Optical system and imaging device

Abstract

There is a need for an optical system that can achieve a better tilt effect than conventional systems. [Solution] The optical system has first and second shift lens groups LA and LB that are movable in a direction perpendicular to the optical axis. When the eccentricity sensitivities of the first and second shift lens groups are Sa and Sb, respectively, and the amount of movement of the first shift lens group is Ma and the amount of movement of the second shift lens group is Mb, the condition 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 is satisfied. Furthermore, when the focal lengths of the first and second shift lens groups are fa and fb, and the maximum values ​​of the amount of movement of the first and second shift lens groups are Mamax and Mbmax, at least one of the conditions 0.05 ≤ |Mamax / fa| ≤ 0.25 and 0.05 ≤ |Mbmax / fb| ≤ 0.25 is satisfied.

Description

[Technical Field]

[0001] This invention relates to an optical system suitable for imaging. [Background technology]

[0002] Some optical systems, as described above, have a mechanism that moves the lenses relative to the optical axis of the optical system to obtain a tilt effect that focuses on the entire surface of an object tilted with respect to the optical axis, or a shift effect that suppresses deformation (tapering) of tall subjects. Patent Document 1 discloses an optical system that obtains a tilt effect by moving multiple lenses in a direction perpendicular to the optical axis. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2019-090952 [Overview of the project] [Problems that the invention aims to solve]

[0004] There is a need for optical systems that can achieve better tilt and shift effects than conventional systems. [Means for solving the problem]

[0005] An optical system as one aspect of the present invention comprises a first shift lens group movable in a direction perpendicular to the optical axis of the optical system, and a second shift lens group positioned on the image side of the first shift lens group and movable in a direction perpendicular to the optical axis. Let the lateral magnifications of the first and second shift lens groups be βa and βb, respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups be βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups be Sa = (1-βa) × βra and Sb = (1-βb) × βrb, respectively, and let the amount of movement of the first shift lens group relative to the optical axis be Ma and the amount of movement of the second shift lens group relative to the optical axis be Mb. 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 When the following conditions are satisfied, and further, the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, the maximum value of the movement amount Ma of the first shift lens group is Mamax, and the maximum value of the movement amount Mb of the second shift lens group is Mbmax, 0.03 ≤ |Mamax / fa| ≤ 0.25 0.03 ≤ |Mbmax / fb| ≤ 0.25 It is characterized by satisfying at least one of the following conditions.

[0006] Another aspect of the present invention is an optical system comprising a first shift lens group movable in a direction perpendicular to the optical axis of the optical system, and a second shift lens group positioned on the image side of the first shift lens group and movable in a direction perpendicular to the optical axis. Let the lateral magnifications of the first and second shift lens groups be βa and βb, respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups be βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups be Sa = (1-βa) × βra and Sb = (1-βb) × βrb, respectively, let the maximum displacement of the first shift lens group relative to the optical axis be Mamax, the maximum displacement of the second shift lens group relative to the optical axis be Mbmax, the focal length of the optical system be f, and the half-angle of view of the optical system when the first and second shift lens groups are not moving relative to the optical axis be ω. 0.3 ≤ |Mamax × Sa + Mbmax × Sb| / (f × tanω) ≤ 1.0 It is characterized by satisfying the following conditions.

[0007] Another aspect of the present invention is an optical system capable of zooming, comprising a first shift lens group movable in a direction perpendicular to the optical axis of the optical system, and a second shift lens group positioned on the image side of the first shift lens group and movable in a direction perpendicular to the optical axis. Further along the image side of the second shift lens group is a focus lens group that moves along the optical axis during focusing. When the maximum movement of the first shift lens group relative to the optical axis is Mamax, the maximum movement of the second shift lens group relative to the optical axis is Mbmax, the focal length of the first shift lens group is fa, and the focal length of the second shift lens group is fb, (Mamax × fa) / (Mbmax × fb) < 0 It is characterized by satisfying the following conditions. Furthermore, an imaging device employing the above optical system also constitutes another aspect of the present invention. [Effects of the Invention]

[0008] According to the present invention, it is possible to provide an optical system that can obtain good tilt and shift effects. [Brief explanation of the drawing]

