USPatent applicationPatented

Zoom lens and image pickup apparatus including the same

Granted 27 Jul 2021 · 4 office actions

Assignee: Canon Inc.

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Attorney: Attorney · Log in to unlock

Inventors: Shinichiro Saito · Examiner: Travis S Fissel · AU 2872 · TC 2800

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Abstract

A zoom lens includes in order from an object side to an image side: a first lens unit having a positive refractive power; a second lens unit having a negative refractive power; and a rear lens group which includes at least one lens unit and has a positive refractive power as a whole. Distances between the adjacent lens units change during zooming. The rear lens group includes a lens P 1 that has a positive refractive power and moves at image stabilization so as to have a component perpendicular to the optical axis. The shape factor SFP 1 of the lens P 1 , a curvature radius R 1 P 1 of a lens surface of the lens P 1 on the object side, and a curvature radius R 2 P 1 of a lens surface of the lens P 1 on the image side are appropriately determined.

Description

12 parts
BACKGROUND OF THE INVENTION
›Field of the Invention

The present invention relates to a zoom lens and an image pickup apparatus.

›Description of the Related Art

In recent years, the pickup optical system used in image pickup apparatuses is required to be a compact zoom lens with a short total lens length, which has a high zoom ratio and uses a focusing method implementing high-speed focusing. Moreover, the pickup optical system is required to have an anti-vibration function to correct blur (image blur) in taken images caused by shake or the like and prevent degradation of optical performances. Some conventionally known zoom lenses use an inner focusing method and perform image stabilization by using some of lens units that constitute the zoom lens.

Japanese Patent Application Laid-Open No. H09-90226 discloses a zoom lens which includes, in order from the object side to the image side, first to fifth lens units which have positive, negative, positive, positive, and negative refractive powers, respectively, and changes distances between the adjacent lens units during zooming. In the Japanese Patent Application Laid-Open No. H09-90226, focusing is performed by using the third lens unit while image stabilization is performed by using the fourth lens unit.

Japanese Patent Application Laid-Open No. 2011-128371 discloses a zoom lens which includes, in order from the object side to the image side, first to fifth lens units which have positive, negative, positive, positive, and positive refractive powers respectively and changes distances between the adjacent lens units during zooming. In the Japanese Patent Application Laid-Open No. 2011-128371, focusing is performed by using the third lens unit while image stabilization is performed by using the fourth lens unit.

Japanese Patent Application Laid-Open No. 2010-145759 discloses a zoom lens which includes, in order from the object side to the image side, first to fourth lens units which have positive, negative, positive, and positive refractive powers respectively and changes distances between the adjacent lens units during zooming. In the Japanese Patent Application Laid-Open No. 2010-145759, focusing is performed by using a part of the fourth lens unit while image stabilization is performed by using all or a part of the third lens unit.

›SUMMARY OF THE INVENTION

Zoom lenses are required to be compact as a whole while having a high zoom ratio and achieving high optical performances throughout the entire zoom range and object distance. Moreover, zoom lenses are required to maintain high optical performances at image stabilization.

Especially when a large image pickup apparatus using an image pickup element is equipped with a correction lens unit that is moved for image stabilization in a direction perpendicular to the optical axis, the correction lens unit is required to be compact and lightweight in order that the mechanism to move the correction lens unit can be downsized and achieve power saving. To satisfy these requirements, it is important to appropriately select the zoom type (the number of lens units, refractive power of each lens unit, and the like) and the lens unit for image stabilization and appropriately set the lens configuration such as refractive powers thereof.

An object of the present invention is to provide a compact zoom lens which has a high zoom ratio while easily maintaining high optical performances at image stabilization and provide an image pickup apparatus including the zoom lens.

A zoom lens of one aspect of the present invention includes in order from an object side to an image side: a first lens unit having a positive refractive power; a second lens unit having a negative refractive power; and a rear lens group which includes at least one lens unit and has a positive refractive power as a whole. Distances between the adjacent lens units change during zooming. The rear lens group includes a lens P 1 that has a positive refractive power and moves at image stabilization so as to have a component perpendicular to the optical axis, and the following conditional expression is satisfied: −2.5<SFP 1 <−0.5 where SFP 1 is a shape factor of the lens P 1 which is expressed by SFP 1 =(R 2 P 1 +R 1 P 1 )/(R 2 P 1 −R 1 P 1 ). Herein, R 1 P 1 is a curvature radius of a lens surface of the lens P 1 on the object side while R 2 P 1 is a curvature radius of a lens surface of the lens P 1 on the image side.

Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings.

›BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a lens cross-sectional view at a wide-angle end of Embodiment 1.

FIG. 1B is a lens cross-sectional view at a middle zoom position of Embodiment 1.

FIG. 1C is a lens cross-sectional view at a telephoto end of Embodiment 1.

FIG. 2A is an aberration diagram at the wide-angle end of Embodiment 1.

FIG. 2B is an aberration diagram at the middle zoom position of Embodiment 1.

FIG. 2C is an aberration diagram at the telephoto end of Embodiment 1.

FIG. 3AW is a lateral aberration diagram at the wide-angle end of the zoom lens of Embodiment 1 before image position displacement of 0.3 degrees.

FIG. 3AT is a lateral aberration diagram at a telephoto end of the zoom lens of Embodiment 1 before image position displacement of 0.3 degrees.

FIG. 3BW is a lateral aberration diagram at a wide-angle end of the zoom lens of Embodiment 1 after image position displacement of 0.3 degrees.

FIG. 3BT is a lateral aberration diagram at the telephoto end of the zoom lens of Embodiment 1 after image position displacement of 0.3 degrees.

FIG. 4A is a lens cross-sectional view at a wide-angle end of Embodiment 2.

FIG. 4B is a lens cross-sectional view at a middle zoom position of Embodiment 2.

FIG. 4C is a lens cross-sectional view at a telephoto end of Embodiment 2.

FIG. 5A is aberration diagram at the w middle zoom position of Embodiment 2.

FIG. 5B is aberration diagram at the telephoto end of Embodiment 2.

FIG. 5C is aberration diagram at the wide-angle end of Embodiment 2.

FIG. 6AW is a lateral aberration diagram at the wide-angle end of the zoom lens of Embodiment 2 before image position displacement of 0.3 degrees.

FIG. 6AT is a lateral aberration diagram at a telephoto end of the zoom lens of Embodiment 2 before image position displacement of 0.3 degrees.

