JPH08234107A - Zoom lens having long back focus - Google Patents

Abstract

PURPOSE: To provide a small-sized zoom lens which is a lens system to be used for electronic cameras formed by using image pickup tubes, solid-state image pickup elements, etc., has high optical performance and has a back focus large enough to allow the insertion of optical elements, such as filters, between the lens system and the image pickup element. CONSTITUTION: This zoom lens consists, successively from an object side, a first lens group G1 which is held stationary at the time of zooming and is positive, a second lens group G2 which moves monotonously along the optical axis at the time of zooming and is negative, a third lens group G3 which moves forward and backward along the optical axis at the time of zooming and is positive or negative and a fourth lens group G4 which moves forward and backward along the optical axis at the time of zooming and is positive. The third lens group G3 is the lens system of the long back focus consisting of, successively from the object side, a positive first lens component and a second lens component of a combined lens of a biconcave lens and a biconvex or negative meniscus lens which is convex on the object side.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is most suitable for an electronic camera using an image pickup tube, a solid-state image pickup device, etc. The present invention relates to a zoom lens having high optical performance and a long back focus.

[0002]

2. Description of the Related Art Generally, an electronic camera uses an image pickup tube having a small image pickup area or a solid-state image pickup device to convert an optical image into an electronic signal, and therefore, a bright lens system is required as an image pickup lens used for this. Also, between the lens system and the image sensor,
Like optical members such as low-pass filters and infrared cut filters, and so-called multi-panel electronic cameras that receive images of each of the three primary colors of RGB with their respective image sensors.
It is necessary to dispose an optical element such as a so-called color separation prism that guides a light beam to each image pickup element, and a large back focus is required as compared with the focal length.

Further, in these cameras, there are many applications for photographing moving images, and it is general to use a zoom lens having a high zoom ratio as a photographing lens.

In particular, with the recent development of manufacturing technology, a solid-state image pickup device having a large number of pixels compared to the size of the image pickup range has been developed, and it becomes possible to obtain a high-definition image such as a high-definition image. became. Therefore, as for the image pickup lens, a zoom lens having an extremely high optical performance that can sufficiently bring out the performance of the image pickup element has been required. Further, as the solid-state image pickup device becomes smaller, for example, as the size of each pixel of the solid-state image pickup device becomes smaller, higher resolution is required, and the demand for optical performance of the image pickup lens system is becoming higher and higher.

As a zoom lens satisfying such requirements, Japanese Patent Laid-Open Nos. 62-153913 and 1-126 are known.
Conventional examples described in Japanese Patent Laid-Open No. 614 and JP-A-6-56453 are known.

On the other hand, as a zoom lens mainly for miniaturization, such as for a camcorder, the zoom lens is arranged in order from the object side.
A first lens group having a positive refractive power, a second lens group having a negative refractive power, a third lens group having a negative refractive power, and a fourth lens group having a positive refractive power. A group zoom lens, a first lens group having a positive refractive power, a second lens group having a negative refractive power, a third lens group having a positive refractive power, and a positive refractive power in order from the object side. There is known a four-group zoom lens including a fourth lens group having These types of 4-group zoom lenses have a simple group configuration and are suitable for downsizing, but it is difficult to obtain a lens system with high optical performance, and a high-definition image such as a high-definition image can be obtained. It is unsuitable as a zoom lens for the purpose. As a conventional example of a zoom lens for obtaining such a high-definition image, there is Japanese Patent Laid-Open No. 6-175022.
No. etc. are only known.

[0007]

Generally, in order to obtain high optical performance, a light ray is refracted as little as possible as many times as possible to form an image, so that the amount of aberration generated on each refracting surface is reduced. However, in this case, a large number of lenses are inevitably required, and as a result, the lens system becomes large.

Further, in the case of a zoom lens, since there are many moving groups, aberration variation occurs due to zooming. for that reason,
Ideally, in each lens group, if aberrations are corrected well, aberration fluctuations will not occur during zooming,
From the wide-angle end to the telephoto end, the path of the light rays in the lens system is not always constant, so some aberration remains. When it is attempted to achieve high optical performance in a zoom lens, the aberration fluctuation due to this residual aberration cannot be ignored. Therefore, in the zoom lens, the number of lenses to be configured is increased, the lens group is complicatedly moved from the wide-angle end to the telephoto end, and the aberration variation is corrected, so that the lens system becomes large.

On the other hand, in recent years, cameras for capturing high-definition images such as high-definition have become common, and have come to be used in many fields, and it is necessary to use them under various conditions, so that the photographing camera and lens system are downsized. The demand is growing.

Among the conventional zoom lenses described above, the zoom lenses described in JP-B-62-153913, JP-A-1-126614, JP-A-6-56453 and the like capture high-definition images. Therefore, the lens system achieves high optical performance. However, for example, JP-A 1-1
The zoom lens disclosed in Japanese Patent No. 26614 is a zoom lens including two compensators and composed of five lens groups, and has a complicated group configuration. The zoom lens disclosed in Japanese Patent Laid-Open No. 6-175022 is a 4-group zoom lens, which is a lens system having high optical performance with a small group configuration. It cannot be said that the back focus is secured long enough, and is insufficient as an imaging lens that can be used in many types of cameras.

The present invention has a relatively simple structure, and an electronic camera using an image pickup tube, a solid-state image pickup device, etc. It is intended to provide a compact zoom lens having a high optical performance most suitable for a camera and having a back focus sufficient for inserting an optical element such as various filters between a lens system and an image pickup element.

[0012]

A zoom lens according to the present invention comprises, in order from the object side, a first lens group having a positive refracting power and fixed during zooming, and a negative lens having a negative refracting power on the optical axis during zooming. A second lens group that moves monotonically along
A third lens group having positive or negative refracting power and moving back and forth along the optical axis during zooming, and a fourth lens group having positive refracting power and moving back and forth along the optical axis during zooming, The third lens group has, in order from the object side, a first lens component having a positive refractive power, a biconcave negative lens, and a biconvex or meniscus-shaped positive lens having a convex surface facing the object side, which are cemented in order as a whole. And a second lens component having a refracting power of.

As described above, as a zoom lens for electronic imaging having a relatively simple structure, as described above, in order from the object side, a positive first lens group that is fixed during zooming, a second lens group that is a negative variator, and a negative lens group are used. The fourth lens group of the compensator of the third lens group and the fourth lens group of the positive relay group fixed at the time of zooming, or in order from the object side, the positive first lens group fixed at the time of zooming, There is known a four-group zoom lens including a second lens group of a negative variator, a positive third lens group fixed during zooming, and a positive fourth lens group having a role of a compensator.

On the other hand, in order to increase the back focus, it is desirable to use a so-called retrofocus type of negative and positive in order from the object side, and it is preferable to increase the power of both negative and positive.

Of the two types of four-group zoom lenses described above, the former type is preferable in order to increase the back focus. That is, in the latter type of zoom lens, the back focus cannot be increased except for increasing the power of the negative second lens group, and the aberration is deteriorated. On the other hand, in the former type of 4-group zoom lens, since the third lens group of the compensator has a negative refractive power in addition to the second lens group, the negative power can be dispersed to these two lens groups, so that the aberration is deteriorated. This is advantageous because the back focus can be secured without doing so. But the former type 4
Since the group zoom lens has a fixed relay group, in order to sufficiently correct aberration fluctuations that occur in the relay group, it is necessary to eliminate changes in the light flux that passes through the relay group from the wide-angle end to the telephoto end. However, for that purpose, the load on the first lens group to the third lens group becomes large, or extremely advanced aberration correction in the relay group by increasing the number of lenses forming the relay group becomes necessary. Also in this case, the lens system becomes large, which is not preferable.

As described above, according to the present invention, in order from the object side, the positive first lens group, the negative second lens group, the positive or negative third lens group, and the positive third lens group which are fixed during zooming are arranged in order. The second lens group and the fourth lens group mainly have a variable power function, and the third lens group has a compensator function.
The lens group and the fourth lens group are shared. Here, a method of moving each lens group in the zoom lens of the present invention will be described in detail. The first lens group is fixed during zooming. The second lens group moves monotonically from the object side to the image side during zooming from the wide-angle end to the telephoto end. Furthermore, both the third lens group and the fourth lens group move from the image side to the object side during zooming from the wide-angle end to the telephoto end, and then move from the object side to the image side. By doing so, it is possible to secure a large zoom ratio and a large back focus while suppressing the occurrence of aberration by making the second lens group have a relatively small negative power.

Further, when the lens aperture of the first lens group becomes large, the center of gravity of the lens system is biased forward, which is not preferable in terms of holding the camera at the time of photographing. In order to avoid this, it is desirable to move the entrance pupil position as close to the object side as possible. Further, it is desirable that the light rays enter the electronic image pickup device as vertically as possible. Therefore, it is desirable that the exit pupil position be located as far as possible. Therefore, in the zoom lens of the present invention, it is desirable to position the diaphragm between the second lens group and the third lens group or between the third lens group and the fourth lens group.

When an optical element such as a color separation prism is arranged between the lens system and the image pickup element, the light beam emitted from the on-axis object point enters this optical element as a convergent light beam. Therefore, positive axial chromatic aberration occurs in the optical element. This chromatic aberration increases as the F-number of the lens system decreases and the thickness of the optical element increases. In particular, this chromatic aberration becomes so large that it cannot be ignored in the case of a taking lens for the purpose of capturing a high-definition image such as high-definition.

On the other hand, when an image pickup element is used, the exit pupil must be located as far as possible, and the chromatic aberration of magnification generated by the above optical element is sufficiently small.

For the above reasons, in order to satisfactorily correct the entire chromatic aberration of the zoom lens and the optical element, the negative axial chromatic aberration for canceling the positive axial chromatic aberration generated in the optical element is used in the lens. It is necessary to sufficiently correct the chromatic aberration of the magnification of the lens system while causing it in the system.

In the zoom lens of the present invention, since the second lens group mainly has a variable power and has a relatively strong negative power, normally positive axial chromatic aberration and negative chromatic aberration occur. Therefore, in order to generate the negative axial chromatic aberration in this second lens group, this lens group must have an extremely complicated structure, which is not preferable. Further, in the first lens group, the fluctuation of the ray height from the wide angle end to the telephoto end is the largest, and if the residual aberration in the first lens group is large, it becomes impossible to correct the aberration fluctuation during zooming. Therefore, the first lens group must be sufficiently corrected for various aberrations, and it is not preferable to generate negative axial chromatic aberration sufficient to cancel the positive axial chromatic aberration generated in the optical element. . When the diaphragm is arranged between the second lens group and the third lens group or between the third lens group and the fourth lens group as described above, negative axial chromatic aberration is generated in the fourth lens group and at the same time. Chromatic aberration of negative magnification occurs. In this case, especially at the wide-angle end, chromatic aberration of negative magnification that occurs in the second lens group and the fourth lens group becomes large. In order to correct this, chromatic aberration of positive magnification must be generated in the third lens group, but since the third lens group has a low off-axis chief ray height, chromatic aberration of negative magnification described above is generated. It is difficult to generate chromatic aberration with a positive magnification that only erases it.

Further, in the third lens group, the off-axis chief ray height is low as described above, and even if axial chromatic aberration occurs, the occurrence of lateral chromatic aberration can be suppressed to a relatively small level.
It is possible to correct with other lens groups. Therefore, in the third lens group, it is possible to generate negative axial chromatic aberration sufficient to cancel the positive axial chromatic aberration generated in the optical element arranged between the lens system and the image pickup element.