[0009] [Figure 1] Cross-sectional view of the optical system of Example 1. [Figure 2] A diagram showing the longitudinal aberration of the optical system of Example 1 when it is in focus at infinity. [Figure 3] Transverse aberration diagram of the optical system of Example 1 during tilt imaging. [Figure 4] Cross-sectional view of the optical system of Example 2 at the wide-angle end. [Figure 5] A diagram showing the longitudinal aberration of the optical system of Example 2 at the wide-angle end and in focus at infinity. [Figure 6] A diagram showing the longitudinal aberration of the optical system of Example 2 at its telephoto end and in focus at infinity. [Figure 7] Transverse aberration diagram of the optical system of Example 2 during tilt imaging at the wide-angle end. [Figure 8] Transverse aberration diagram during tilt imaging at the telephoto end of the optical system in Example 2. [Figure 9] Cross-sectional view of the optical system of Example 3 at the wide-angle end. [Figure 10]Longitudinal aberration diagram of the optical system of Example 3 at the wide-angle end and in the infinite focus state. [Figure 11] Longitudinal aberration diagram of the optical system of Example 3 at the telephoto end and in the infinite focus state. [Figure 12] Lateral aberration diagram of the optical system of Example 3 during tilt imaging at the wide-angle end. [Figure 13] Lateral aberration diagram of the optical system of Example 3 during tilt imaging at the telephoto end. [Figure 14] Diagram explaining the principle of shine-proof. [Figure 15] Cross-sectional view of the optical system of Example 4. [Figure 16] Longitudinal aberration diagram of the optical system of Example 4 in the infinite focus state. [Figure 17] Lateral aberration diagram of the optical system of Example 5 during shift imaging. [Figure 18] Cross-sectional view of the optical system of Example 5 at the wide-angle end. [Figure 19] Longitudinal aberration diagram of the optical system of Example 5 at the wide-angle end and in the infinite focus state. [Figure 20] Longitudinal aberration diagram of the optical system of Example 5 at the telephoto end and in the infinite focus state. [Figure 21] Lateral aberration diagram of the optical system of Example 5 during shift imaging at the wide-angle end. [Figure 22] Lateral aberration diagram of the optical system of Example 5 during shift imaging at the telephoto end. [Figure 23] Cross-sectional view of the optical system of Example 6 at the wide-angle end. [Figure 24] Longitudinal aberration diagram of the optical system of Example 6 at the wide-angle end and in the infinite focus state. [Figure 25] Longitudinal aberration diagram of the optical system of Example 6 at the telephoto end and in the infinite focus state. [Figure 26] Lateral aberration diagram of the optical system of Example 6 during shift imaging at the wide-angle end. [Figure 27] Lateral aberration diagram of the optical system of Example 6 during shift imaging at the telephoto end. [Figure 28] Cross-sectional views of the optical system of Example 7 at the wide-angle end and the telephoto end. [Figure 29] Longitudinal aberration diagrams of the optical system of Example 7 at the wide-angle end and the telephoto end. [Figure 30] Transverse aberration diagrams of the optical system of Example 7 at the wide-angle and telephoto ends. [Figure 31] Cross-sectional views of the optical system of Example 8 at the wide-angle and telephoto ends. [Figure 32] Longitudinal aberration diagrams of the optical system of Example 8 at the wide-angle and telephoto ends. [Figure 33] Transverse aberration diagrams of the optical system of Example 8 at the wide-angle and telephoto ends. [Figure 34] Cross-sectional views of the optical system of Example 9 at the wide-angle and telephoto ends. [Figure 35] Longitudinal aberration diagrams of the optical system of Example 9 at the wide-angle and telephoto ends. [Figure 36] Transverse aberration diagrams at the wide-angle and telephoto ends of the optical systems of Examples 1 to 9. [Figure 37] A diagram showing the optical system described in any one of Examples 1 to 9. [Modes for carrying out the invention]

[0010] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0011] Figures 1, 4, and 9 show cross-sections of the optical systems of Examples 1 to 3, respectively. The optical systems of Examples 2 and 3 are zoom lenses capable of zooming between the wide-angle and telephoto ends. In each cross-sectional view, the left side is the object side (front), and the right side is the image side (rear). The optical systems of each example can be used in various imaging devices such as digital video cameras, digital cameras, television cameras, silver halide film cameras, and surveillance cameras.