FIG. 6BW is a lateral aberration diagram at a wide-angle end of the zoom lens of Embodiment 2 after image position displacement of 0.3 degrees.

FIG. 6BT is a lateral aberration diagram at the telephoto end of the zoom lens of Embodiment 2 after image position displacement of 0.3 degrees.

FIG. 7A is a lens cross-sectional view at a wide-angle end of Embodiment 3.

FIG. 7B is a lens cross-sectional view at a middle zoom position of Embodiment 3.

FIG. 7C is a lens cross-sectional view at a telephoto end of Embodiment 3.

FIG. 8A is an aberration diagram at the wide-angle end of Embodiment 3.

FIG. 8B is an aberration diagram at the middle zoom position of Embodiment 3.

FIG. 8C is an aberration diagram at the telephoto end of Embodiment 3.

FIG. 9AW is a lateral aberration diagram at the wide-angle end of the zoom lens of Embodiment 3 before image position displacement of 0.3 degrees.

FIG. 9AT is a lateral aberration diagram at a telephoto end of the zoom lens of Embodiment 3 before image position displacement of 0.3 degrees.

FIG. 9BW is a lateral aberration diagram at a wide-angle end of the zoom lens of Embodiment 3 after image position displacement of 0.3 degrees.

FIG. 9BT is a lateral aberration diagram at the telephoto end of the zoom lens of Embodiment 3 after image position displacement of 0.3 degrees.

FIG. 10A is a lens cross-sectional view at a wide-angle end of Embodiment 4.

FIG. 10B is a lens cross-sectional view at a middle zoom position of Embodiment 4.

FIG. 10C is a lens cross-sectional view at a telephoto end of Embodiment 4.

FIG. 11A is an aberration diagram at the wide-angle end of Embodiment 4.

FIG. 11B is an aberration diagram at the middle zoom position of Embodiment 4.

FIG. 11C is an aberration diagram at the telephoto end of Embodiment 4.

FIG. 12AW is a lateral aberration diagram at the wide-angle end of the zoom lens of Embodiment 4 before image position displacement of 0.3 degrees.

FIG. 12AT is a lateral aberration diagram at a telephoto end of the zoom lens of Embodiment 4 before image position displacement of 0.3 degrees.

FIG. 12BW is a lateral aberration diagram at a wide-angle end of the zoom lens of Embodiment 4 after image position displacement of 0.3 degrees.

FIG. 12BT is a lateral aberration diagram at the telephoto end of the zoom lens of Embodiment 4 after image position displacement of 0.3 degrees.

FIG. 13A is a lens cross-sectional view at a wide-angle end of Embodiment 5.

FIG. 13B is a lens cross-sectional view at a middle zoom position of Embodiment 5.

FIG. 13C is a lens cross-sectional view at a telephoto end of Embodiment 5.

FIG. 14A is an aberration diagram at the wide-angle end of Embodiment 5.

FIG. 14B is an aberration diagram at the middle zoom position of Embodiment 5.

FIG. 14C is an aberration diagram at the telephoto end of Embodiment 5.

FIG. 15AW is a lateral aberration diagram at the wide-angle end of the zoom lens of Embodiment 5 before image position displacement of 0.3 degrees.

FIG. 15AT is a lateral aberration diagram at a telephoto end of the zoom lens of Embodiment 5 before image position displacement of 0.3 degrees.

FIG. 15BW is a lateral aberration diagram at a wide-angle end of the zoom lens of Embodiment 5 after image position displacement of 0.3 degrees.

FIG. 15BT is a lateral aberration diagram at the telephoto end of the zoom lens of Embodiment 5 after image position displacement of 0.3 degrees.

FIG. 16 is a schematic diagram of main parts of an image pickup apparatus.

›DESCRIPTION OF THE EMBODIMENTS · 1 of 7

Preferred embodiments of the present invention will now be described in detail in accordance with the accompanying drawings. A zoom lens of the present invention includes the following lens units arranged in order from the object side to the image side. The zoom lens includes a first lens unit L 1 having a positive refractive power (optical power=the reciprocal of focal length), a second lens unit L 2 having a negative refractive power, and a rear lens group LR which includes at least one lens unit and has a positive refractive power as a whole.

At zooming, the lens units move so that distances between the adjacent lens units change. The lens unit closest to an object in the rear lens group LR or the lens closest to the object is referred to as a lens P 1 . The lens P 1 has a positive refractive power. The lens P 1 moves so as to have a component perpendicular to the optical axis as a correction lens unit for image stabilization.

FIGS. 1A, 1B, and 1C are lens cross-sectional views of a zoom lens of Embodiment 1 of the present invention at the wide-angle end (the short focal length end), a middle zoom position, and the telephoto end (the long focal length end), respectively. FIGS. 2A, 2B, and 2C are aberration diagrams of the zoom lens of Embodiment 1 at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 3AW and 3AT are lateral aberration diagrams of the zoom lens of Embodiment 1 at the wide-angle end and telephoto end, respectively. FIGS. 3BW and 3BT are lateral aberration diagrams of the zoom lens of Embodiment 1 at the wide-angle end and telephoto end after 0.3 degree-image stabilization, respectively. The zoom lens of Embodiment 1 has a zoom ratio of 3.34 and an aperture ratio (F-number) of about 3.30 to 5.50.

FIGS. 4A, 4B, and 4C are lens cross-sectional views of a zoom lens of Embodiment 2 of the present invention at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 5A, 5B, and 5C are aberration diagrams of the zoom lens of Embodiment 2 at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 6AW and EAT are lateral aberration diagrams of the zoom lens of Embodiment 2 at the wide-angle end and telephoto end, respectively. FIGS. 6BW and 6BT are lateral aberration diagrams of the zoom lens of Embodiment 2 after 0.3 degree-image stabilization at the wide-angle end and telephoto end, respectively. The zoom lens of Embodiment 2 has a zoom ratio of 3.25 and an aperture ratio of about 3.84 to 5.84.

FIGS. 7A, 7B, and 7C are lens cross-sectional views of a zoom lens of Embodiment 3 of the present invention at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 8A, 8B, and 8C are aberration diagrams of the zoom lens of Embodiment 3 at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 9 AW and 9 AT are lateral aberration diagrams of the zoom lens of Embodiment 3 at the wide-angle end and telephoto end, respectively. FIGS. 9BW and 9BT are lateral aberration diagrams of the zoom lens of Embodiment 3 after 0.3 degree-image stabilization at the wide-angle end and telephoto end, respectively. The zoom lens of Embodiment 3 has a zoom ratio of 2.88 and an aperture ratio of about 4.12 to 5.7.