As described above, in order to correct the positive axial chromatic aberration generated in the optical element, it is preferable to generate the negative axial chromatic aberration in the third lens group in the zoom lens.

In order to generate a negative axial chromatic aberration in this third lens group, the third lens group should have a positive power. However, if the third lens group has a large positive power, it becomes difficult to secure the back focus of the lens system. Therefore, it is necessary to make the third lens group have a negative power or a weak positive power as a whole, and to generate a negative axial chromatic aberration.

Therefore, in the present invention, in consideration of correction of various aberrations such as spherical aberration, as described above, the third lens group is arranged in order from the object side, that is, the first lens component of the positive lens component and the negative lens component. The second lens component is composed of a cemented lens of a biconcave lens and a positive lens having a convex surface facing the object side. By this, the third
The lens groups are configured to generate negative axial chromatic aberration while weakening the powers of the first lens component and the second lens component.

If the third lens unit is arranged in this order from the object side in the order of the negative lens component and the positive lens component, the axial ray height in the positive lens component will be high and spherical aberration will be large, which is preferable. Absent. Therefore, in the zoom lens of the present invention, the third lens unit is composed of, in order from the object side, the positive first lens component and the negative second lens component. Further, if both lens components are composed of a single lens, the positive power becomes strong in order to generate the negative axial chromatic aberration in the entire third lens group, which is not preferable. If the negative second lens component is cemented in order from the object side to the positive lens and the negative lens, various aberrations generated on each refracting surface when an appropriate negative axial chromatic aberration is generated become large, Aberration occurs, which is not preferable.

In order to effectively generate the above-mentioned negative axial chromatic aberration, the cemented surface of the second lens component of the third lens unit is made to have a positive power, and the negative axial chromatic aberration is generated at this cemented surface. It is preferable to do so. For that purpose, the negative lens of the second lens component may have a low refractive index and low dispersion, and the positive lens may have a high refractive index and high dispersion. That is, the following condition (1),
It suffices to satisfy (2).

(1) n _32n <n _32p (2) ν _32p <ν _32n where n _32n and n _32p are the refractive indices of the negative lens and the positive lens of the second lens component of the third lens group, ν _32n and ν, respectively.
_32p is the Abbe number of the negative lens and the positive lens of the second lens component of the third lens group, respectively.

If either the condition (1) or the condition (2) is not satisfied, the positive axial chromatic aberration of the lens system cannot be sufficiently corrected, which is not preferable.

As described above, the third aspect of the zoom lens of the present invention.
The lens group has a negative power or a weak positive power to ensure the back focus of the lens system. It is more preferable that the power of the third lens group be within the range of the following condition (3).

[0031] _{(3) -0.30 <f w /} f 3 <0.10 However, f _w is a focal length of the entire system at the wide angle end, f ₃ is the focal length of the third lens group.

When the upper limit of 0.10 to condition (3) is exceeded,
The positive power of the third lens group becomes too strong, and it becomes difficult to secure the back focus. The lower limit of −
If it exceeds 0.30, the negative power of the third lens group becomes too strong, and the negative power of the second lens group becomes too small due to the distribution of the negative power with the second lens group, and the total lens length becomes large. Become.

In the zoom lens of the present invention, in order to realize a higher degree of aberration correction, the fourth lens group is arranged in order from the object side, the 41st lens group having a positive refracting power as a whole, and a positive lens group as a whole. A positive meniscus lens having a concave surface facing the object side and at least a negative meniscus lens having a concave surface facing the object side; or A biconcave lens having a surface having a strong negative refractive power facing the object side, and the 42nd lens group includes at least one positive lens and at least one negative lens, and the following condition (4):
It is desirable to satisfy (5).

(4) 0 <f ₄₂ / f ₄₁ <0.90 (5) 0.10 < _fw / f ₄₂ <0.50 where f ₄₁ and f ₄₂ are the 41st lens of the 4th lens group, respectively. It is a focal length of the lens unit and the 42nd lens unit.

In the zoom lens of the present invention, when a diaphragm is arranged between the third lens group and the fourth lens group, if negative axial chromatic aberration is generated in the third lens group, chromatic aberration of positive magnification will occur. The action of correcting the chromatic aberration of negative magnification that is generated and is generated in the second lens group occurs. However, in this case, if an attempt is made to correct the positive axial chromatic aberration generated by an optical element such as a prism arranged between the lens system and the image pickup element by the third lens group, the chromatic aberration of positive magnification becomes too large. Will be overcorrected. Therefore, a relatively small negative axial chromatic aberration and negative chromatic aberration of negative magnification are generated in the fourth lens group, and
It is preferable that both the lens group and the fourth lens group correct the positive axial chromatic aberration generated in the optical element. For that purpose, it is necessary for the fourth lens group to generate negative axial chromatic aberration and negative chromatic aberration of negative magnification, which are smaller than the power of the positive lens group.

In the zoom lens of the present invention, when the diaphragm is arranged between the second lens group and the third lens group,
In the third lens group, negative axial chromatic aberration and negative lateral chromatic aberration occur. It is possible to control the magnitude of chromatic aberration by the power arrangement of each lens constituting the third lens group. However, when the chromatic aberration of magnification generated in this third lens group becomes relatively large, the fourth lens group Therefore, it becomes necessary to generate chromatic aberration of positive magnification. If the chromatic aberration of magnification that occurs in the third lens group can be corrected to be sufficiently small,
Also in the fourth lens group, the chromatic aberration of magnification must be corrected to be sufficiently small. Therefore, positive axial chromatic aberration and chromatic aberration of positive magnification are generated in the fourth lens group, or negative axial chromatic aberration and negative chromatic aberration of small magnification are generated in comparison with the power of the positive lens group. Will be required.

Therefore, a negative lens is arranged in the fourth lens group to generate positive axial chromatic aberration and positive chromatic aberration, and
It is necessary to correct or excessively correct the chromatic aberration generated by the positive lens, but in the image side region of the fourth lens group, the ray height of the off-axis chief ray is high, so that the chromatic aberration of magnification is extremely large. Therefore, it is not preferable to place strong negative power. However, it is difficult to sufficiently correct lateral chromatic aberration in the object-side region of the fourth lens group because the off-axis ray height is low. Therefore, the fourth lens group is configured by the positive 41st lens group and the positive 42nd lens group in order from the object side, and the negative power is arranged by being distributed to the 41st lens group and the 42nd lens group. Is good. In this case, since a divergent light beam is incident on the 41st lens group, in order to prevent deterioration of various aberrations, a positive meniscus lens having a concave surface facing the object side and a negative meniscus lens having a concave surface facing the object side are provided. Alternatively, it is desirable to include a biconcave lens with the surface having a strong negative refractive power facing the object side.

Conditions (4) and (5) define the power distribution when the fourth lens group is divided into two positive powers.

When the value goes below the lower limit of the condition (4), the power of the 41st lens group of the 4th lens group becomes small, and the power of the 42nd lens group of the 4th lens group becomes large. Therefore, in order to secure the back focus. Is preferable, but the Petzval sum is deteriorated because the positive power is excessively collected in the 42nd lens group of the 4th lens group, the meridional image surface is largely fluctuated particularly at the wide-angle end, and particularly the g-line spherical aberration is corrected. It will be difficult. If the upper limit is exceeded, the 41st lens unit of the 4th lens unit
Since the power of the lens group is large and the power of the 42nd lens group of the 4th lens group is small, it is difficult to secure the back focus. In addition, the 41st lens of the 4th lens group
When the power of the lens group becomes large, the power of the negative lens constituting this 41st lens group becomes small, and the negative axial chromatic aberration and the chromatic aberration of magnification that occur in the 4th lens group become large, which makes correction difficult. . In the condition (5), when f _w / f ₄₂ becomes smaller than the lower limit of 0.10, the power of the 42nd lens group of the 4th lens group becomes small, so that the positive power required for image formation is reduced. It must be ensured by the 41st lens group of the 4th lens group, various aberrations, especially Petzval sum, deteriorate, and the negative power in the 42nd lens group of the 4th lens group must be reduced. As the system becomes larger, it becomes difficult to correct distortion. When f _w / f ₄₂ exceeds the upper limit of 0.50 of condition (5) and becomes a large value,
The power of the 42nd lens group of the 4th lens group becomes large, and the 41st lens group of the 4th lens group has a weak positive power or negative power. In this case, it is advantageous to secure the back focus, but the positive power is excessively collected in the 42nd lens group, the Petzval sum is deteriorated, and the fluctuation of the meridional image surface becomes large especially at the wide-angle end, and ,
In particular, the spherical aberration of the g-line becomes large, which makes correction difficult.

Furthermore, it is desirable that the following conditions be satisfied regarding the distribution of the positive power and the negative power of the 41st lens unit of the 4th lens unit.

[0041] (6) -0.40 <Σ (f w / f 41n) <- 0.03 , however, f _41n is the focal length of the negative lens in the first lens subunit of the fourth lens group.

This condition (6) applies to the 41st lens of the 4th lens group.
It defines the total sum of the negative powers of the lens groups. When the lower limit of -0.40 is exceeded, the positive power of the 41st lens group of the 4th lens group becomes small, and it is necessary to secure it by the 3rd lens group. There is. As a result, the balance of spherical aberrations other than the reference wavelength is lost, and positive spherical aberration becomes large in the long wavelength region and negative spherical aberration becomes large in the short wavelength region. The upper limit is 0.0
When it exceeds 3, the negative power in the fourth lens group becomes small, so that it becomes difficult to secure the back focus.
Since the axial chromatic aberration and the chromatic aberration of magnification that occur in the lens unit move in the negative direction, it is difficult to correct the chromatic aberration of negative magnification that occurs in the second lens unit especially at the wide-angle end.

Further, in the 41st lens group of the 4th lens group, in order to effectively generate positive axial chromatic aberration without deteriorating various aberrations, the 41st lens group of the 4th lens group is
It is desirable to have positive and negative configurations in order from the object side. Specifically, the 41st lens group of the 4th lens group includes, in order from the object side, a positive meniscus lens having a concave surface facing the object side, a first lens component including at least one positive lens, and an object It may be configured with the second lens component of the negative meniscus lens with the concave surface facing the side.

However, if the negative axial chromatic aberration produced by the third lens group is relatively large, then the fourth lens group must produce large positive axial chromatic aberration and chromatic aberration of magnification. In the case of such a configuration, a negative lens having a strong power is required for the second lens component of the 41st lens group,
It causes deterioration of other aberrations. Therefore, the 41st lens group of the 4th lens group is arranged in order from the object side to have a negative positive negative polarity,
Dispersing the negative power is advantageous for ensuring the back focus, and it is possible to generate positive axial chromatic aberration and lateral chromatic aberration without deteriorating various aberrations.

Specifically, the forty-first lens group of the fourth lens group has, in order from the object side, a first lens component consisting of at least one negative lens having a concave surface facing the object side and a convex surface facing the image side. At least one positive meniscus lens facing the lens or a biconvex positive lens with a surface having a strong positive refractive power facing the image side.
It is preferable that the second lens component is composed of a positive lens including a single lens and the third lens component is composed of a negative meniscus lens having a concave surface facing the object side.

In the zoom lens of the present invention, the following conditions (7),
It is desirable to satisfy (8).

[0047] _{(7) 0.05 <f w /} f 1 <0.15 (8) -0.70 <f w / f 2 <-0.30 However f _1, f ₂ are respectively the first lens group, It is the focal length of the second lens group.