[0012] The optical system of each embodiment has multiple lens groups. A lens group is a collection of one or more lenses that move or remain stationary as a whole during zooming and focusing. That is, the distance between adjacent lens groups changes during zooming and focusing. A lens group is also a collection of one or more lenses that move in a direction perpendicular to the optical axis of the optical system during tilt imaging. "Moving in a direction perpendicular to the optical axis" includes not only cases where it moves only in a direction perpendicular to the optical axis, but also cases where it moves in a direction that is a combination of a directional component perpendicular to the optical axis and a directional component parallel to the optical axis, such as when it rotates around a central point on the optical axis. In the following description, the direction perpendicular to the optical axis is referred to as the shift direction. A lens group may include an aperture diaphragm.

[0013] In a zoom lens, the wide-angle end and telephoto end represent the zoom state at which the lens group, which moves during zooming, is positioned at the ends of its mechanically or controllably movable range along the optical axis, resulting in the maximum angle of view (shortest focal length) and minimum angle of view (longest focal length), respectively. Each cross-sectional diagram shows the direction of movement of the lens group during focusing with an arrow.

[0014] In each cross-sectional view, SP is the aperture diaphragm. IP is the image plane. The image plane IP is where the imaging surface (light-receiving surface) of an image sensor such as a CCD sensor or CMOS sensor, or the film surface (photosensitive surface) of a silver halide film, is located.

[0015] The principle by which the tilt effect for tilt imaging is obtained in the optical system of each embodiment will be explained using Figure 14. An object plane tilted by an angle θobj with respect to the optical axis of the optical system satisfies the Scheinproof principle with respect to a lens having a principal plane perpendicular to the optical axis, and has an image plane tilted by an angle θimg with respect to the vertical plane. Since the normal imaging plane is perpendicular to the optical axis, good focus cannot be obtained for an object plane tilted beyond the depth of field.

[0016] As a method for correcting the tilt (tilt) θimg of the image plane caused by the tilt (tilt) θobj of the object plane, there is a method that utilizes aberration due to the optical eccentricity (shift) of the lens, as disclosed in Patent Document 1. This method utilizes the tilt of the image plane caused by the shift of the lens. However, with this method, the amount of correction for image tilt is smaller compared to when the lens is tilted relative to the optical axis, making it difficult to obtain good focus for a greatly tilted object plane.

[0017] Therefore, in order to obtain good focus even on objects with a large inclination, the optical system of each embodiment is equipped with multiple (two) shift lens groups that move in the shift direction, and the focal length and amount of movement of each shift lens group are appropriately set. Furthermore, in order to minimize composition shift during tilt imaging, the direction of movement and amount of movement of each shift lens group are appropriately set so that the direction of composition shift, which depends on the power and shift direction of the multiple shift lens groups, is in opposite directions for each shift lens group. As a result, good focus can be obtained even on objects with a large inclination while keeping composition shift to a minimum.

[0018] Next, the characteristic configurations of the optical systems of Examples 1 to 3 will be described. The optical system of each example has a first shift lens group LA that is movable in the shift direction, and a second shift lens group LB that is positioned on the image side of the first shift lens group LA and is movable in the shift direction.

[0019] Furthermore, when the eccentricity sensitivity of the first shift lens group LA is Sa, the eccentricity sensitivity of the second shift lens group LB is Sb, the amount of movement of the first shift lens group LA in the shift direction relative to the optical axis is Ma, and the amount of movement of the second shift lens group LB in the shift direction relative to the optical axis is Mb, it is preferable that the optical system of each embodiment satisfies the conditions of the following equation (1). The eccentricity sensitivities Sa and Sb are expressed by the following equations, where the lateral magnifications of the first and second shift lens groups LA and LB are βa and βb respectively, and the combined lateral magnification of all one or more lens groups arranged on the image side of the first and second shift lens groups LA and LB is βra and βrb.

[0020] Sa = (1 - βa) × βra Sb = (1 - βb) × βrb Furthermore, if no lens group is positioned on the image side of the second shift lens group LB, βrb will be 1.