FIGS. 10A, 10B, and 10C are lens cross-sectional views of a zoom lens of Embodiment 4 of the present invention at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 11A, 11B, and 11C are aberration diagrams of the zoom lens of Embodiment 4 at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 12AW and 12AT are lateral aberration diagrams of the zoom lens of Embodiment 4 at the wide-angle end and telephoto end, respectively. FIGS. 12BW and 12BT are lateral aberration diagrams of the zoom lens of Embodiment 4 after 0.3 degree-image stabilization at the wide-angle end and telephoto end, respectively. The zoom lens of Embodiment 4 has a zoom ratio of 2.87 and an aperture ratio of about 3.64 to 5.29.

FIGS. 13A, 13B, and 13C are lens cross-sectional views of a zoom lens of Embodiment 5 of the present invention at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 14A, 14B, and 14C are aberration diagrams of the zoom lens of Embodiment 5 at the wide-angle end, middle zoom position, and telephoto end, respectively. FIGS. 15AW and 15AT are lateral aberration diagrams of the zoom lens of Embodiment 5 at the wide-angle end and telephoto end, respectively. FIGS. 15BW and 15BT are lateral aberration diagrams of the zoom lens of Embodiment 5 after 0.3 degree-image stabilization at the wide-angle end and telephoto end, respectively. The zoom lens of Embodiment 5 has a zoom ratio of 3.17 and an aperture ratio of about 4.12 to 5.82.

The zoom lens of each embodiment is an image pickup optical system used in an image pickup apparatus, such as a video camera, a digital still camera, a silver-halide film camera, or a TV camera. The zoom lens of each embodiment can be used as a projection optical system for a projection apparatus (a projector). The left side in the lens cross-sectional views corresponds to the object side (the front side) while the right side corresponds to the image side (the rear side). In the lens cross-sectional views, i indicates the number of lens units arranged on the object side of the lens unit of interest. Li indicates an i-th lens unit. L 1 indicates a first lens unit having a positive refractive power while L 2 indicates a second lens unit having a negative refractive power.

LR indicates a rear lens group which includes at least one lens unit having a positive refractive power and has a positive refractive power as a whole. SP indicates an aperture stop having a maximum aperture F-number (Fno) and determines (limits) a light flux. FP indicates a flare cut stop to cut unnecessary light. IP indicates an image plane. When the zoom lens of each embodiment is used as the image pickup optical system of a video camera or digital still camera, the image pickup plane of a solid-state image sensing device (a photoelectric conversion element) such as a CCD sensor or a CMOS sensor is placed at the image plane IP. When the zoom lens of each embodiment is used as the image pickup optical system of a silver-halide film camera, the photosensitive plane corresponding to the film plane is placed.

›DESCRIPTION OF THE EMBODIMENTS · 2 of 7

Arrows indicate movement loci of the respective lens units at zooming from the wide-angle end to the telephoto end. Each arrow relating to focusing indicates the direction of movement of the lens unit at focusing from infinity to a close distance.

In each embodiment, the rear lens group LR includes in order from the object side to the image side: a third lens unit L 3 having a positive refractive power; a fourth lens unit L 4 having a positive refractive power; and a fifth lens unit L 5 having a positive refractive power. The third lens unit L 3 is composed of one positive lens, which is the lens P 1 for image stabilization. Moreover, the rear lens group LR includes in order from the object side to the image side: a third lens unit L 3 having a positive refractive power; a fourth lens unit L 4 having a negative refractive power; and a fifth lens unit L 5 having a positive refractive power. The third lens unit L 3 is composed of one positive lens, which is a lens P 1 for image stabilization.

Moreover, the rear lens group LR includes in order from the object side to the image side: a third lens unit L 3 having a positive refractive power; a fourth lens unit L 4 having a negative refractive power; and a fifth lens unit L 5 having a positive refractive power. The third lens unit L 3 is composed of a plurality of lenses including a positive lens P 1 located closest to the object. The positive lens P 1 is the lens for image stabilization.

In Embodiment 1 of FIGS. 1A, 1B, and 1C , L 1 indicates the first lens unit having a positive refractive power; L 2 , the second lens unit having a negative refractive power; L 3 , the third lens unit having a positive refractive power; L 4 , the fourth lens unit having a positive refractive power; and L 5 , the fifth lens unit having a positive refractive power. The rear lens group LR is composed of the third, fourth, and fifth lens units L 3 , L 4 , and L 5 .

In the zoom lens of Embodiment 1, at zooming from the wide-angle end to the telephoto end, the first lens unit L 1 monotonically moves toward the object side. The second lens unit L 2 to fifth lens unit L 5 move toward the object side so that the distance between the first and second lens units L 1 and L 2 at the telephoto end is longer than that at the wide-angle end while the distance between the second and third lens units L 2 and L 3 is shorter. In Embodiment 1, at image stabilization, the third lens unit L 3 moves so as to have a component perpendicular to the optical axis. The third lens unit L 3 is the lens P 1 for image stabilization composed of a single lens and is configured to correct the image position.

In Embodiment 1, the third lens unit L 3 moves on the optical axis for focusing. Solid curve 3 a of the third lens unit L 3 indicates the locus of movement to correct a change in image plane during zooming from the wide-angle end to the zoom position at the telephoto end when the zoom lens is focused on infinity. Dotted curve 3 b of the third lens unit L 3 indicates the locus of movement to correct a change in image plane during zooming from the wide-angle end to the zoom position at the telephoto end when the zoom lens is focused on a close distance. In the process of focusing from infinity to a close distance at the zoom position of the telephoto end, the third lens unit L 3 is retracted rearward as indicated by arrow 3 c.

In Embodiment 2 of FIGS. 4A, 4B, and 4C and Embodiment 3 of FIGS. 7A, 7B, and 7C , L 1 indicates a first lens unit having a positive refractive power; L 2 , a second lens unit having a negative refractive power; L 3 , a third lens unit having a positive refractive power; L 4 , a fourth lens unit having a negative refractive power; and L 5 , a fifth lens unit having a positive refractive power. The rear lens group LR is composed of the third, fourth, and fifth lens units L 3 , L 4 , and L 5 .