F _w / f ₁ is 0.0, which is the lower limit of the condition (7).
If it becomes smaller than 5, the first lens group cannot sufficiently convert the light flux into a focused light flux. Therefore, unless the power of the second lens group is weakened, the amount of aberration generated in the third lens group and thereafter becomes large. Not preferable. If the power of the second lens group is weakened to avoid this, the amount of movement of the second lens group becomes large and the lens system becomes large in order to make the lens system have a large zoom ratio. In order to avoid this, if the power of the fourth lens group is increased to secure a large zoom ratio,
It becomes difficult to correct the chromatic aberration generated in the fourth lens group. Further, f _w / f ₁ is 0.1, which is the upper limit of the condition (7).
When the value exceeds 5 and becomes large, the power of the first lens group becomes too strong, and the back focus cannot be secured unless the power of the second lens group is made strong. Second like this
When the power of the lens group is increased, the Petzval sum is overcorrected, and the chromatic aberration of magnification becomes large especially at the wide-angle end,
Greater fluctuation during zooming.

F _w / f ₂ is the lower limit of the condition (8) −0.
When it becomes smaller than 70, the negative power of the second lens group becomes too large and the Petzval sum is overcorrected,
In addition, the chromatic aberration of magnification becomes large especially at the wide-angle end, and the fluctuation during zooming becomes large. Also, f _w / f ₂ is the condition (8)
When the value exceeds the upper limit value of −0.30, the power of the second lens group becomes too small and the lens system becomes large in size in order to obtain a lens system having a large zoom ratio, or the fourth lens group. If the power of is increased to increase the variable power ratio of the lens system, the chromatic aberration generated in the fourth lens group becomes large and correction cannot be performed.

In the zoom lens of the present invention, in order to improve the correction balance of various aberrations and achieve a higher performance optical system, any one of the following conditions may be used alone or in any combination. It is desirable to be satisfied.

[0051] _{(1 ') n 32p -n 32n} > 0.05 (2') ν 32n -ν 32p> 20 (3 ') -0.25 <f w / f 3 <0.07 (4') 0 _{<f 42 / f 41 <0.80} (5 ') 0.15 <f w / f 42 <0.40 (6') -0.35 <Σf w / f 41n <-0.03 (7 ') _{0.07 <f w / f 1 <} 0.13 (8 ') -0.65 <f w / f 2 <-0.40 further, the above condition (3'), (4 ') and (5 By setting each of () independently or as an arbitrary combination within the following limited range, the aberration correction balance particularly in the 41st lens group and the 42nd lens group of the third lens group and the fourth lens group Can be improved.

[0052] _{(3 ") -0.15 <f w} / f 3 <0.07 (4") 0 <f 42 / f 41 <0.60 (5 ") -0.35 <Σ (f w / f _41n ) <− 0.
10

Example 1 f = 9.003 to 25.461 to 71.999, F number = 2.0 2ω = 50.081 ° to 18.243 ° to 6.437 ° r ₁ = 145.8232 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 90.5174 d ₂ ＝ 4.8326 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -61802.0252 d ₃ ＝ 0.1000 r ₄ ＝ 68.5326 d ₄ ＝ 4.9088 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 289.2693 d ₅ ＝ 0.1000 r ₆ ＝ 45.2183 d ₆ 4.7684 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 110.2733 d ₇ ＝ D ₁ (variable) r ₈ ＝ 130.0005 d ₈ = 1.5000 n ₅ ＝ 1.69401 ν ₅ ＝ 54.84 r ₉ ＝ 17.9333 d ₉ ＝ 5.7785 r ₁₀ ＝ -77.2818 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 26.0959 d ₁₁ ＝ 3.3382 n ₇ ＝ 1.85504 ν ₇ ＝ 23.78 r ₁₂ ＝ 87.2042 d ₁₂ ＝ 2.0422 r ₁₃ ＝ -57.7479 d ₁₃ = 1.2000 n ₈ ＝ 1.65376 ν ₈ = 56.15 r ₁₄ = 137.8726 d ₁₄ = D ₂ (variable) r ₁₅ = ∞ (aperture) d ₁₅ = D ₃ (variable) r ₁₆ = 53.5876 d ₁₆ = 2.8000 n ₉ = 1.57098 ν ₉ = 71.3 0 r ₁₇ = -74.0937 d ₁₇ = 3.2700 r ₁₈ = -26.1734 d ₁₈ = 1.5740 n ₁₀ = 1.65425 ν ₁₀ = 58.52 r ₁₉ = 32.1163 d ₁₉ = 4.2818 n ₁₁ = 1.80680 ν ₁₁ = 22.60 r ₂₀ = 1464.1882 d ₂₀ = D _{4 (variable) r 21 = -35.5567 d 21 =} 1.2000 n 12 = 1.85649 ν 12 = 32.28 r 22 = -1525.8582 d 22 = 0.4033 r 23 = -131.9150 d 23 = 3.0000 n 13 = 1.58566 ν 13 = 46.33 r 24 _{= -25.8275 d 24 = 0.1000 r 25} = 178.4315 d 25 = 3.0000 n 14 = 1.57098 ν 14 = 71.30 r 26 = -70.7083 d 26 = 2.0231 r 27 = -68.2584 d 27 = 3.9158 n 15 = 1.57098 ν 15 = 71.30 r ₂₈ = -66.9715 d ₂₈ = 0.1000 r ₂₉ = -1182.0414 d ₂₉ = 3.8514 n ₁₆ = 1.57098 ν ₁₆ = 71.30 r ₃₀ = -108.3802 d ₃₀ = 0.1000 r ₃₁ = 48.3274 d ₃₁ = 3.4092 n ₁₇ = 1.57098 ν ₁₇ = 71.30 r ₃₂ = -514.8558 d ₃₂ = 0.1000 r ₃₃ = 36.7340 d ₃₃ = 1.5000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ ＝ 20.1027 d ₃₄ = 6.6448 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r _{35 = -310.0257 d 35 = D 5} ( _{variable) r 36 = ∞ d 36 =} 33.0000 n 20 = 1.61170 ν 20 = 46.44 r 37 = ∞ d 37 = 13.2000 n 21 = 1.51825 ν 21 = 64.15 r 38 = ∞ f 9.0029 _{25.4610 71.9991 D 1 1.4000 25.9019 42.3117 D} 2 42.1651 17.6633 1.2534 D 3 4.6101 2.3406 5.2577 D 4 9.8059 6.8659 1.5098 D 5 2.0000 7.2103 9.6484 n 32p -n 32n = 0.15255, ν 32n -ν 32p = 35.92, f w / f 1 = 0.1103 f _w / f ₂ = -0.5680, f _w / f ₃ = -0.0084, f ₄₂ / f ₄₁ = 0.3065 f _w / f ₄₂ = 0.2562, Σ (f _w / f _41n ) =-0.2117

Example 2 f = 8.999 to 25.462 to 71.999, F number = 2.0 2ω = 49.989 ° to 18.287 ° to 6.440 ° r ₁ = 152.1078 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 92.7850 d ₂ = 5.0417 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -8434.2837 d ₃ ＝ 0.1000 r ₄ ＝ 67.5271 d ₄ ＝ 4.9566 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 284.0311 d ₅ ＝ 0.1000 r ₆ ＝ 44.0992 d ₆ 4.7865 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 103.2640 d ₇ ＝ D ₁ (variable) r ₈ ＝ 120.0204 d ₈ = 1.5000 n ₅ ＝ 1.69401 ν ₅ ＝ 54.84 r ₉ ＝ 17.9629 d ₉ ＝ 5.6218 r ₁₀ ＝ -60.7234 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 25.5098 d ₁₁ ＝ 3.0593 n ₇ ＝ 1.85504 ν ₇ ＝ 23.78 r ₁₂ ＝ 74.2896 d ₁₂ ＝ 1.9001 r ₁₃ ＝ -88.8881 d ₁₃ = 1.2000 n ₈ ＝ 1.65 ₈ = 56.15 r ₁₄ = 201.7392 d ₁₄ = D ₂ (variable) r ₁₅ = ∞ (aperture) d ₁₅ = D ₃ (variable) r ₁₆ = 47.2843 d ₁₆ = 2.8000 n ₉ = 1.57098 ν ₉ = 71.30 r ₁₇ = -115.4330 d ₁₇ = 2.9944 r ₁₈ = -24.4366 d ₁₈ = 1.6853 n ₁₀ = 1.65425 ν ₁₀ = 58.52 r ₁₉ = 29.8853 d ₁₉ = 4.2812 n ₁₁ = 1.80680 ν ₁₁ = 22.60 r ₂₀ = 199.7227 d ₂₀ = D ₄ (variable) r ₂₁ = -49.8342 d ₂₁ = 3.0000 n ₁₂ = 1.58566 v ₁₂ = 46.33 r ₂₂ = -22.3568 d ₂₂ = 0.1000 r ₂₃ = -1320.2311 d ₂₃ = 3.0000 n ₁₃ = 1.57098 v ₁₃ = 71.30 r ₂₄ = _{-74.5661 d 24 = 2.1080 r 25 =} -23.2929 d 25 = 1.2000 n 14 = 1.85649 ν 14 = 32.28 r 26 = -58.3296 d 26 = 0.4328 r 27 = -82.0999 d 27 = 3.9979 n 15 = 1.57098 ν 15 = 71.30 r ₂₈ = -38.8330 d ₂₈ = 0.1000 r ₂₉ = -726.2143 d ₂₉ = 3.9509 n ₁₆ = 1.57098 ν ₁₆ = 71.30 r ₃₀ = -57.6117 d ₃₀ = 0.1000 r ₃₁ = 103.4079 d ₃₁ = 3.6463 n ₁₇ = 1.57098 ν ₁₇ = 71.30 r ₃₂ = -146.5860 d ₃₂ = 0.1000 r ₃₃ = 35.3066 d ₃₃ = 1.5000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ ＝ 21.4002 d ₃₄ ＝ 6.6753 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r ₃₅ = -135.9502 d ₃₅ = D _{5 (variable) r 36 = ∞ d 36 =} 33.0000 n 20 = 1.61170 ν 20 = 46.44 r 37 = ∞ d 37 = 13.2000 n 21 = 1.51825 ν 21 = 64.15 r 38 = ∞ f 8.9992 25.4624 71.9992 D ₁ 1.4000 26.1738 42.2625 D ₂ 42.1721 17.3974 1.3095 D ₃ 4.4969 2.5422 5.2558 D ₄ 9.6962 6.9004 1.4000 D ₅ 2.0000 6.7516 9.5373 n _32p −n _32n = 0.15255, ν _32n −ν _32p = 35.92, f _w / f ₁ = 0.1100 _{w / f 2 = -0.5324, f} w / f 3 = -0.0626, f 42 / f 41 = 0.0350 f w / f 42 = 0.3623, Σ (f w / f 41n) = - 0.1956