[0021] 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 (1) Furthermore, let fa be the focal length of the first shift lens group LA, fb be the focal length of the second shift lens group LB, Mamax be the maximum value of the amount of movement Ma of the first shift lens group LA, and Mbmax be the maximum value of the amount of movement Mb of the second shift lens group LB. In this case, it is preferable that the optical system of each embodiment satisfies at least one of the conditions of equations (2) and (3).

[0022] 0.03 ≤ |Mamax / fa| ≤ 0.25 (2) 0.03 ≤ |Mbmax / fb| ≤ 0.25 (3) The sign of the movement amount of the first and second shift lens groups LA and LB is defined as positive for the direction of movement of the first shift lens group LA and negative for the opposite direction. The maximum value of the movement amount of each shift lens group (hereinafter referred to as the maximum movement amount) is the amount of movement of each shift lens group when the maximum tilt effect is obtained in the specifications of the optical system of each embodiment.

[0023] The conditions in equation (1) indicate an appropriate relationship between the amount of composition shift generated by the movement of the first shift lens group LA and the amount of composition shift generated by the movement of the second shift lens group LB. If -(Ma×Sa) / (Mb×Sb) falls below the lower limit or exceeds the upper limit of equation (1), the amount of composition shift during tilt imaging becomes too large, which is undesirable.

[0024] Furthermore, it is more preferable to set the lower limit of equation (1) to 0.6, 0.7, or 0.75. Also, it is more preferable to set the upper limit of equation (1) to 1.1, 1.0, or 0.97.

[0025] The conditions in equations (2) and (3) indicate an appropriate relationship between the maximum movement of the first and second shift lens groups LA and LB and their focal lengths. If the focal lengths of each shift lens group are too short, such that Mamax / |fa| and Mbmax / |fb| exceed the upper limits of equations (2) and (3), respectively, it becomes difficult to correct chromatic aberration and coma aberration caused by the movement of each shift lens group, which is undesirable. If the maximum movement of each shift lens group is too small, such that Mamax / |fa| and Mbmax / |fb| fall below the lower limits of equations (2) and (3), respectively, the amount of correction for image distortion becomes small, making it difficult to achieve good focus on a highly inclined object plane, which is also undesirable.

[0026] Furthermore, it is more preferable to set the lower limit of equations (2) and (3) to 0.04 or 0.05. Also, it is more preferable to set the upper limit of equations (2) and (3) to 0.20, 0.15, or 0.12.

[0027] Furthermore, in the optical system of each embodiment, it is preferable that the first shift lens group LA has a positive lens Lap and a negative lens Lan, and the second lens group LB has a positive lens Lbp and a negative lens Lbn. This allows for achromatic aberration to be performed by the positive and negative lenses of each shift lens group, thereby reducing chromatic aberration during tilt imaging.

[0028] Furthermore, it is preferable that the optical system of each embodiment satisfies at least one of the following conditions and configurations.

[0029] In each embodiment, the optical system preferably satisfies the following condition (4), where Rfa is the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group LA, and Rra is the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group LA.

[0030] -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 (4) The conditions in equation (4) indicate the appropriate shape of the first shift lens group LA. If the shape of the first shift lens group LA approaches a meniscus shape such that (Rfa + Rra) / (Rra - Rfa) exceeds the upper limit or falls below the lower limit of equation (4), it is undesirable because the refractive power of the first shift lens group LA becomes too small, resulting in a small correction amount for image distortion.

[0031] Furthermore, it is more preferable to set the lower limit of equation (4) to -0.6, -0.4, -0.2, or +0.1. Also, it is more preferable to set the upper limit of equation (4) to 0.6, 0.5, or 0.4.

[0032] Furthermore, in each embodiment, it is preferable that the optical system satisfies the following condition (5), where Rfb is the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group LB, and Rrb is the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group LB.

[0033] -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 (5) The conditions in equation (5) indicate the appropriate shape for the entire second shift lens group LA. If the shape of the second shift lens group LB approaches a meniscus shape such that (Rfb+Rrb) / (Rrb-Rfb) exceeds the upper limit or falls below the lower limit of equation (5), it is undesirable because the refractive power of the second shift lens group LAB becomes too small, resulting in a small amount of image distortion correction.