In the zoom lenses of Embodiments 2 and 3, at zooming from the wide-angle end to the telephoto end, the first lens unit L 1 monotonically moves toward the object side. The second lens unit L 2 to fifth lens unit L 5 move toward the object side, so that the distance between the first and second lens units L 1 and L 2 at the telephoto end is longer than that at the wide-angle end while the distance between the second and third lens units L 2 and L 3 is shorter. In Embodiments 2 and 3, at image stabilization, the third lens unit L 3 moves so as to have a component perpendicular to the optical axis. The third lens unit L 3 is the lens P 1 for image stabilization composed of a single lens.

In Embodiments 2 and 3, the fourth lens unit L 4 is moved on the optical axis for focusing. Solid curve 4 a of the fourth lens unit L 4 indicates the locus of movement to correct a change in image plane at zooming from the wide-angle end to the zoom position of the telephoto end when the zoom lens is focused on infinity. Dotted curve 4 b of the fourth lens unit L 4 indicates the locus of movement to correct a change in image plane at zooming from the wide-angle end to the zoom position at the telephoto end when the zoom lens is focused on a close distance. In the process of focusing from infinity to a close distance at the zoom position of the telephoto end, the fourth lens unit L 4 is advanced forward as indicated by arrow 4 c.

In Embodiment 4 of FIGS. 10A, 10B, and 10C , L 1 indicates a first lens unit having a positive refractive power; L 2 , a second lens unit having a negative refractive power; L 3 , a third lens unit having a positive refractive power; L 4 , a fourth lens unit having a negative refractive power; and L 5 , a fifth lens unit having a positive refractive power. The rear lens group LR is composed of the third, fourth, and fifth lens units L 3 , L 4 , and L 5 .

In the zoom lens of Embodiment 4, at zooming from the wide-angle end to the telephoto end, the first lens unit L 1 monotonically moves toward the object side. The second lens unit L 2 to fifth lens unit L 5 move toward the object side so that the distance between the first and second lens units L 1 and L 2 at the telephoto end is longer than that at the wide-angle end; the distance between the second and third lens units L 2 and L 3 is shorter; the distance between the third and fourth lens units L 3 and L 4 is shorter; and the distance between the fourth and fifth lens units L 4 and L 5 is longer.

›DESCRIPTION OF THE EMBODIMENTS · 3 of 7

In Embodiment 4, at image stabilization, the positive lens P 1 closest to the object in the third lens unit L 3 moves so as to have a component perpendicular to the optical axis. In Embodiment 4, the fourth lens unit L 4 of the fourth lens unit L 4 is moved on the optical axis for focusing. Solid curve 4 a of the fourth lens unit L 4 indicates the locus of movement to correct a change in image plane at zooming from the wide-angle end to the zoom position of the telephoto end when the zoom lens is focused on infinity. Dotted curve 4 b of the fourth lens unit L 4 indicates the locus of movement to correct a change in image plane at zooming from the wide-angle end to the zoom position of the telephoto end when the zoom lens is focused on a close distance. In the process of focusing from infinity to a close distance at the zoom position of the telephoto end, the fourth lens unit L 4 is retracted rearward as indicated by arrow 4 c.

In Embodiment 5 of FIGS. 13A, 13B, and 13C , L 1 indicates a first lens unit having a positive refractive power; L 2 , a second lens unit having a negative refractive power; L 3 , a third lens unit having a positive refractive power; L 4 , a fourth lens unit having a negative refractive power; and L 5 , a fifth lens unit having a positive refractive power. The rear lens group LR is composed of the third, fourth, and fifth lens units L 3 , L 4 , and L 5 .

In the zoom lens of Embodiment 5, at zooming from the wide-angle end to the telephoto end, the first lens unit L 1 monotonically moves toward the object side. The second lens unit L 2 to fifth lens unit L 5 move toward the object side so that the distance between the first and second lens units L 1 and L 2 at the telephoto end is longer than that at the wide-angle end and the distance between the second and third lens units L 2 and L 3 is shorter. In Embodiment 5, at image stabilization, the third lens unit L 3 moves so as to have a component perpendicular to the optical axis. The third lens unit L 3 is the positive lens P 1 for image stabilization which is composed of a single lens. The focusing process in Embodiment 5 is the same as that in Embodiment 1.

In the aberration diagrams, Fno is the F-number, and ω is a half angle of view (degree), which is calculated by optical ray tracing. In the spherical aberration diagrams, d indicates aberration for the d-line (wavelength: 587.56 nm), and g indicates aberration for the g-line (wavelength: 435.835 nm).

In the astigmatism diagrams, ΔS indicates astigmatism for the d-line in the sagittal plane, and ΔM indicates astigmatism for the d-line in the meridional image plane. The distortion is illustrated for the d-line. In the lateral chromatic aberration diagrams, g indicates aberration for the g-line. In the lateral aberration diagrams, curves at the top to bottom in each diagram correspond to image heights of 10, 0, and −10 mm, respectively. ΔS indicates aberration for the d-line in the sagittal cross section, and ΔM indicates aberration for the d-line in the meridional cross section.

In each embodiment, the wide-angle end and telephoto end refer to zoom positions where the lens unit to change the magnification is located at both ends of a mechanically movable range on the optical axis.

The zoom lens of the present invention includes in order from the object side to the image side: the first lens unit L 1 having a positive refractive power; the second lens unit L 2 having a negative refractive power; and the rear lens group LR which includes at least one lens unit and has a positive refractive power as a whole. The distances between the adjacent lens units change during zooming. The rear lens group LR includes the lens P 1 which has a positive refractive power and moves so as to have a component perpendicular to the optical axis at image stabilization.

The lens P 1 has a shape factor SFP 1 that satisfies the conditional expression (1):

−2.5< SFP 1<−0.5  (1).

The shape factor SFP 1 is expressed by:

SFP 1=( R 2 P 1+ R 1 P 1)/( R 2 P 1− R 1 P 1)

where R 1 P 1 is the curvature radius of the lens surface of the lens P 1 on the object side and R 2 P 1 is the curvature radius of the lens surface of the lens P 1 on the image side (when the lens surfaces are aspherical, the curvature radius thereof is a paraxial curvature radius (the radius of a referential quadric surface).