Example 3 f = 8.995 to 25.463 to 71.999, F number = 2.0 2ω = 49.916 ° to 18.284 ° to 6.437 ° r ₁ = 150.7079 d ₁ = 2.5000 n ₁ = 1.84281 ν ₁ = 21.00 r ₂ = 96.4869 d ₂ = 5.0999 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ 55624.1680 d ₃ ＝ 0.1000 r ₄ ＝ 67.9123 d ₄ ＝ 4.9743 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 279.3658 d ₅ ＝ 0.1000 r ₆ ＝ 44.2522 d ₆ ＝ 4.73 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 104.7758 d ₇ ＝ D ₁ (variable) r ₈ ＝ 124.5373 d ₈ = 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 18.0241 d ₉ ＝ 5.6876 r ₁₀ ＝ -67.0984 d ₁₀ = 1.2000 n ₆ = 1.60520 ν ₆ ＝ 65.48 r ₁₁ ＝ 32.2992 d ₁₁ ＝ 0.1000 r ₁₂ ＝ 29.1214 d ₁₂ ＝ 3.0517 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₃ ＝ 79.5017 d ₁₃ ＝ 1.8814 r ₁₄ ＝ -102.4919 d ₁₄ = 1.2000 n ₈ = 1.65425 ν ₈ = 58.52 r ₁₅ = 230.4498 d ₁₅ = D ₂ (variable) r ₁₆ = ∞ (diaphragm) d ₁₆ = D ₃ (variable) r ₁₇ = 37.6438 d ₁₇ = 2 .8000 n ₉ = 1.57098 ν ₉ ＝ 71.30 r ₁₈ ＝ -235.8532 d ₁₈ ＝ 3.1202 r ₁₉ ＝ -25.8267 d ₁₉ ＝ 1.6736 n ₁₀ ＝ 1.69979 ν ₁₀ ＝ 55.52 r ₂₀ ＝ 22.8481 d ₂₀ ＝ 4.2370 n ₁₁ ＝ 1.75702 ν _{11 = 25.14 r 21 = 156.4186 d 21} = D 4 ( _{variable) r 22 = -50.6939 d 22 =} 3.0000 n 12 = 1.59911 ν 12 = 39.21 r 23 = -22.3869 d 23 = 0.1000 r 24 = -10720.3059 d 24 = 3.0000 n ₁₃ = 1.57098 ν ₁₃ = 71.30 r ₂₅ = -70.8766 d ₂₅ = 2.0832 r ₂₆ = -23.1822 d ₂₆ = 1.2000 n ₁₄ = 1.87987 ν ₁₄ = 35.26 r ₂₇ = -65.8048 d ₂₇ = 0.4135 r ₂₈ = -97.7950 d ₂₈ = 3.9806 n ₁₅ = 1.57098 ν ₁₅ ＝ 71.30 r ₂₉ ＝ -38.4883 d ₂₉ ＝ 0.1000 r ₃₀ ＝ 1311.7663 d ₃₀ ＝ 3.9346 n ₁₆ ＝ 1.57098 ν ₁₆ ＝ 71.30 r ₃₁ ＝ -57.7807 d ₃₁ ＝ 0.1000 r ₃₂ ＝ 89.3259 d ₃₂ ＝ 3.7747 n ₁₇ = 1.57098 ν ₁₇ ＝ 71.30 r ₃₃ ＝ -151.3823 d ₃₃ ＝ 0.1000 r ₃₄ ＝ 37.5112 d ₃₄ ＝ 1.5000 n ₁₈ ＝ 1.85504 ν ₁₈ ＝ 23.78 r ₃₅ ＝ 21.4437 d ₃₅ ＝ 7.0792 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r ₃₆ = -112.5533 d ₃₆ = D ₅ (variable) r ₃₇ = ∞ d ₃₇ = 33.0000 n ₂₀ = 1.61170 ν ₂₀ = 46.44 r ₃₈ = ∞ d ₃₈ = 13.2000 n ₂₁ = 1.51825 ν ₂₁ = 64.15 r ₃₉ = ∞ f 8.9953 25.4634 71.9994 D ₁ 1.4000 26.3095 42.2318 D ₂ 42.1921 17.2815 1.3610 D ₃ 4.3914 2.6638 5.2600 D ₄ 9.7056 6.8905 1.4000 D ₅ 2.0000 6.5440 9.4365 n _32p −n _32n = 0.05723, ν _32n −ν _{32p , f w / f 1 = 0.1100} f w / f 2 = -0.5147, f w / f 3 = -0.0862, f 42 / f 41 = 0.0097 f w / f 42 = 0.3795, Σ (f w / f 41n) = -0.2182

Example 4 f = 11.004 to 31.110 to 88.000, F number = 2.0 2ω = 55.600 ° to 20.571 ° to 7.253 ° r ₁ = 178.7498 d ₁ = 3.2000 n ₁ = 1.84281 ν ₁ = 21.00 r ₂ = 115.9572 d _{2 = 5.2820 n 2 = 1.43985 ν 2} = 94.97 r 3 = -1182.4883 d 3 = 0.1000 r 4 = 86.2685 d 4 = 5.7184 n 3 = 1.43985 ν 3 = 94.97 r 5 = 333.1102 d 5 = 0.1000 r 6 = 52.6495 d 6 = 6.8154 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 116.2758 d ₇ ＝ D ₁ (variable) r ₈ ＝ 77.0661 d ₈ ＝ 2.0000 n ₅ = 1.60548 ν ₅ ＝ 60.70 r ₉ ＝ 20.2083 d ₉ ＝ 7.6232 r ₁₀ ＝ -74.6907 d ₁₀ = 1.5000 n ₆ = 1.49845 ν ₆ ＝ 81.61 r ₁₁ ＝ 33.5619 d ₁₁ ＝ 4.7340 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₂ ＝ 76.8483 d ₁₂ ＝ 2.6544 r ₁₃ ＝ -46.7574 d ₁₃ = 1.5000 n ₈ = 1.60520 ν ₈ = 65.48 r ₁₄ = 139.9542 d ₁₄ = D ₂ (variable) r ₁₅ = ∞ (aperture) d ₁₅ = D ₃ (variable) r ₁₆ = 61.2274 d ₁₆ = 3.8500 n ₉ = 1.49845 ν ₉ = 81.61 _{r 17 = -64.9332 d 17 = 1.3611} r 18 = -27.2621 d 18 = 1.5000 n 10 = 1.65425 ν 10 = 58.52 r 19 = 39.8671 d 19 = 4.4266 n 11 = 1.81264 ν 11 = 25.43 r 20 = -181.3907 d 20 = D ₄ (Variable) r ₂₁ = -139.4864 d ₂₁ = 1.5000 n ₁₂ = 1.85649 ν ₁₂ ＝ 32.28 r ₂₂ ＝ 158.6517 d ₂₂ ＝ 0.6554 r ₂₃ ＝ -2148.8716 d ₂₃ ＝ 3.4777 n ₁₃ ＝ 1.61770 ν ₁₃ = 51.17 r ₂₄ ＝ -38.8299 d ₂₄ = 0.1000 r ₂₅ = 115.1586 d ₂₅ = 3.4027 n ₁₄ = 1.57098 ν ₁₄ = 71.30 r ₂₆ = -60.5320 d ₂₆ = 0.9939 r ₂₇ = -47.9618 d ₂₇ = 2.2031 n ₁₅ = 1.67766 ν ₁₅ = 32.10 r ₂₈ = -138.1261 d ₂₈ = 0.1000 r ₂₉ = 5296.7511 d ₂₉ = 3.6524 n ₁₆ = 1.48915 ν ₁₆ = 70.20 r ₃₀ = -88.8671 d ₃₀ = 0.1000 r ₃₁ = 68.5345 d ₃₁ = 3.3578 n ₁₇ = 1.57098 ν ₁₇ = 71.30 r ₃₂ = -606.5419 d ₃₂ = 0.1000 r ₃₃ = 44.7907 d ₃₃ = 1.8000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ ＝ 24.2239 d ₃₄ ＝ 7.5078 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r ₃₅ ＝ -278.6806 d ₃₅ ＝ D ₅ (variable) r ₃₆ ＝ ∞ d ₃₆ ＝ 33.0000 n ₂₀ ＝ 1.61169 ν ₂₀ ＝ 46.44 r ₃₇ ＝ ∞ d ₃₇ ＝ 13.2000 n ₂₁ ＝ 1.51825 ν ₂₁ ＝ 64.15 r ₃₈ ＝ ∞ f 11.0043 31.1104 87.9997 D ₁ 1.5000 29.7044 49.5945 D ₂ 49.5948 21.3908 1.5000 D ₃ 5.0097 2.7556 6.2413 D ₄ 11.6551 7.9611 2.0932 D ₅ 2.0000 7.9479 10.3305 n _32p −n _32n = 0.15839, ν _32n −ν _32p = 33.09, f _w / f ₁ = 0.1104 _{w / f 2 = -0.5911, f} w / f 3 = 0.0095, f 42 / f 41 = 0.4226 f w / f 42 = 0.2645, Σ (f w / f 41n) = - 0.2278

Example 5 f = 9.027 to 25.471 to 71.958, F number = 2.0 2ω = 49.998 ° to 18.234 ° to 6.443 ° r ₁ = 140.4173 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 88.9774 d ₂ ＝ 4.8151 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -16970.9304 d ₃ ＝ 0.1000 r ₄ ＝ 67.8805 d ₄ ＝ 4.8927 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 253.0108 d ₅ ＝ 0.1000 r ₆ ＝ 43.3688 d ₆ ＝ 4.7549 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 99.5581 d ₇ ＝ D ₁ (variable) r ₈ ＝ 112.6250 d ₈ ＝ 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 16.8647 d ₉ ＝ 6.5590 r ₁₀ ＝ -47.7082 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 27.0971 d ₁₁ ＝ 4.0087 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₂ ＝ 76.7508 d ₁₂ ＝ 2.2508 r ₁₃ ＝ -54.0700 d ₁₃ = 1.2000 n ₈ = 1.64648 ν ₈ = 47.85 r ₁₄ = -379.8740 d ₁₄ = D ₂ (variable) r ₁₅ = ∞ (aperture) d ₁₅ = D ₃ (variable) r ₁₆ = 58.2033 d ₁₆ = 2.8000 n ₉ = 1.49845 ν ₉ = 81.6 1 r ₁₇ = -49.7295 d ₁₇ = 1.7351 r ₁₈ = -24.9037 d ₁₈ = 1.5550 n ₁₀ = 1.65425 ν ₁₀ = 58.52 r ₁₉ = 31.9743 d ₁₉ = 4.2508 n ₁₁ = 1.81264 ν ₁₁ = 25.43 r ₂₀ = -115.5952 d ₂₀ = D _{4 (variable) r 21 = -58.6224 d 21 =} 1.2000 n 12 = 1.85649 ν 12 = 32.28 r 22 = 169.3788 d 22 = 0.5458 r 23 = -202.8153 d 23 = 3.0000 n 13 = 1.58566 ν 13 = 46.33 r 24 _{= -27.2801 d 24 = 0.1000 r 25} = 167.0337 d 25 = 3.0000 n 14 = 1.57098 ν 14 = 71.30 r 26 = -44.4329 d 26 = 0.8475 r 27 = -34.2208 d 27 = 1.9730 n 15 = 1.67766 ν 15 = 32.10 r ₂₈ = -103.9462 d ₂₈ = 0.1000 r ₂₉ = -185.7218 d ₂₉ = 3.5478 n ₁₆ = 1.48915 ν ₁₆ = 70.20 r ₃₀ = -60.3914 d ₃₀ = 0.1000 r ₃₁ = 64.1378 d ₃₁ = 3.2047 n ₁₇ = 1.57098 ν ₁₇ = 71.30 r ₃₂ = -404.2552 d ₃₂ = 0.1000 r ₃₃ = 38.4608 d ₃₃ = 1.5000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ ＝ 22.1046 d ₃₄ = 5.8244 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r ₃₅ ＝ -95.3577 d ₃₅ ＝ D ₅ (variable) r ₃₆ ＝ ∞ d ₃₆ ＝ 33.0000 n ₂₀ ＝ 1.61170 ν ₂₀ ＝ 46.44 r ₃₇ ＝ ∞ d ₃₇ ＝ 13.2000 n ₂₁ ＝ 1.51825 ν ₂₁ ＝ 64.15 r ₃₈ ＝ ∞ f 9.0272 25.4706 71.9582 D ₁ 1.4000 25.5472 42.3956 D ₂ 42.1455 17.9989 1.1487 D ₃ 4.7687 2.1606 5.2248 D ₄ 9.9086 6.7891 1.4107 D ₅ 2.0000 7.7272 10.0426 n _32p −n _32n = 0.15839, ν _32n −ν _32p = 33.09, f _w / f ₁ = 0.1108 _{w / f 2 = -0.6018, f} w / f 3 = 0.0445, f 42 / f 41 = 0.1168 f w / f 42 = 0.2751, Σ (f w / f 41n) = - 0.2965