[0034] Furthermore, it is more preferable to set the lower limit of equation (5) to -0.6, -0.4, -0.2, or +0.1. Also, it is more preferable to set the upper limit of equation (5) to 0.7, 0.6, or 0.5.

[0035] Furthermore, it is preferable that the optical system of each embodiment satisfies the following condition (6) when the focal length of the entire optical system is f.

[0036] 1.0 < |fa| / f ≤ 10.0 (6) The conditions in equation (6) indicate an appropriate relationship between the focal length of the first shift lens group LA and the focal length of the entire optical system. If the focal length of the first shift lens group LA is too long, such that |fa| / f exceeds the upper limit of equation (6), the refractive power of the first shift lens group LA becomes too small, resulting in a small correction amount for image distortion, which is undesirable. If the focal length of the first shift lens group LA is too short, such that |fa| / f falls below the lower limit of equation (6), the refractive power of the first shift lens group LA becomes too large, resulting in large chromatic aberrations during tilt imaging, which is also undesirable.

[0037] Furthermore, it is more preferable to set the lower limit of equation (6) to 1.5, 2.0, 2.5, or 3.0. Also, it is more preferable to set the upper limit of equation (6) to 9.0, 8.0, or 7.0.

[0038] Furthermore, it is preferable that the optical system of each embodiment satisfies the following conditions of formula (7).

[0039] 1.0 < |fb| / f ≤ 10.0 (7) The conditions in equation (7) indicate an appropriate relationship between the focal length of the second shift lens group LB and the focal length of the entire optical system. If the focal length of the second shift lens group LB is too long, such that |fb| / f exceeds the upper limit of equation (7), the refractive power of the second shift lens group LB becomes too small, resulting in a small correction amount for image distortion, which is undesirable. If the focal length of the second shift lens group LB is too short, such that |fb| / f falls below the lower limit of equation (7), the refractive power of the second shift lens group LB becomes too large, resulting in large chromatic aberrations during tilt imaging, which is also undesirable.

[0040] Furthermore, it is more preferable to set the lower limit of equation (7) to 1.5 or 2.0. Also, it is more preferable to set the upper limit of equation (7) to 8.0, 6.0, 5.0, or 4.5.

[0041] Furthermore, in the optical system of each embodiment, it is preferable that the second shift lens group LB has a negative refractive power. In this case, when Dbi is the distance along the optical axis from the lens surface closest to the object of the second shift lens group LB to the image plane IP, and TTL is the total distance along the optical axis from the lens surface closest to the object of the optical system to the image plane IP, it is preferable that the following condition of equation (8) is satisfied.

[0042] 0.1 ≤ Dbi / TTL ≤ 0.9 (8) The conditions in equation (8) indicate the appropriate position of the second shift lens group LB. If the second shift lens group LB is positioned on the object side such that Dbi / TTL exceeds the upper limit of equation (8), the height of the off-axis light beam incident on the second shift lens group LB becomes too low, resulting in a small amount of image distortion correction, which is undesirable. If the second shift lens group LB is positioned on the image side such that Dbi / TTL falls below the lower limit of equation (8), it becomes difficult to secure the required back focus (the air-equivalent distance from the lens surface closest to the image in the optical system to the image plane), which is also undesirable.

[0043] Furthermore, it is more preferable to set the lower limit of equation (8) to 0.2 or 2.5. Also, it is more preferable to set the upper limit of equation (8) to 0.7, 0.6, or 0.5.

[0044] Furthermore, in the optical system of each embodiment, when the second shift lens group LB is composed of a positive lens Lbp and a negative lens Lbn, the Abbe number with respect to the d line of the positive lens Lbp is denoted as νbp, and the Abbe number with respect to the d line of the negative lens Lbn is denoted as νbn. In this case, it is preferable that the following condition of equation (9) is satisfied.

[0045] 10 ≤ |νbp - νbn| ≤ 70 (9) The conditions in equation (9) indicate an appropriate Abbe number difference for achromatic aberration between the positive and negative lenses of the second shift lens group LB. If the Abbe number difference is large such that |νbp-νbn| exceeds the upper limit of equation (9), it means that a low-dispersion material with a low refractive index will be used for either the positive or negative lens, making it difficult to maintain the refractive power of the second shift lens group LB, which is undesirable. If the Abbe number difference is small such that |νbp-νbn| falls below the lower limit of equation (9), it is undesirable because it becomes difficult to correct chromatic aberration.