In order to shorten the total lens length at the wide-angle end while successfully correcting various aberrations throughout the entire zoom range, the zoom lens has a lens configuration composed, in order from the object side to the image side, of the first lens unit L 1 having a positive refractive power; the second lens unit L 2 having a negative refractive power; and the rear lens group LR having a positive refractive power as a whole. The configuration including at least three lens units allows for effective correction of various aberrations, such as spherical aberration and coma caused by the first and second lens units L 1 and L 2 .

In order to implement downsize of the zoom lens and high zoom ratio, zooming is performed by changing the distances between the lens units so that the distance between the first and second lens units L 1 and L 2 at the telephoto end is longer than that at the wide-angle end and the distance between the second and third lens units L 2 and L 3 is shorter. The rear lens group LR having a positive refractive power as a whole is provided with the aperture stop SP, and the lens P 1 having a positive refractive power is provided adjacent to the aperture stop SP. The lens P 1 having a positive refractive power (the correction lens unit) is moved so as to have a component perpendicular to the optical axis for image stabilization. This allows for correction of large image blur with small movement of the lens P 1 .

The conditional expression (1) defines the shape factor of the lens P 1 to reduce decentration aberration mainly caused by image stabilization and maintain good optical performances. When the shape factor SFP 1 is greater than the upper limit of the conditional expression (1) and the lens P 1 is decentered, it is difficult to secure a high imaging performance due to large decentration partial blur although decentration coma can be corrected successfully, which is not preferred. When the shape factor SFP 1 is less than the lower limit in the conditional expression (1), the decentration partial blur and decentration astigmatism can be corrected successfully, but decentration coma is hardly reduced. It is therefore difficult to downsize the zoom lens while securing the amount of movement required to shift the image by a predetermined amount for image stabilization.

›DESCRIPTION OF THE EMBODIMENTS · 4 of 7

In order to reduce the size and weight of the correction lens for image stabilization and reduce the number of lenses of the zoom lens, image stabilization is performed by using the lens P 1 having a positive refractive power in the rear lens group LR. Moreover, in order to minimize the lens configuration of the correction lens for image stabilization, the correction lens is composed of the one lens P 1 having a positive refractive power.

In each embodiment, the numerical range of the conditional expression (1) is preferably set as follows:

−2.1< SFP 1<−0.6  (1a).

By satisfying the conditional expression (1a), the sensitivity of the lens P 1 to decentration coma at the wide-angle end can be reduced, facilitating securing a high imaging performance. Moreover, the numerical range of the conditional expression (1a) is more preferably set as follows:

−1.6< SFP 1<−0.7  (1b).

By employing the lens units having an appropriate configuration and satisfying the conditional expression (1) as described above, the zoom lens can be downsized, and the zoom lens has a high zoom ratio and provides a high imaging performance throughout the entire zoom range. Moreover, the lens P 1 for image stabilization can be easily reduced in size and weight.

In each embodiment, it is still more preferable that the zoom lens satisfies at least one of the following conditional expressions:

0.01<β st/βsw< 3.20  (2);

1.8< D 23 w/D 23 t< 20.0  (3);

1.0<|1−β Pw|< 25.0  (4);

1.1< fP/fRt< 4.8  (5);

0.7< fRt/fw< 2.0  (6);

0.5<(1−β Pt )×β Rt< 1.8  (7);

1.45< nP< 1.75  (8); and

45.0<ν P< 100.0  (9).

In the above conditional expressions, βsw is a lateral magnification of a composite system of the second lens unit L 2 to the lens P 1 at the wide-angle end, and βst is a lateral magnification of the composite system of the second lens unit L 2 to the lens P 1 at the telephoto end. D 23 w is a distance on the optical axis between the second and third lens units L 2 and L 3 at the wide-angle end, and D 23 t is a distance on the optical axis between the second and third lens units L 2 and L 3 at the telephoto end.

βPw is a lateral magnification of the lens P 1 at the wide-angle end. fP is the focal length of the lens P 1 , and fRt is the focal length of the rear lens group LR at the telephoto end. fw is the focal length of the zoom lens at the wide-angle end. βPt is a lateral magnification of the lens P 1 at the telephoto end, and βRt is a lateral magnification of the optical system provided on the image side of the lens P 1 at the telephoto end. nP and νP are the refractive power and Abbe number of the material of the lens P 1 for the d-line, respectively.

The Abbe number νd of the material is defined as follows:

ν d =( Nd− 1)/( NF−NC ),

where Nd, NF, and NC are refractive powers for the d-line, F-line, and C-line of the Fraunhofer lines, respectively.

Next, a description is given of the technical meaning of each of the aforementioned conditional expressions. The conditional expression (2) relates to variations in lateral magnification at zooming in the composite system of the second lens unit L 2 to the lens P 1 . The conditional expression (2) is to optimize the magnification changing effect of the second lens unit L 2 and maintain good optical performances at image stabilization by the lens P 1 . When βst/βsw is greater than the upper limit in the conditional expression (2), the magnification changing effect of the second lens unit L 2 at the telephoto end is increased, so that it is easy to obtain the magnification changing effect at the telephoto end. However, it is difficult to maintain good optical performances at image stabilization and especially reduce decentration coma, which is not preferred.

When βst/βsw is less than the lower limit in the conditional expression (2), it is difficult to obtain a desired zoom ratio of the zoom lens. Alternatively, other lens units are configured to be responsible for a large magnification changing effect. This increases the total lens length at the telephoto end, making it difficult to downsize the zoom lens.

The conditional expression (3) defines an appropriate range of a ratio of air space between the second and third lens units L 2 and L 3 on the optical axis at the telephoto end to that at the wide-angle end. When the ratio is less than the lower limit in the conditional expression (3), the total lens length is increased at the telephoto end, and the front lens effective diameter is increased. Moreover, spherical aberration is not corrected sufficiently at the telephoto end, which is not preferred.

Furthermore, the magnification changing effect of the rear lens group LR at zooming is increased. This increases the sensitivity of spherical aberration and coma to manufacturing error of the rear lens group LR, thus making it difficult to implement a high zoom ratio. When the ratio exceeds the upper limit in the conditional expression (3), it is difficult to equalize the aberration correction effect of each lens unit at zooming, and it is difficult to reduce variations in field curvature at zooming. Moreover, the field curvature is increased to the negative side in the telephoto side, and in the wide-angle side, considerable flare could be produced due to light fluxes below the principal ray, which is not preferred.