Example 6 f = 9.267 to 25.768 to 72.026, F number = 2.0 2ω = 48.679 ° to 18.001 ° to 6.431 ° r ₁ = 141.4469 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 88.4204 d ₂ = 4.7971 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ 14402.6077 d ₃ ＝ 0.1000 r ₄ ＝ 68.3129 d ₄ ＝ 4.8903 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 263.9446 d ₅ ＝ 0.1000 r ₆ ＝ 44.0755 d ₆ n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 103.0901 d ₇ ＝ D ₁ (variable) r ₈ ＝ 101.3520 d ₈ = 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 17.0532 d ₉ ＝ 6.5214 r ₁₀ ＝ -51.6363 d _{10 = 1.2000 n 6 = 1.57098 ν} 6 = 71.30 r 11 = 27.2398 d 11 = 4.2110 n 7 = 1.84281 ν 7 = 21.00 r 12 = 88.8964 d 12 = 2.2608 r 13 = -49.3724 d 13 = 1.2000 n 8 = 1.64648 ν 8 = 47.85 r ₁₄ = -640.5589 d ₁₄ = D ₂ (variable) r ₁₅ = ∞ (aperture) d ₁₅ = D ₃ (variable) r ₁₆ = 60.1064 d ₁₆ = 2.8000 n ₉ = 1.49845 ν ₉ = 81.6 1 r ₁₇ = -55.2486 d ₁₇ = 1.8668 r ₁₈ = -24.6822 d ₁₈ = 1.5386 n ₁₀ = 1.65425 v ₁₀ = 58.52 r ₁₉ = 35.9037 d ₁₉ = 4.2856 n ₁₁ = 1.81264 v ₁₁ = 25.43 r ₂₀ = -111.4255 d ₂₀ = D ₄ (Variable) r ₂₁ = -70.0702 d ₂₁ = 1.2000 n ₁₂ = 1.85649 ν ₁₂ ＝ 32.28 r ₂₂ ＝ 202.5118 d ₂₂ ＝ 0.5712 r ₂₃ ＝ −164.0556 d ₂₃ ＝ 3.0000 n ₁₃ ＝ 1.58566 ν ₁₃ = 46.33 r _{24 = -25.2763 d 24 = 0.1000 r 25} = 174.6641 d 25 = 3.0000 n 14 = 1.57098 ν 14 = 71.30 r 26 = -50.8538 d 26 = 1.0172 r 27 = -30.9938 d 27 = 1.9757 n 15 = 1.67766 ν 15 = 32.10 r _{28 = -87.1312 d 28 = 1.5184 r} 29 = -197.3657 d 29 = 3.5550 n 16 = 1.48915 ν 16 = 70.20 r 30 = -65.1624 d 30 = 0.1000 r 31 = 67.2524 d 31 = 3.2391 n 17 = 1.57098 ν 17 = 71.30 _{r 32 = -542.8520 d 32 = 0.1000} r 33 = 40.6770 d 33 = 1.5000 n 18 = 1.85504 ν 18 = 23.78 r 34 = 23.0952 d 34 = 5.8458 n 19 = 1.57098 ν 19 = 71.30 r 35 -77.4624 d ₃₅ = D _{5 (variable) r 36 = ∞ d 36 =} 33.0000 n 20 = 1.61170 ν 20 = 46.44 r 37 = ∞ d 37 = 13.2000 n 21 = 1.51825 ν 21 = 64.15 r 38 = ∞ f 9.2673 25.7684 72.0264 _{D 1 1.4000 25.5454 42.4030 D 2 42.1456} 18.0017 1.1415 D 3 4.7466 2.2143 5.1855 D 4 9.9060 6.8033 1.4217 D 5 2.0000 7.6331 10.0463 n 32p -n 32n = 0.15839, ν 32n -ν 32p = 33.09, f w / f 1 = 0.1127 f w _{/ f 2 = -0.6002, f w} / f 3 = 0.0299, f 42 / f 41 = 0.1715 f w / f 42 = 0.2765, Σ (f w / f 41n) = - 0.2815

Example 7 f = 7.022 to 24.245 to 84.001, F number = 2.0 2ω = 61.864 ° to 19.075 ° to 5.507 ° r ₁ = 136.3344 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 85.1617 d ₂ ＝ 4.8188 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -838.1164 d ₃ ＝ 0.1000 r ₄ ＝ 67.7557 d ₄ ＝ 4.8748 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 297.5656 d ₅ ＝ 0.1000 r ₆ ＝ 41.5540 d ₆ ＝ 4.7423 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 98.7617 d ₇ ＝ D ₁ (variable) r ₈ ＝ 95.9993 d ₈ = 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 14.9789 d ₉ ＝ 6.7852 r ₁₀ ＝ -45.8782 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 25.1047 d ₁₁ ＝ 4.1385 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₂ ＝ 73.3913 d ₁₂ ＝ 2.2159 r ₁₃ ＝ -39.1057 d ₁₃ = 1.2000 n ₈ ＝ 1.60520 _{8 = 65.48 r 14 = 576.8239 d} 14 = D 2 ( variable) r ₁₅ = ∞ (stop) d ₁₅ = D _{3 (variable) r 16 = 57.7049 d 16 =} 2.8000 n 9 = 1.49845 ν 9 = 81.61 _{17 = -47.0008 d 17 = 0.8630 r} 18 = -21.9095 d 18 = 1.4996 n 10 = 1.65425 ν 10 = 58.52 r 19 = 32.3298 d 19 = 4.1698 n 11 = 1.81264 ν 11 = 25.43 r 20 = -131.1763 d 20 = D _{4 (variable) r 21 = -99.9616 d 21 =} 1.2000 n 12 = 1.85649 ν 12 = 32.28 r 22 = 365.3211 d 22 = 0.4819 r 23 = -454.8400 d 23 = 3.0000 n 13 = 1.61770 ν 13 = 51.17 r 24 = - 29.5683 d ₂₄ = 0.1000 r ₂₅ = 129.4439 d ₂₅ = 3.0000 n ₁₄ = 1.57098 v ₁₄ = 71.30 r ₂₆ = -48.3303 d ₂₆ = 0.7012 r ₂₇ = -32.3216 d ₂₇ = 1.8257 n ₁₅ = 1.67766 v ₁₅ = 32.10 r ₂₈ = -96.1285 d ₂₈ = 0.1000 r ₂₉ = -423.0648 d ₂₉ = 3.3087 n ₁₆ = 1.48915 ν ₁₆ = 70.20 r ₃₀ = -61.8069 d ₃₀ = 0.1000 r ₃₁ = 57.6576 d ₃₁ = 3.2000 n ₁₇ = 1.57098 ν ₁₇ = 71.30 r ₃₂ = -538.1491 d ₃₂ = 0.1000 r ₃₃ = 37.7207 d ₃₃ = 1.5000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ = 19.6821 d ₃₄ = 5.8813 n ₁₉ = 1.57098 ν ₁₉ = 71.30 r ₃₅ = -1 69.5462 d ₃₅ = D _{5 (variable) r 36 = ∞ d 36 =} 25.3000 n 20 = 1.61170 ν 20 = 46.44 r 37 = ∞ d 37 = 11.1000 n 21 = 1.51825 ν 21 = 64.15 r 38 = ∞ f 7.0224 24.2449 84.0010 D _{1 1.4000 26.1876 42.2596 D 2 42.2374 17.4498} 1.3778 D 3 4.8102 1.8600 5.3819 D 4 9.9701 6.4733 1.5242 D 5 2.0000 8.4469 9.8742 n 32p -n 32n = 0.15839, ν 32n -ν 32p = 33.09, f w / f 1 = 0.0944 f w / _{f 2 = -0.5748, f w /} f 3 = 0.0076, f 42 / f 41 = 0.4125 f w / f 42 = 0.2034, Σ (f w / f 41n) = - 0.1733

Example 8 f = 7.003 to 24.254 to 84.001, F number = 2.0 2ω = 61.907 ° to 19.044 ° to 5.490 ° r ₁ = 146.2824 d ₁ = 2.5000 n ₁ = 1.84281 ν ₁ = 21.00 r ₂ = 93.5893 d ₂ = 5.2000 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -971.6065 d ₃ ＝ 0.1000 r ₄ ＝ 67.8139 d ₄ ＝ 5.0000 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 360.0745 d ₅ ＝ 0.1000 r ₆ ＝ 44.2204 d ₆ ＝ 4.8000 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 113.3784 d ₇ ＝ D ₁ (variable) r ₈ ＝ 125.0652 d ₈ ＝ 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 16.7301 d ₉ ＝ 5.8313 r ₁₀ ＝ -57.1448 d ₁₀ = 1.2000 n ₆ = 1.60520 ν ₆ ＝ 65.48 r ₁₁ ＝ 29.0077 d ₁₁ ＝ 0.1000 r ₁₂ ＝ 26.1635 d ₁₂ ＝ 3.2000 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₃ ＝ 85.0470 d ₁₃ ＝ 1.9184 r ₁₄ ＝ -65.2017 d _{14 = 1.2000 n 8 = 1.65425 ν} 8 = 58.52 r 15 = 104.2200 d 15 = D 2 ( variable) r ₁₆ = ∞ (stop) d ₁₆ = D _{3 (variable) r 17 = 40.7143 d 17 =} 2.8 000 n ₉ = 1.57098 ν ₉ = 71.30 r ₁₈ = -186.6835 d ₁₈ = 1.7189 r ₁₉ = -21.4608 d ₁₉ = 1.6873 n ₁₀ = 1.6979 ν ₁₀ = 55.52 r ₂₀ = 21.1637 d ₂₀ = 4.2457 n ₁₁ = 1.75724 ν ₁₁ = 27.69 r ₂₁ = 261.3456 d ₂₁ = D ₄ (variable) r ₂₂ = -57.7116 d ₂₂ = 3.0000 n ₁₂ = 1.59911 ν ₁₂ = 39.21 r ₂₃ = -23.3427 d ₂₃ = 0.1000 r ₂₄ = 447.7101 d ₂₄ = 3.0000 n ₁₃ = 1.57098 v ₁₃ = 71.30 r ₂₅ = -59.3506 d ₂₅ = 1.8026 r ₂₆ = -23.1676 d ₂₆ = 1.2000 n ₁₄ = 1.87987 v ₁₄ = 35.26 r ₂₇ = -57.0205 d ₂₇ = 0.4124 r ₂₈ = -98.4112 d ₂₈ = 4.0000 n ₁₅ = 1.57098 ν ₁₅ ＝ 71.30 r ₂₉ ＝ -37.5092 d ₂₉ = 0.1000 r ₃₀ ＝ 2981.9622 d ₃₀ ＝ 4.0000 n ₁₆ ＝ 1.57098 ν ₁₆ ＝ 71.30 r ₃₁ ＝ -56.1948 d ₃₁ ＝ 0.1000 r ₃₂ ＝ 104.2210 d ₃₂ ＝ 4.0000 n _{17 = 1.57098 ν 17 = 71.30 r} 33 = -163.5388 d 33 = 0.1000 r 34 = 39.1136 d 34 = 1.5000 n 18 = 1.85504 ν 18 = 23.78 r 35 = 21.2235 d 35 = 7.0310 n 19 _{1.57098 ν 19 = 71.30 r 36 =} -97.4293 d 36 = D 5 ( _{variable) r 37 = ∞ d 37 =} 25.3000 n 20 = 1.61170 ν 20 = 46.44 r 38 = ∞ d 38 = 11.1000 n 21 = 1.51825 ν 21 = 64.15 r ₃₉ = ∞ f 7.0033 24.2538 84.0008 D ₁ 1.4000 26.7324 42.1681 D ₂ 42.2746 16.9420 1.5066 D ₃ 4.4893 2.4252 5.3509 D ₄ 9.9953 6.3675 1.4000 D ₅ 2.0000 7.6926 9.7338 n _32p −n _32n = 0.05745, ν _32n −ν _32p = 27.83 _{w / f 1 = 0.0937 f w} / f 2 = -0.4940, f w / f 3 = -0.0987, f 42 / f 41 = 0.1344 f w / f 42 = 0.2873, Σ (f w / f 41n) = - 0.1553