[0046] Furthermore, it is more preferable to set the lower limit of formula (9) to 20, 30, or 35. Also, it is more preferable to set the upper limit of formula (9) to 60, 55, 50, or 47.

[0047] Furthermore, in the optical system of each embodiment, when the first shift lens group LA is composed of a positive lens Lap and a negative lens Lan, the Abbe number with respect to the d line of the positive lens Lap is denoted as νap, and the Abbe number with respect to the d line of the negative lens Lan is denoted as νan. In this case, it is preferable that the following condition of equation (10) is satisfied.

[0048] 10 ≤ |νap - νan| ≤ ​​70 (10) The conditions in equation (10) indicate an appropriate Abbe number difference for achromaticity of the positive and negative lenses of the first shift lens group LA. If the Abbe number difference is large such that |νap-νan| exceeds the upper limit of equation (10), it means that a low-dispersion material with a low refractive index will be used for either the positive or negative lens, making it difficult to maintain the refractive power of the first shift lens group LA, which is undesirable. If the Abbe number difference is small such that |νap-νan| falls below the lower limit of equation (10), it is undesirable because it becomes difficult to correct chromatic aberration.

[0049] Furthermore, it is more preferable to set the lower limit of equation (10) to 20, 30, or 35. Also, it is more preferable to set the upper limit of equation (10) to 60, 55, or 50.

[0050] Furthermore, in the optical systems of each embodiment, it is preferable that the second shift lens group LB has a negative refractive power. This makes it possible to suppress an increase in the lens diameter of the second shift lens group LB.

[0051] Furthermore, in the optical system of each embodiment, it is preferable to place an intermediate lens group with positive refractive power between the first shift lens group LA and the second shift lens group LB to focus the light beam incident on the second shift lens group LB. This makes it possible to increase the negative refractive power of the second shift lens group LB and enhance the tilt effect obtained by the movement of the second shift lens group LB. In this case, when the focal length of the intermediate lens group is fi, it is preferable to satisfy the condition of the following equation (11).

[0052] 1.0 <fi / f≦10.0 (11) Equation (11) shows the appropriate relationship between the focal length of the intermediate lens group and the focal length of the entire optical system. If the focal length of the intermediate lens group is too long, such that fi / f exceeds the upper limit of equation (11), the convergence of the light beam incident on the second shift lens group LB will be insufficient, making it difficult to increase the negative refractive power of the second shift lens group LB, which is undesirable. If the focal length of the intermediate lens group is too short, such that fi / f falls below the lower limit of equation (11), the convergence of the light beam incident on the second shift lens group LB will be too strong, making it difficult to correct coma aberration during tilt imaging, which is also undesirable.

[0053] Furthermore, it is more preferable to set the lower limit of equation (11) to 1.5 or 2.0. Also, it is more preferable to set the upper limit of equation (11) to 8.0, 7.0, 6.0, or 5.0.

[0054] Furthermore, it is preferable that the optical system of each embodiment has a first lens group with negative refractive power closest to the object. By adopting this retrofocus type power arrangement, the necessary back focus can be secured.

[0055] Furthermore, it is preferable that the optical system of each embodiment includes a first lens group with negative refractive power, a first shift lens group LA with positive refractive power, an intermediate lens group with positive refractive power, and a second shift lens group LB with negative refractive power, all arranged in order from the object side to the image side.

[0056] Furthermore, if the optical system of each embodiment is a zoom lens, it is preferable that at least one of the conditions of equations (1) to (3) and equations (4) to (11) is satisfied at all zoom positions from the wide-angle end to the telephoto end.

[0057] Furthermore, in the optical system of each embodiment, the first shift lens group LA and the second shift lens group LB may move to opposite sides of each other in the shift direction, or they may move to the same side.

[0058] The optical systems of Examples 1 to 3 will be described in detail below. Following Example 3, numerical examples 1 to 3 corresponding to Examples 1 to 3 are shown. [Examples]

[0059] The optical system of Embodiment 1 (Numerical Example 1) shown in Figure 1 consists of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, an aperture diaphragm SP, a fourth lens group with positive refractive power, a fifth lens group with positive refractive power, a sixth lens group with negative refractive power, and a seventh lens group with positive refractive power, arranged in order from the object side to the image side.