The conditional expression (4) defines the lateral magnification of the lens P 1 for image stabilization at the wide-angle end. In the case where |1−βPw| is greater than the upper limit in the conditional expression (4), the image is shifted by a small amount when the lens P 1 is decentered by a predetermined amount so as to have a component perpendicular to the optical axis. Accordingly, the lens needs to be moved by a large amount in order to correct image displacement for image blurring, making it difficult to downsize the zoom lens. In the case where |1−βPw| is less than the lower limit in the conditional expression (4), the decentration sensitivity of the lens P 1 is increased. When the lens P 1 is decentered by a predetermined amount so as to have a component perpendicular to the optical axis, decentration field curvature is therefore increased, which is not preferred.

›DESCRIPTION OF THE EMBODIMENTS · 5 of 7

The conditional expression (5) defines the focal length of the lens P 1 which is moved so as to have a component perpendicular to the optical axis for image stabilization based on the focal length of the rear lens group LR at the telephoto end. The conditional expression (5) is to successfully correct various aberrations due to image stabilization, especially decentration coma in the telephoto side. Moreover, the conditional expression (5) is to facilitate reduction of the lens effective diameter of the rear lens group LR through the light flux convergence of the lens P 1 .

When fP/fRt is greater than the upper limit in the conditional expression (5), the low positive refractive power of the lens P 1 reduces image shift sensitivity TS, so that the amount of displacement of the lens P 1 at image stabilization is increased, which is not preferred.

Herein, the image shift sensitivity TS refers to the ratio of perpendicular displacement ΔL of a shift lens when the shift lens is moved in the direction perpendicular to the optical axis to displacement ΔI of an image (an imaging position) perpendicular to the optical axis on the image plane:

TS=ΔI/ΔL.

When fP/fRt is less than the lower limit in the conditional expression (5), the excessively high positive refractive power of the lens P 1 makes it difficult to secure backfocus of a predetermined length, which is not preferred.

The conditional expression (6) defines the ratio of the focal length of the rear lens group LR at the telephoto end to the focal length of the zoom lens at the wide-angle end. The conditional expression (6) is mainly to successfully correct various aberrations, such as spherical aberration and coma, while shortening the total lens length at the wide-angle end. When fRt/fw is greater than the upper limit in the conditional expression (6), the positive refractive power of the rear lens group LR is excessively low, so that displacements of lens units necessary for changing the magnification in the rear lens group LR are increased, which is not preferred. Moreover, the total lens length at the wide-angle end tends to be increased, which is not preferred. When fRt/fw is less than the lower limit in the conditional expression (6), the excessively high positive refractive power of the rear lens group LR makes it difficult to correct spherical aberration, coma, astigmatism, and the like in a balanced manner.

The conditional expression (7) defines the image shift sensitivity at image stabilization of the lens P 1 . When (1−βPt)×βRt is greater than the upper limit in the conditional expression (7), the displacement of the lens P 1 necessary to shift the image by a predetermined amount is increased, so that it is difficult to downsize the zoom lens. Moreover, it is difficult to reduce variations in aberration when the lens P 1 is moved in order to shift the image by a predetermined amount. When (1−βPt)×βRt is less than the lower limit in the conditional expression (7), the image is shifted by a large amount with very small movement of the lens unit P 1 . It is therefore necessary to control image displacement with a high level of accuracy, which is not preferred.

The conditional expressions (8) and (9) define the material constituting the lens P 1 . The conditional expressions (8) and (9) are to mainly reduce the occurrence of axial chromatic aberration at the wide-angle end while reducing the occurrence of chromatic aberration when the lens P 1 is decentered. When the refractive index and Abbe number of the material of the lens P 1 are within the ranges of the conditional expressions (8) and (9), the field curvature and decentering chromatic curvature are easily corrected at image stabilization.

It is desirable in each embodiment that the rear lens group LR includes at least one aspherical surface. The rear lens group LR desirably includes at least one aspherical surface in order to effectively correct field curvature at the wide-angle end while downsizing the zoom lens.

According to the present invention, as described above, it is possible to easily obtain a zoom lens which is short in total lens length at the wide-angle end, easily performs image stabilization with a simple configuration, successfully corrects various aberrations, such as spherical aberration, coma, and field curvature, and therefore provides high optical performances. More preferably, the numerical ranges of the conditional expressions (2) to (9) are set as follows:

0.1<β st/βsw< 2.5  (2a);

2.4< D 23 w/D 23 t< 18.0  (3a);

1.3<|−β Pw|< 22.0  (4a);

1.25< fP/fRt< 4.00  (5a);

1.0< fRt/fw< 1.8  (6a);

0.6<(1−β Pt )×β Rt< 1.7  (7a);

1.47< nP< 1.70  (8a); and

50.0<ν P< 85.0  (9a).

Satisfying the conditional expression (2a) further optimizes the magnification changing effect of the second lens unit L 2 , so that correction of field curvature is easily implemented when the angle of view is increased. Satisfying the conditional expression (3a) further optimizes the distances between the second and third lens units L 2 and L 3 at the wide-angle end and telephoto end, facilitating reduction of the front lens effective diameter. Satisfying the conditional expression (4a) optimizes the image shift sensitivity of the lens P 1 while easily reducing deterioration in image quality at image stabilization.

Satisfying the conditional expression (5a) allows for shortening of the total lens length at the wide-angle end while facilitating optimization of the shift sensitivity of the lens P 1 . Satisfying the conditional expression (6a) secures long enough backfocus at the wide-angle end while facilitating an increase in angle of view. Moreover, it becomes easy to further reduce variations in field curvature due to focusing throughout the entire zoom range.

Satisfying the conditional expression (7a) optimizes the image shift sensitivity of the lens P 1 at the telephoto end and facilitates reduction in size and weight of the lens P 1 . Satisfying the conditional expressions (8a) and (9a) facilitates further reducing variations in axial chromatic aberration and variations in lateral chromatic aberration and image curvature at image stabilization. Still More preferably, the numerical ranges of the conditional expressions (2a) to (9a) are set as follows:

›DESCRIPTION OF THE EMBODIMENTS · 6 of 7

0.2<β st/βsw< 2.3  (2b);

3.0< D 23 t/D 23 w< 17.0  (3b);

1.58<|1−β Pw|< 20.00  (4b);

1.5< fP/fRt< 3.4  (5b);

1.3< fRt/fw< 1.6  (6b);

0.7<(1−β Pt )×β Rt< 1.4  (7b);

1.48< nP< 1.65  (8b); and

58.0<ν P< 72.0  (9b).