Example 9 f = 7.155 to 24.465 to 83.910, F number = 2.0 2ω = 60.893 ° to 18.904 ° to 5.512 ° r ₁ = 136.9170 d ₁ = 2.5000 n ₁ = 1.81675 ν ₁ = 22.62 r ₂ = 86.4105 d ₂ = 4.8770 n ₂ = 1.45720 ν ₂ ＝ 90.31 r ₃ ＝ -1105.8914 d ₃ ＝ 0.1000 r ₄ ＝ 67.2156 d ₄ ＝ 4.8718 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 321.6843 d ₅ ＝ 0.1000 r ₆ ＝ 41.9228 d ₆ ＝ 4.7359 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 97.6361 d ₇ ＝ D ₁ (variable) r ₈ ＝ 96.0751 d ₈ ＝ 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 15.1537 d ₉ ＝ 6.8524 r ₁₀ ＝ -45.6173 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 25.2829 d ₁₁ ＝ 4.1985 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₂ ＝ 72.8410 d ₁₂ ＝ 2.2663 r ₁₃ ＝ -41.3982 d ₁₃ = 1.2000 n ₈ ＝ 1.60520 _{8 = 65.48 r 14 = 689.6540 d} 14 = D 2 ( variable) r ₁₅ = ∞ (stop) d ₁₅ = D _{3 (variable) r 16 = 63.5969 d 16 =} 2.8000 n 9 = 1.49845 ν 9 = 81.61 _{17 = -43.9834 d 17 = 0.8168 r} 18 = -21.6087 d 18 = 1.5183 n 10 = 1.65425 ν 10 = 58.52 r 19 = 30.5604 d 19 = 4.2066 n 11 = 1.81264 ν 11 = 25.43 r 20 = -154.8455 d 20 = D _{4 (variable) r 21 = -92.6100 d 21 =} 1.2000 n 12 = 1.85649 ν 12 = 32.28 r 22 = 244.1506 d 22 = 0.5289 r 23 = -1252.7705 d 23 = 3.0000 n 13 = 1.61770 ν 13 = 51.17 r 24 = - _{29.3060 d 24 = 0.1000 r 25 =} 101.7847 d 25 = 3.0000 n 14 = 1.48915 ν 14 = 70.20 r 26 = -46.0196 d 26 = 0.6517 r 27 = -30.7276 d 27 = 1.8614 n 15 = 1.67766 ν 15 = 32.10 r 28 = -89.4379 d ₂₈ = 0.1000 r ₂₉ = 553.7467 d ₂₉ = 3.3387 n ₁₆ = 1.48915 ν ₁₆ = 70.20 r ₃₀ = -56.8903 d ₃₀ = 0.1000 r ₃₁ = 48.3949 d ₃₁ = 3.2000 n ₁₇ = 1.48915 ν ₁₇ = 70.20 r ₃₂ = -270.6782 d ₃₂ = 0.1000 r ₃₃ = 34.7963 d ₃₃ = 1.5000 n ₁₈ = 1.85504 ν ₁₈ = 23.78 r ₃₄ = 19.3652 d ₃₄ = 5.8936 n ₁₉ = 1.48915 ν ₁₉ = 70.20 r ₃₅ =- 124.7933 d ₃₅ = D _{5 (variable) r 36 = ∞ d 36 =} 25.3000 n 20 = 1.61170 ν 20 = 46.44 r 37 = ∞ d 37 = 11.1000 n 21 = 1.51825 ν 21 = 64.15 r 38 = ∞ f 7.1553 24.4649 83.9096 D _{1 1.4000 26.1841 42.2536 D 2 42.2501 17.4676} 1.3959 D 3 4.8383 1.9240 5.3889 D 4 9.9995 6.5228 1.5229 D 5 2.0000 8.3892 9.9268 n 32p -n 32n = 0.15839, ν 32n -ν 32p = 33.09, f w / f 1 = 0.0956 f w / _{f 2 = -0.5729, f w /} f 3 = -0.0006, f 42 / f 41 = 0.3241 f w / f 42 = 0.2185, Σ (f w / f 41n) = - 0.1937

Example 10 f = 9.036 to 25.501 to 71.999, F number = 2.0 2ω = 50.638 ° to 17.879 ° to 6.349 ° r ₁ = 131.8451 d ₁ = 2.5000 n ₁ = 1.85504 ν ₁ = 23.78 r ₂ = 88.0849 d ₂ ＝ 4.5274 n ₂ = 1.48915 ν ₂ ＝ 70.20 r ₃ ＝ 1681.9312 d ₃ ＝ 0.1000 r ₄ ＝ 119.3273 d ₄ ＝ 4.8890 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ -592.3035 d ₅ ＝ 0.1000 r ₆ ＝ 54.5541 d ₆ 4.9646 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 93.3891 d ₇ ＝ D ₁ (variable) r ₈ ＝ 78.9576 d ₈ = 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ = 19.4022 d ₉ ＝ 8.7988 r ₁₀ ＝ -25.6474 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 48.8813 d ₁₁ ＝ 0.2105 r ₁₂ ＝ 38.3508 d ₁₂ ＝ 4.6080 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₃ ＝ 162.9271 d ₁₃ ＝ D ₂ (variable) r ₁₄ = ∞ (stop) d ₁₄ = D _{3 (variable) r 15 = 44.5857 d 15 =} 2.8000 n 8 = 1.43985 ν 8 = 94.97 r 16 = -299.4193 d 16 = 2.3703 r 17 = -16.1949 d 17 _{1.5000 n 9 = 1.62508 ν 9 =} 53.20 r 18 = 32.8795 d 18 = 5.0744 n 10 = 1.84281 ν 10 = 21.00 r 19 = 276.5631 d 19 = D 4 ( _{variable) r 20 = -37.0690 d 20 =} 3.0000 n 11 = 1.49845 v ₁₁ = 81.61 r ₂₁ = -16.3675 d ₂₁ = 0.1000 r ₂₂ = -283.3894 d ₂₂ = 3.0000 n ₁₂ = 1.57098 v ₁₂ = 71.30 r ₂₃ = -33.9268 d ₂₃ = 0.9710 r ₂₄ = -22.8177 d ₂₄ = 2.0000 n ₁₃ = 1.76859 ν ₁₃ ＝ 26.55 r ₂₅ ＝ -33.0829 d ₂₅ ＝ 0.1000 r ₂₆ ＝ 190.2420 d ₂₆ ＝ 5.9951 n ₁₄ ＝ 1.57098 ν ₁₄ ＝ 71.30 r ₂₇ ＝ -65.7782 d ₂₇ ＝ 0.1000 r ₂₈ ＝ 25.4244 d ₂₈ ＝ 1.5000 n ₁₅ = 1.85504 ν ₁₅ ＝ 23.78 r ₂₉ = 17.9389 d ₂₉ ＝ 5.4604 n ₁₆ = 1.49845 ν ₁₆ ＝ 81.61 r ₃₀ ＝ -99.8569 d ₃₀ ＝ D ₅ (variable) r ₃₁ ＝ ∞ d ₃₁ ＝ 33.0000 n ₁₇ ＝ 1.61168 ν ₁₇ ＝ 46.44 r ₃₂ = ∞ d ₃₂ = 13.2000 n ₁₈ = 1.51825 ν ₁₈ = 64.15 r ₃₃ = ∞ f 9.0358 25.5008 71.9989 D ₁ 1.4000 32.2919 54.7379 D ₂ 54.4864 23.5944 1.1487 D ₃ 5.52 _{54 2.0555 1.8798 D 4 2.0360 1.5162 1.4107} D 5 2.0000 5.9893 6.2715 n 32p -n 32n = 0.21773, ν 32n -ν 32p = 32.20, f w / f 1 = 0.0893 f w / f 2 = -0.4343, f w / f 3 _{= -0.2004, f 42 / f 41} = 0.7439 f w / f 42 = 0.2725, Σ (f w / f 41n) = - 0.0864