[0060] The second lens group is a focusing lens group that moves toward the image side when focusing from infinity to close. The fourth lens group corresponds to the first shift lens group LA and consists of a negative lens Lan and a positive lens Lap arranged in order from the object side. The fifth lens group corresponds to the intermediate lens group. The sixth lens group corresponds to the second shift lens group LB and consists of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0061] Figure 2 shows the longitudinal aberrations (spherical aberration, astigmatism, distortion, and chromatic aberration) of the optical system of Numerical Example 1 when it is in focus on an object at infinity (infinity focus state). In the spherical aberration diagram, Fno indicates the F number, the solid line shows the spherical aberration at the d line (wavelength 587.6 nm), and the dashed line shows the spherical aberration at the g line (wavelength 435.8 nm). In the astigmatism diagram, the solid line S shows the astigmatism of the sagittal image plane, and the dashed line M shows the astigmatism of the meridional image plane. The distortion diagram shows the distortion at the d line. The chromatic aberration diagram shows the lateral chromatic aberration at the g line. ω is the half-angle of view (°).

[0062] Figure 3 shows the lateral aberration of the optical system in numerical example 1 during tilt imaging with a subject distance of 1m and an object angle of 75°. Here, the lateral aberration is shown when the focus shift caused by the movement of the first and second shift lens groups LA and LB is corrected by the movement of the focus lens group. The solid line M shows the amount of lateral aberration in the meridional cross-section, and the dashed line S shows the amount of lateral aberration in the sagittal cross-section. The explanation of the longitudinal and lateral aberration diagrams described above is the same for the other numerical examples described later. [Examples]

[0063] The optical system of Embodiment 2 (Numerical Example 2) shown in Figure 4 is a zoom lens. This optical system is composed of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, a fourth lens group with positive refractive power, an aperture diaphragm SP, a fifth lens group with negative refractive power, a sixth lens group with positive refractive power, a seventh lens group with positive refractive power, an eighth lens group with negative refractive power, a ninth lens group with positive refractive power, and a tenth lens group with positive refractive power, arranged in order from the object side to the image side.

[0064] The second lens group is a focusing lens group that moves toward the image side when focusing from infinity to close. The sixth lens group corresponds to the first shift lens group LA and consists of a negative lens Lan and a positive lens Lap arranged in order from the object side. The seventh lens group corresponds to the intermediate lens group. The eighth lens group corresponds to the second shift lens group LB and consists of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0065] Figures 5 and 6 show the longitudinal aberrations of the optical system of Numerical Example 2 at the wide-angle and telephoto ends in an infinity focus state, respectively. Figures 7 and 8 show the lateral aberrations of the optical system of Numerical Example 2 at the wide-angle and telephoto ends during tilt imaging with a subject distance of 1m and an object angle of 70°, respectively. [Examples]

[0066] The optical system of Embodiment 3 (Numerical Example 3) shown in Figure 9 is a zoom lens. This optical system is composed of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, a fourth lens group with negative refractive power including an aperture diaphragm SP, a fifth lens group with positive refractive power, a sixth lens group with positive refractive power, a seventh lens group with negative refractive power, an eighth lens group with positive refractive power, a ninth lens group with negative refractive power, and a tenth lens group with positive refractive power, arranged in order from the object side to the image side.

[0067] The ninth lens group is a focusing lens group that moves toward the image side when focusing from infinity to close. The fifth lens group corresponds to the first shift lens group LA and consists of a negative lens Lan and a positive lens Lap arranged in order from the object side. The sixth lens group corresponds to the intermediate lens group. The seventh lens group corresponds to the second shift lens group LB and consists of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0068] Figures 10 and 11 show the longitudinal aberrations of the optical system of Numerical Example 3 at the wide-angle and telephoto ends in an infinity focus state, respectively. Figures 12 and 13 show the lateral aberrations of the optical system of Numerical Example 3 at the wide-angle and telephoto ends during tilt imaging with a subject distance of 1m and an object angle of 70°, respectively.