Next, a description is given of an embodiment of a digital still camera using a zoom lens of the present invention as an image pickup optical system with reference to FIG. 16 . In FIG. 16 , reference numeral 10 denotes a camera body, and reference numeral 11 denotes an image pickup optical system composed of any one of the zoom lenses described in Embodiments 1 to 5. Reference numeral 12 denotes a solid-state image sensing element (a photoelectric conversion element), such as a CCD sensor or a CMOS sensor, which is incorporated in the camera body and is configured to receive an object image formed by the image pickup system 11 .

Hereinafter, specific numerical data corresponding to Embodiments 1 to 5 are shown. In the numerical data, i indicates a surface number located between the object and the surface of interest. ri indicates a curvature radius of the i-th optical surface (the i-th surface). di indicates an on-axis distance between the i-th and (i+1)-th surfaces. ndi and νdi are the refractive index and Abbe number of the material of the optical member between the i-th and (i+1)-th surfaces for the d line. Aspherical shapes are expressed by:

X = H 2 R 1 + 1 - ( 1 + K ) ⁢ ( H R ) 2 + A ⁢ ⁢ 4 ⁢ H 4 + A ⁢ ⁢ 6 ⁢ H 6 + A ⁢ ⁢ 8 ⁢ H 8 + A ⁢ ⁢ 10 ⁢ ⁢ H 10 + A ⁢ ⁢ 12 ⁢ H 12

where the X axis corresponds to the optical axis direction, the H axis corresponds to the direction perpendicular to the optical axis, the light travel direction is set to positive, R is a paraxial curvature radius, K is a conic constant, and A4, A6, A8, A10, and A12 are aspheric coefficients. * denotes a surface having an aspheric profile. “e-x” means “×10 −x ”. BF means backfocus, indicating the distance between the last lens surface and image plane. The total lens length is a sum of the distance between the first lens surface and the last lens surface and the backfocus distance. “Wide” indicates the wide-angle end, “Middle” indicates the middle zoom position, and “Telephoto” indicates the telephoto end. Table 1 shows the relationship between parameters concerning the aforementioned conditional expressions and numerical examples corresponding to each conditional expression.

[Numerical Data 1]

[unit: mm] Surface data Surface number r d nd νd  1 62.156 1.80 1.90366 31.3  2 36.268 7.54 1.71300 53.9  3 −4672.434 (variable)  4 59.690 1.20 1.83481 42.7  5 11.796 6.97  6* −30.926 1.10 1.55332 71.7  7 26.683 0.30  8 22.131 3.21 1.85478 24.8  9 130.703 (variable) 10 330.831 1.90 1.48749 70.2 11 −41.976 (variable) 12(stop) ∞ 2.00 13* 12.178 5.65 1.55332 71.7 14 −32.945 0.55 15 −44.850 1.00 1.91082 35.3 16 27.804 3.05 17 −306.745 2.07 1.59551 39.2 18 −24.487 0.75 1.83481 42.7 19 102.330 (variable) 20 25.065 2.34 1.58313 59.4 21* −51.815 (variable) Image plane ∞ Aspheric surface data 6th surface K = 0.00000e+000 A4 = 4.75383e−006 A6 = −2.99582e−008 A8 = −3.56889e−010 13th surface K = 0.00000e+000 A4 = −1.72486e−005 A6 = −3.11927e−009 A8 = −1.97961e−009 21st surface K = 0.00000e+000 A4 = 9.34164e−005 A6 = 2.72542e−007 A8 = 1.85157e−009 Various data Zoom ratio 3.34 Wide angle Middle Telephoto Focal length 17.52 35.37 58.59 F-number 3.30 4.63 5.50 Half angle of view (deg) 29.71 15.79 9.69 Image height 10.00 10.00 10.00 Total lens length 107.58 123.02 144.65 BF 35.15 52.16 63.16 d3 1.00 13.15 29.09 d9 22.16 8.55 3.81 d11 6.50 6.83 6.40 d19 1.35 0.91 0.78 d21 35.15 52.16 63.16 Lens unit data Unit Start surface Focal length 1 1 105.29 2 4 −15.61 3 10 76.54 4 12 276.55 5 20 29.30

[Numerical Data 2]

[unit: mm] Surface data Surface number r d nd νd  1 50.263 1.50 1.84666 23.8  2 38.708 5.77 1.65160 58.5  3 307.011 (variable)  4* 38.523 1.10 1.95375 32.3  5 10.858 6.82  6 −40.949 0.90 1.65844 50.9  7 27.291 1.00  8 22.625 2.65 1.89286 20.4  9 346.462 (variable) 10 −144.105 1.50 1.48749 70.2 11 −31.973 1.50 12(stop) ∞ (variable) 13 −34.224 0.80 1.77250 49.6 14 −267.275 (variable) 15 11.193 4.16 1.49700 81.5 16 82.620 0.30 17 21.750 4.18 1.53775 74.7 18 −18.579 1.00 1.90366 31.3 19 −25.563 0.54 20* −95.955 1.00 1.83220 40.1 21* 30.818 (variable) Image plane ∞ Aspheric surface data 4th surface K = 0.00000e+000 A4 = 3.40292e−006 A6 = −1.01860e−008 A8 = 9.24689e−012 20th surface K = 0.00000e+000 A4 = −2.08307e−004 A6 = 2.91060e−006 A8 = −1.29153e−007 A10 = 3.29179e−009 A12 = −3.47581e−011 21st surface K = −3.91679e+001 A4 = 1.29989e−004 A6 = 7.26953e−007 A8 = −4.36629e−008 A10 = 2.14923e−009 A12 = −2.27788e−011 Various data Zoom ratio 3.25 Wide angle Middle Telephoto Focal length 16.37 34.52 53.28 F-number 3.84 4.98 5.84 Half angle of view (deg) 31.42 16.16 10.63 Image height 10.00 10.00 10.00 Total lens length 100.08 115.04 131.43 BF 35.60 50.02 59.56 d3 1.00 15.73 27.04 d9 20.26 6.37 2.30 d12 6.26 6.33 6.54 d14 2.22 1.85 1.27 d21 35.60 50.02 59.56 Lens unit data Unit Start surface Focal length 1 1 101.33 2 4 −16.20 3 10 83.92 4 13 −50.89 5 15 20.48

[Numerical Data 3]