Example 11 f = 9.008 to 25.499 to 72.000, F number = 2.0 2ω = 49.368 ° to 18.198 ° to 6.423 ° r ₁ = 135.2340 d ₁ = 2.5000 n ₁ = 1.84281 ν ₁ = 21.00 r ₂ = 89.8690 d ₂ = 5.5914 n ₂ = 1.43985 ν ₂ ＝ 94.97 r ₃ ＝ -2424.8261 d ₃ ＝ 0.1000 r ₄ ＝ 62.5584 d ₄ ＝ 5.1383 n ₃ ＝ 1.43985 ν ₃ ＝ 94.97 r ₅ ＝ 322.3434 d ₅ ＝ 0.1000 r ₆ ＝ 44.8533 d ₆ ＝ 5.2432 n ₄ = 1.43985 ν ₄ ＝ 94.97 r ₇ ＝ 105.7142 d ₇ ＝ D ₁ (variable) r ₈ ＝ 58.2529 d ₈ = 1.5000 n ₅ ＝ 1.69974 ν ₅ ＝ 56.49 r ₉ ＝ 17.1142 d ₉ ＝ 6.3067 r ₁₀ ＝ -50.1323 d ₁₀ = 1.2000 n ₆ = 1.57098 ν ₆ ＝ 71.30 r ₁₁ ＝ 32.5452 d ₁₁ ＝ 3.8858 n ₇ ＝ 1.84281 ν ₇ ＝ 21.00 r ₁₂ ＝ 98.2711 d ₁₂ ＝ 1.7246 r ₁₃ ＝ -42.3395 d ₁₃ = 1.2000 n ₈ ＝ 1.57098 ν ₈ = 71.30 r ₁₄ = -617.1230 d ₁₄ = D ₂ (variable) r ₁₅ = 130.4158 d ₁₅ = 2.8000 n ₉ = 1.49845 ν ₉ = 81.61 r ₁₆ = -48.3741 d ₁₆ = 3.5968 r ₁₇ = -18. 2382 d ₁₇ = 1.5550 n ₁₀ = 1.65425 ν ₁₀ ＝ 58.52 r ₁₈ ＝ 28.4284 d ₁₈ ＝ 2.9233 n ₁₁ = 1.81264 ν ₁₁ ＝ 25.43 r ₁₉ ＝ -1296.3792 d ₁₉ ＝ D ₃ (variable) r ₂₀ ＝ ∞ (diaphragm) d ₂₀ = D _{4 (variable) r 21 = 1174.2678 d 21 =} 1.2000 n 12 = 1.85504 ν 12 = 23.78 r 22 = 98.5353 d 22 = 0.5458 r 23 = -192.9060 d 23 = 3.0000 n 13 = 1.58547 ν 13 = 59.36 r 24 _{= -27.7205 d 24 = 0.1000 r 25} = 137.9285 d 25 = 3.0000 n 14 = 1.57098 ν 14 = 71.30 r 26 = -59.4159 d 26 = 10.1687 r 27 = -37.7650 d 27 = 1.8000 n 15 = 1.67882 ν 15 = 29.25 r ₂₈ = -60.5864 d ₂₈ = 0.1000 r ₂₉ = -282.2635 d ₂₉ = 5.5000 n ₁₆ = 1.49845 v ₁₆ = 81.61 r ₃₀ = -60.7652 d ₃₀ = 0.1000 r ₃₁ = 68.6 130 d ₃₁ = 5.5000 n ₁₇ = 1.57098 v ₁₇ = 71.30 _{r 32 = -79.2517 d 32 = 1.5000} n 18 = 1.85504 ν 18 = 23.78 r 33 = -123.3612 d 33 = 0.1000 r 34 = 48.7551 d 34 = 5.5000 n 19 = 1.57098 ν 19 = 71.30 _{35 = -33.1127 d 35 = 1.5000 n} 20 = 1.85504 ν 20 = 23.78 r 36 = -59.8194 d 36 = D 5 ( _{variable) r 37 = ∞ d 37 =} 25.3000 n 21 = 1.61169 ν 21 = 46.44 r 38 = ∞ d _{38 = 11.1000 n 22 = 1.51825 ν} 22 = 64.15 r 39 = ∞ f 9.0076 25.4994 71.9996 D 1 1.4000 24.4807 39.3443 D 2 34.8531 10.3337 1.4000 D 3 5.8912 7.3296 1.4000 D 4 4.4708 1.4000 1.7910 D 5 2.0000 5.0712 4.6797 n 32p -n 32n = _{0.15839, ν 32n -ν 32p = 33.09} , f w / f 1 = 0.1191 f w / f 2 = -0.5350, f w / f 3 = -0.1241, f 42 / f 41 = 0.5736 f w / f 42 = 0.3025, Σ (f _w / f _41n ) =-0.1306 where r ₁ , r ₂ , ... Are the radii of curvature of the respective lens surfaces, d
₁ , d ₂ , ... Is the thickness of each lens and the lens interval, n
₁ , n ₂ , ... Are the refractive indices of each lens at the e-line, ν ₁ , ν
₂ , ... are Abbe numbers of d-line of each lens.

The lens system of Example 1 has a lens configuration as shown in FIG. 1, and comprises, in order from the object side, a first lens group G ₁ having a positive refractive power and a second lens group G ₂ having a negative refractive power. , Aperture S
When, a third lens group G ₃ having a negative refractive power and a positive refractive power a fourth lens group G ₄ Prefecture of the optical element such as a color separation prism or various filters between the lens system and the imaging device The glass block shown is arranged.

In each lens group, the first lens group G ₁ is, in order from the object side, a negative meniscus lens whose convex surface faces the object side, and a positive lens whose positive refractive power surface faces the object side. The second lens group G ₂ is composed of a cemented lens in which is cemented together with 2 and a positive meniscus lens whose convex surface faces the object side.
However, in order from the object side, a negative meniscus lens with a convex surface facing the object side, a cemented lens with a biconcave lens and a positive meniscus lens with a convex surface facing the object side, and a lens with a strong negative refractive power on the object side The third lens group G ₃ includes, in order from the object side, the first lens component of positive refracting power composed of a biconvex lens, the biconcave lens, and the positive refracting power to the object side. The second lens component G ₄ has a negative refracting power and is made up of a cemented lens in which a positive lens having one surface facing the other surface is cemented. It is composed of a lens group G ₄₁ and a forty-second lens group G ₄₂ having a positive refractive power, and the 41st lens group G ₄₁ is a negative lens having a surface having a negative refractive power strong toward the object side in order from the object. , A positive meniscus lens with a concave surface facing the object side, and one with a strong positive refractive power on the image side A positive meniscus lens with the concave surface facing the object side,
The second lens group G ₄₂ includes, in order from the object side, a positive lens having a surface having a strong positive refractive power facing the image side, and a positive lens having a surface having a strong positive refractive power facing the object side. It is composed of a negative meniscus lens having a convex surface facing the object side and a cemented lens in which a positive lens having a positive refractive power surface facing the object side is bonded to each other.

Further, the first lens group G ₁ and the diaphragm S are fixed during zooming. The second lens group G ₂ monotonously moves from the object side to the image side during zooming from the wide-angle end to the telephoto end. Further, the third lens group G ₃ moves from the image side to the object side during zooming from the wide-angle end to the telephoto end, has an extreme point after passing the intermediate focal length, and then moves to the image side. The fourth lens group G ₄ taking extreme point at the telephoto side than is the same motion as the third lens group G ₃ third lens group G _3.

Although the first embodiment has a variable power ratio of 8 times,
Since the second lens group G ₂ shares a zoom ratio of about 4.6 times and the fourth lens group G ₄ about 1.7 times, the second lens group G ₂ has a relatively weak refractive power. However, it has a large zoom ratio, a long back focus, and extremely high optical performance.

The chromatic aberrations of the C line and the F line with respect to the e line generated in each lens unit and the optical element at the intermediate focal length are
It is as shown in the table below.

Axial chromatic aberration coefficient Magnification chromatic aberration coefficient First lens group -0.00284 0.00622 Second lens group 0.01896 -0.02259 Third lens group -0.11359 -0.01061 Fourth lens group 0.04480 0.01554 Prism etc. 0.05314 0.00398 Total 0.00047 -0.00745 In this table As shown, in the zoom lens of Example 1, the chromatic aberration is largely negatively generated even though the third lens group G ₃ has a negative refractive power, and conversely, the fourth lens group G _{4 is used.}
It can be seen that is configured to generate positive chromatic aberration despite having a positive refractive power. Further, as can be seen from the above table, the third lens group G ₃ has less chromatic aberration of magnification as compared with the axial chromatic aberration, while the fourth lens group G ₄ is less than the third lens group G _3. Although the amount of axial chromatic aberration is small, a large amount of chromatic aberration of magnification is generated, and by the balance between these, both axial chromatic aberration and lateral chromatic aberration are well corrected from the wide-angle end to the telephoto end.

As described above, the distribution and configuration of the refractive power of the negative lenses included in the fourth lens group G ₄ are controlled by the magnitude of the negative axial chromatic aberration produced by the third lens group G ₃ , and the fourth lens group G ₄ is controlled. _The axial chromatic aberration generated in ₄ is set to an appropriate value from a positive value to a negative value.

The aberrations of the first embodiment are shown in FIGS.
3, as shown in FIG.

The second embodiment has the lens structure shown in FIG. 2, and the fourth lens group G ₄ is different from the first embodiment. That is, in the fourth lens group, the forty-first lens group G ₄₁ includes, in order from the object side, a positive meniscus lens having a concave surface facing the object side,
It is composed of a positive lens whose positive refractive power is directed toward the image side and a negative meniscus lens whose concave surface is directed toward the object side. The 42nd lens group G ₄₂ is arranged in order from the object side toward the image side. , Two positive lenses with the surface with the stronger refractive power, the positive lens with the surface with the positive refractive power facing the object side, and the negative meniscus lens with the convex surface facing the object side and the object It is composed of a cemented lens in which a positive lens having a surface having a strong positive refractive power is directed to the side and a positive lens is attached.

The aberrations of the zoom lens of the second embodiment are as shown in FIGS. 15, 16 and 17.

The third embodiment is a zoom lens having the construction shown in FIG. 3, and the constructions of the second lens group G ₂ are different from those of the second embodiment. That is, the second lens group G ₂ includes, in order from the object side, a negative meniscus lens having a convex surface directed toward the object side, a biconcave lens, a positive meniscus lens having a convex surface directed toward the object side, and a negative refraction toward the object side. It is composed of a negative lens with the side with stronger power.

The aberrations of the zoom lens of the third embodiment are as shown in FIGS. 18, 19 and 20.

The fourth embodiment is a zoom lens having the configuration shown in FIG. 4, and is different from the first embodiment in that the third lens group G ₃ has a positive refracting power and the configuration of the fourth lens group G ₄ is different. It is different from that. That is, the fourth lens group G ₄ includes
The lens group G ₄₁ includes, in order from the object side, a negative lens having a surface having a strong negative refractive power facing the object side, and two positive lenses having a surface having a strong positive refractive power facing the image side. A negative meniscus lens having a concave surface directed toward the object side. The 42nd lens group G ₄₂
, In order from the object side, a positive lens with the positive refractive power surface facing the image side, a positive lens with the positive refractive power surface facing the object side, and a convex surface facing the object side. It is composed of a cemented lens in which a negative meniscus lens directed to it and a positive lens having a surface having a strong positive refractive power directed to the object side are bonded together.

In Example 4, since the third lens group G ₃ has a positive refractive power, a zoom lens having a long back focus is used and a positive chromatic aberration is generated in the fourth lens group G _4. In addition, the fourth lens group G ₄ and the forty-first lens group G ₄₁ are configured to be negative, positive, and negative. Therefore, the chromatic aberration of positive magnification that occurs in the fourth lens group G ₄ becomes large especially at the wide-angle end, and the angle of view at the wide-angle end is about 55.6 °, which is wider than in Examples 1 to 3. Nevertheless, lateral chromatic aberration is well corrected from the wide-angle end to the telephoto end.

The aberrations of the zoom lens of the fourth embodiment are as shown in FIGS. 21, 22 and 23.

The zoom lenses of Example 5 and Example 6 have the configurations as shown in FIGS. 5 and 6, respectively, and both have the same configurations as Example 4.

The aberrations of the zoom lens of the fifth embodiment are as shown in FIGS. 24, 25 and 26, and the aberrations of the zoom lens of the sixth embodiment are shown in FIGS. 27, 28 and 29. On the street.

Example 7 has the same configuration as that of Example 4 in the configuration shown in FIG. 7, but each lens group, especially the first lens group G ₁
By increasing the refracting power of the second lens group G ₂ , the zoom lens has a wide angle of view of 62 ° and a wide angle of view of 12 and a high zoom ratio.

The aberrations of the seventh embodiment are shown in FIGS.
1, as shown in FIG.

The eighth embodiment has a structure as shown in FIG. 8 and is the same as the third embodiment. In Example 8, by increasing the refracting power of each lens group, particularly the first lens group G ₁ and the second lens group G ₂ , the angle of view at the wide-angle end is 62 ° and the zoom ratio is 12. The zoom lens has a high angle of view and a high zoom ratio.

The aberrations of the eighth embodiment are shown in FIGS.
4, as shown in FIG.

Example 9 is a zoom lens having a configuration as shown in FIG. 9, and has the same configuration as the zoom lens of Example 7, except that the refracting power of the third lens group is substantially zero. This differs from Example 7.

The aberrations of the ninth embodiment are shown in FIGS.
7, as shown in FIG.

