to the object side, and the second lens group is composed of a plurality of lenses, the lens having the most positive refractive power on the object side and the lens having the negative refractive power on the most image side. The fourth lens group includes a lens having a positive refractive power closest to the object side and a lens having a negative refractive power closest to the image side. The fourth lens group has at least one aspheric surface in the fourth lens group. A wide-angle zoom lens characterized by satisfying a conditional expression.
Conditional expression 0.15 ≤ D1Sw / OVLw ≤ 0.3
However,
D1Sw: From the surface closest to the image plane of the first lens unit at the wide-angle end at an infinite subject distance
Distance to aperture
OVLw: Full length of the lens system at the wide-angle end (length from the most object-side surface to the most image-side surface)
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