[unit: mm] Surface data Surface number r d nd νd  1 46.149 1.60 1.80518 25.4  2 35.132 6.92 1.60311 60.6  3 266.045 (variable)  4 38.823 1.00 1.91082 35.3  5 11.173 6.60  6 −54.453 0.85 1.69680 55.5  7 24.324 0.21  8 19.094 3.98 1.85478 24.8  9 532.538 (variable) 10(stop) ∞ 2.75 11 387.889 1.51 1.48749 70.2 12 −32.737 (variable) 13 −23.815 0.68 1.77250 49.6 14 −547.091 (variable) 15 14.949 4.35 1.59522 67.7 16 −65.249 0.20 17 18.168 4.00 1.72000 50.2 18 −29.900 0.65 1.91082 35.3 19 17.833 1.22 20 54.000 1.70 1.53110 55.9 21* −153.320 (variable) 22 ∞ 35.50  Image plane ∞ Aspheric surface data 21st surface K = 0.00000e+000 A4 = 1.61053e−004 A6 = 7.92230e−007 A8 = 1.89252e−008 A10 = −2.39009e−010 A12 = 3.76860e−012 Various data Zoom ratio 2.28 Wide angle Middle Telephoto Focal length 18.57 34.92 53.41 F-number 4.12 4.93 5.71 Half angle of view (deg) 36.34 21.36 14.35 Image height 13.66 13.66 13.66 Total lens length 104.14 116.44 129.94 BF 35.50 35.50 35.50 d3 0.92 16.52 26.85 d9 21.93 8.73 3.40 d12 4.07 4.14 4.63 d14 2.21 2.14 1.65 d21 1.29 11.18 19.69 Lens unit data Unit Start surface Focal length 1 1 103.44 2 4 −18.76 3 10 62.00 4 13 −32.25 5 15 19.03 6 22 ∞

›DESCRIPTION OF THE EMBODIMENTS · 7 of 7

[Numerical Data 4]

[unit: mm] Surface data Surface number r d nd νd  1 50.000 1.48 1.84666 23.8  2 41.418 4.76 1.71300 53.9  3 203.270 (variable)  4 36.287 1.00 1.95375 32.3  5 9.913 4.91  6* −42.835 1.10 1.76802 49.2  7 37.510 0.10  8 20.227 2.84 1.92286 20.9  9 −4006.687 (variable) 10 ∞ 1.83 1.59282 68.6 11 −23.120 1.50 12(stop) ∞ 2.18 13 22.780 4.70 1.53775 74.7 14 −9.334 1.00 1.80518 25.4 15 −17.675 0.57 16 −9.500 2.90 1.83400 37.2 17* −9.226 (variable) 18* 14.158 1.00 1.85135 40.1 19* 7.730 (variable) 20 33.857 2.83 1.58144 40.8 21 −603.167 (variable) Image plane ∞ Aspheric surface data 6th surface K = 0.00000e+000 A4 = −1.21910e−005 A6 = −4.30589e−008 A8 = 3.99751e−010 A10 = −1.18058e−011 17th surface K = 0.00000e+000 A4 = 1.10442e−004 A6 = −7.36507e−007 A8 = 2.70190e−008 A10 = −1.59983e−010 18th surface K = 0.00000e+000 A4 = −9.45110e−004 A6 = 2.24365e−005 A8 = −3.76588e−007 A10 = 3.00125e−009 19th surface K = 0.00000e+000 A4 = −1.31918e−003 A6 = 2.72203e−005 A8 = −5.61796e−007 A10 = 4.26501e−009 Various data Zoom ratio 2.87 Wide angle Middle Telephoto Focal length 18.58 28.13 53.38 F-number 3.64 4.15 5.29 Half angle of view (deg) 28.28 19.57 10.61 Image height 10.00 10.00 10.00 Total lens length 79.30 90.34 115.50 BF 18.85 25.06 41.51 d3 1.10 11.98 27.44 d9 13.62 7.35 0.82 d17 3.76 3.20 1.10 d19 7.27 8.05 9.93 d21 18.85 25.06 41.51 Lens unit data Unit Start surface Focal length 1 1 95.93 2 4 −17.62 3 10 16.23 4 18 −21.54 5 20 55.23

[Numerical Data 5]

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

This application claims the benefit of Japanese Patent Application No. 2016-241043, filed Dec. 13, 2016, which is hereby incorporated by reference herein in its entirety.

›Tables in the description — 1
TABLE 1 — Embodiment
12345
fw17.52416.37218.56718.58418.540
ft58.58753.27553.41053.38358.786
f1105.287101.326103.43595.93594.073
f2−15.607−16.196−18.758−17.622−18.264
f376.53983.92062.00016.23065.000
f4276.550−50.886−32.250−21.539−56.349
f529.29820.48219.02755.22524.957
ft/fw3.3433.2542.8772.8733.171
R1P1330.831−144.105387.8890.000725.432
R2P1−41.976−31.973−32.737−23.120−44.098
β2w−0.191−0.207−0.245−0.243−0.271
β2t−0.292−0.310−0.370−0.381−0.442
β3w2.9652.60420.650−0.44910.512
β3t1.7971.7303.232−0.6303.007
β4w1.2530.2640.0262.8280.083
β4t0.8910.4250.18410.6460.290
β5w−0.234−1.136−1.3820.628−0.835
β5t−1.190−2.306−2.3490.218−1.622
D23w22.16320.26124.68013.62324.481
D23t3.8072.2956.1530.8215.920
fP76.53983.92062.00039.00065.000
fR27.11526.01426.90625.33328.479
βPw2.9652.60420.6509.11910.512
Conditional(1)SFP1−0.775−1.570−0.844−1.000−0.885
Expression(2)βst/βsw0.9250.9950.2372.2010.467
(3)D23w/D23t5.8218.8274.01116.5984.135
(4)|1 − βPw|1.9651.60419.6508.1199.512
(5)fP/fRt2.8233.2262.3041.5392.282
(6)fRt/fw1.5471.5891.4491.3631.536
(7)(1 − βPt) × βRt0.8450.7150.9641.3120.944
(8)nP1.487491.522491.487491.592821.64000
(9)vP70.23059.84070.23068.63060.080

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6 codes
IPC · International Patent Classification
Section G — Physics
  • G02B15/14
  • G02B13/02
  • G02B13/18
  • G02B27/64
  • G02B27/00
  • G02B15/173

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