The tenth embodiment has a construction as shown in FIG. 10, and in order from the object side, the positive first lens group G ₁ , the negative second lens group G ₂ , the diaphragm S, and the negative third lens. It is composed of a group G ₃ and a positive fourth lens group G ₄ . In each lens group, the first lens group G ₁ includes, in order from the object side, a negative meniscus lens having a convex surface directed to the object side and a positive lens having a surface having a strong positive refractive power directed to the object side. The second lens group G _{2 includes the} cemented lens, the positive lens with the surface having a strong positive refractive power facing the object side, and the positive meniscus lens with the convex surface facing the object side. From the object side, the third lens group G ₃ includes, in order from the object side, a negative meniscus lens having a convex surface facing the object side, a biconcave lens, and a positive meniscus lens having a convex surface facing the object side. And the negative second lens component of the cemented lens in which the biconcave lens and the positive lens with the positive refractive power facing the object side are cemented together, lens group G _4, in order from the object side, a positive first lens subunit G ₄₁ positive 42 Les And a's group G ₄₂ Prefecture. In the fourth lens group G ₄ , the 41st lens group G ₄₁ includes, in order from the object side, a positive meniscus lens having a concave surface facing the object side,
It consists of a positive lens with the positive refractive power facing the image side, and a negative meniscus lens with the concave surface facing the object side.
The 42nd lens group G ₄₂ includes, in order from the object side, a positive lens having a positive refractive power surface facing the image side, a negative meniscus lens having a convex surface facing the object side, and positive refraction toward the object side. It is made up of a cemented lens in which a positive lens with the stronger surface of the lens is attached.

The tenth embodiment is an example in which the number of lenses is the smallest in the tenth embodiment, the negative refracting power of the third lens group G ₃ is increased, and the 41st lens of the fourth lens group G ₄ is used. Aberrations are satisfactorily corrected by making the positive refractive powers of the group G ₄₁ and the 42nd lens group G ₄₂ close to even distribution.

The aberrations of the tenth embodiment are as shown in FIGS. 40, 41 and 42.

The eleventh embodiment has a configuration as shown in FIG. 11, and the first lens group G ₁ having a positive refractive power is arranged in order from the object side.
A second lens group G ₂ having a negative refractive power, a third lens group G ₃ having a negative refractive power, a diaphragm S, and a fourth lens group G ₄ having a positive refractive power. In each lens group, the first lens group G ₁ includes, in order from the object side, a negative meniscus lens having a convex surface directed toward the object side and a positive lens having a surface having a strong positive refractive power directed toward the object side. The second lens group G includes a cemented lens and two positive meniscus lenses each having a convex surface directed toward the object side.
₂ is, in order from the object side, a negative meniscus lens with a convex surface facing the object side, a cemented lens of a biconcave lens and a positive meniscus lens with a convex surface facing the object side, and a strong negative refractive power on the object side. The third lens group G ₃ includes, in order from the object side, a positive first biconvex lens.
It is composed of a lens component and a second lens component of a cemented lens of a biconcave lens and a positive lens having a surface having a strong positive refractive power facing the object side, and the fourth lens group G ₄ has a positive refractive power. The 41st lens group G ₄₁ and the 42nd lens group G having a positive refractive power
It consists of ₄₂ and. The 41st lens group G ₄₁ of the 4th lens group G ₄ includes, in order from the object side, a negative lens having a surface having a negative refractive power strong toward the image side and a lens having a positive refractive power strong toward the image side. Of two positive lenses and a negative meniscus lens having a concave surface facing the object side, and the 42nd lens group G ₄₂ includes, in order from the object side, a lens having a strong positive refractive power toward the image side. Of the positive lens, a cemented lens of a biconvex lens and a negative meniscus lens with a concave surface facing the object side, and a cemented lens of a biconvex lens and a negative meniscus lens with a concave surface facing the object side. ing.

In Example 11, since the diaphragm S is arranged between the third lens group G ₃ and the fourth lens group G ₄ , the third lens group G ₃ has negative axial chromatic aberration and positive axial chromatic aberration. The chromatic aberration of magnification has occurred, and the method of correcting the chromatic aberration of magnification is different from the other examples. Therefore, a large number of negative lenses are used in the fourth lens group G ₄ so as to suppress the occurrence of lateral chromatic aberration as much as possible so that the fourth lens group G ₄ is sufficiently corrected. In addition, since the diaphragm S is arranged between the third lens group G ₃ and the fourth lens group G ₄ in this way, the aperture diameter of the first lens group G ₁ is an example in which the angle of view is wide. The size is close to that of the lens system of Example 7. However, conversely, the apertures of the third lens group G ₃ and the fourth lens group G ₄ are small, which is an advantageous structure for disposing the diaphragm mechanism.

In the aberration curve diagrams of each of the above-mentioned examples, the e-line is the fundamental wavelength.

In the zoom lens of the present invention, in addition to the lens system described in each of the claims, the zoom lens described in each of the following items can also achieve the object of the present invention.

(1) In the lens system described in claim 1, the fourth lens group has, in order from the object side, a forty-first lens group having a positive refracting power as a whole,
It is composed of a 42nd lens group having a positive refracting power as a whole, and the 41st lens group has a positive meniscus lens having a concave surface facing at least one object side and a negative meniscus lens having a concave surface facing at least one object side. A meniscus lens or a biconcave lens having a surface having a negative refractive power facing the object side, and the 42nd lens group includes at least one positive lens and at least one negative lens, (4),
A zoom lens with a long back focus that satisfies (5).

(4) 0 <f ₄₂ / f ₄₁ <0.90 (5) 0.10 < _fw / f ₄₂ <0.50 (2) The lens system described in the item (1) above. so,
The 41st lens group of the 4th lens group includes, in order from the object side, a positive meniscus lens having a concave surface facing the object side, a first lens component of at least one positive lens, and a negative lens having a concave surface facing the object side. A zoom lens with a long back focus consisting of the second lens component of the meniscus lens.

(3) In the lens system described in the item (1), the 41st lens group of the 4th lens group has, in order from the object side, a negative surface having a concave surface facing at least one object side. A first lens component comprising a lens and a positive lens including at least a positive meniscus lens having a convex surface directed toward the image side or a positive lens having at least a biconvex positive lens having a positive refractive power surface directed toward the image side; A zoom lens with a long back focus, which is composed of two lens components and a third lens component which is a negative meniscus lens having a concave surface facing the object side.

[0097]

According to the present invention, an electronic camera using an image pickup tube, a solid-state image pickup device, and the like, which has a relatively simple zoom structure, has a large number of pixels suitable for use in capturing high-definition images in recent years. It has high optical performance, which is optimal for electronic cameras using image pickup devices, and it is possible to insert optical devices such as various filters and optical path splitting prisms between the optical system and the image pickup device. It is possible to obtain a zoom lens having a large back focus.

[Brief description of drawings]

FIG. 1 is a sectional view of a first embodiment of the present invention.

FIG. 2 is a sectional view of a second embodiment of the present invention.

FIG. 3 is a sectional view of a third embodiment of the present invention.

FIG. 4 is a sectional view of a fourth embodiment of the present invention.

FIG. 5 is a sectional view of a fifth embodiment of the present invention.

FIG. 6 is a sectional view of a sixth embodiment of the present invention.

FIG. 7 is a sectional view of a seventh embodiment of the present invention.

FIG. 8 is a sectional view of an eighth embodiment of the present invention.

FIG. 9 is a sectional view of a ninth embodiment of the present invention.

FIG. 10 is a sectional view of Example 10 of the present invention.

FIG. 11 is a sectional view of Embodiment 11 of the present invention.

FIG. 12 is an aberration curve diagram at the wide-angle end according to Example 1 of the present invention.

FIG. 13 is an aberration curve diagram for Example 1 of the present invention at an intermediate focal length.

FIG. 14 is an aberration curve diagram of Example 1 of the present invention at the telephoto end.

FIG. 15 is an aberration curve diagram at the wide-angle end according to Example 2 of the present invention.

FIG. 16 is an aberration curve diagram for Example 2 of the present invention at an intermediate focal length.

FIG. 17 is an aberration curve diagram for Example 2 of the present invention at the telephoto end.

FIG. 18 is an aberration curve diagram for Example 3 of the present invention at the wide-angle end.

FIG. 19 is an aberration curve diagram for Example 3 of the present invention at an intermediate focal length.

FIG. 20 is an aberration curve diagram for Example 3 of the present invention at the telephoto end.

FIG. 21 is an aberration curve diagram at the wide-angle end according to Example 4 of the present invention.

FIG. 22 is an aberration curve diagram for Example 4 of the present invention at an intermediate focal length.

FIG. 23 is an aberration curve diagram for Example 4 of the present invention at the telephoto end.

FIG. 24 is an aberration curve diagram at the wide-angle end according to Example 5 of the present invention.

FIG. 25 is an aberration curve diagram for Example 5 of the present invention at an intermediate focal length.

FIG. 26 is an aberration curve diagram for Example 5 of the present invention at the telephoto end.

FIG. 27 is an aberration curve diagram at the wide-angle end according to Example 6 of the present invention.

FIG. 28 is an aberration curve diagram for Example 6 of the present invention at an intermediate focal length.

FIG. 29 is an aberration curve diagram for Example 6 of the present invention at the telephoto end.

FIG. 30 is an aberration curve diagram at the wide-angle end according to Example 7 of the present invention.

FIG. 31 is an aberration curve diagram for Example 7 of the present invention at an intermediate focal length.

FIG. 32 is an aberration curve diagram for Example 7 of the present invention at the telephoto end.

FIG. 33 is an aberration curve diagram at the wide-angle end according to Example 8 of the present invention.

34 is an aberration curve diagram for Example 8 of the present invention at an intermediate focal length. FIG.

FIG. 35 is an aberration curve diagram for Example 8 of the present invention at the telephoto end.

FIG. 36 is an aberration curve diagram at the wide-angle end according to Example 9 of the present invention.

FIG. 37 is an aberration curve diagram at an intermediate focal length of Example 9 of the present invention.

FIG. 38 is an aberration curve diagram for Example 9 of the present invention at the telephoto end.

FIG. 39 is an aberration curve diagram at the wide-angle end according to Example 10 of the present invention.

FIG. 40 is an aberration curve diagram for Example 10 of the present invention at an intermediate focal length.

FIG. 41 is an aberration curve diagram for Example 10 of the present invention at the telephoto end.

FIG. 42 is an aberration curve diagram at the wide-angle end according to Example 11 of the present invention.

FIG. 43 is an aberration curve diagram at the intermediate focal length of Example 11 of the present invention.

FIG. 44 is an aberration curve diagram for Example 11 of the present invention at the telephoto end.

Claims (3)

[Claims] 1. A first lens group having a positive refracting power and fixed during zooming, and a second lens group having a negative refracting power and monotonically moving along the optical axis during zooming, in order from the object side. A third lens group having positive or negative refracting power and moving back and forth along the optical axis during zooming, and a fourth lens group having positive refracting power and moving back and forth along the optical axis during zooming, The third lens group,
A first lens component having a positive refractive power in order from the object side;
A back focus composed of a second lens component of a cemented lens having a negative refracting power as a whole obtained by bonding a biconcave negative lens and a biconvex or meniscus negative lens having a convex surface facing the object side. Long zoom lens. 2. A zoom lens with a long back focus according to claim 1, which satisfies the following conditions (1) and (2). (1) n _32n <n _32p (2) ν _32p <ν _32n where n _32p and n _32n are the refractive indices of the positive lens and the negative lens of the second lens component of the third lens group, and ν _32p and ν, respectively.
_32n is the Abbe number of the positive lens and the negative lens of the second lens component of the third lens group, respectively. 3. The method according to claim 1 or 2, which satisfies the following condition (3).
Long back focus zoom lens. _{(3) -0.30 <f w /} f 3 <0.10 where the f _w focal length, f ₃ of the entire system at the wide angle end is the focal length of the third lens group.