[0069] Numerical examples 1 to 3 are shown below. In each numerical example, the surface number indicates the order of the optical surfaces from the object side. r is the radius of curvature of the i-th surface (mm), d is the distance on the optical axis between the i-th surface and the (i+1)-th surface (mm), nd is the refractive index of the optical material at the d-line between the i-th surface and the (i+1)-th surface, and νd is the Abbe number of the optical material with respect to the d-line. The Abbe number νd with respect to the d-line is given by Nd, NF, and NC, respectively, when the refractive indices at the d-line (587.6 nm), F-line (486.1 nm), and C-line (656.3 nm) are Nd, NF, and NC, respectively. νd = (Nd-1) / (NF-NC) It is represented as follows.

[0070] BF is the back focus, which is the air-equivalent distance along the optical axis from the image-side lens surface (final surface) of the optical system to the paraxial image plane. The total lens length is the sum of the back focus and the distance along the optical axis from the object-side lens surface to the final surface of the optical system, and corresponds to TTL in equation (8).

[0071] The asterisk (*) next to the surface number indicates that the surface has an aspherical shape. The aspherical shape is expressed by the following formula, where X is the displacement from the surface vertex in the optical axis direction, H is the height from the optical axis in the direction perpendicular to the optical axis, the direction of light propagation is positive, R is the radius of paraxial curvature, K is the cone constant, and A3 to A10 are aspherical coefficients. Note that "e±XX" in the cone constant and aspherical coefficients is equivalent to "×10 ±XX It means "...".

[0072] X=(H 2 / R) / [1+√{1-(1+K)(H / R) 2}] +A3×H 3 +A4×H 4 +A5×H 5 +A6×H 6+A7×H 7 +A8×H 8 +A9×H 9 +A10×H 10 +A11×H 11 +A12×H 12 +… [Numerical Example 1] Unit: mm Surface data Surface number r d nd νd 1 75.602 2.00 1.59349 67.0 2 26.168 1.81 3 26.628 2.00 1.53110 56.0 4* 17.854 10.47 5 168.713 1.50 1.69680 55.5 6 24.836 (variable) 7 116.768 1.40 1.94594 18.0[[ID=3T]] 8 19.797 8.46 2.00069 25.5 9 -250.903 (variable) 10 -37.653 1.00 1.59282 68.6 11 24.500 7.52 1.80810 22.8 12 -40.206 0.17 13 93.268 3.68 1.48749 70.2 14 -22.866 0.85 1.85478 24.8 15 -127.251 1.91 16 (aperture) ∞ 2.11 17 72.106 1.50 1.74951 35.3 18 �6.148 8.18 1.49700 81.5 19* -47.133 1.00 20 91.847 4.86 1.49700 81.5 21 -19.344 1.00 1.84666 23.8 22 -30.995 3.43 23 -53.041 3.53 1.83481 42.7 24 -32.661 1.50 1.49700 81.5 25* 34.477 3.47 26* 22.318 6.60 1.49700 81.5 27 -163.512 0.15 28 60.785 1.40 1.85150 40.8 29 14.156 8.52 1.49700 81.5 30 60.056 6.39 31* -64.692 1.80 1.85135 40.1 32* ∞ 2.91 33 82.673 6.75 1.84666 23.8 34 -86.311 17.00 Image plane ∞ Aspherical data Side 4 K =-1.06257e+00 A 4= 2.61763e-05 A 6= 1.80820e-07 A 8= 5.40828e-11 A 3=-6.25355e-05 A 5=-2.47371e-06 A 7=-5.84128e-09 Page 19 K = 0.00000e+00 A 4= 1.11459e-05 A 6= 9.20747e-08 A 8= 9.48311e-11 A 3=-2.08171e-05 A 5=-1.08285e-06 A 7=-4.55214e-09 Page 25 K = 0.00000e+00 A 4=-1.25468e-05 A 6=-1.06656e-07 A 8=-9.58494e-11 A 3= 1.78148e-05 A 5= 1.24198e-06 A 7= 5.05714e-09 Page 26 K = 0.00000e+00 A 4=-9.46395e-07 A 6= 1.17509e-08 A 8=-3.76333e-11 Page 31 K = 1.05315e+01 A 4=-1.48719e-04 A 6= 1.49154e-06 A 8= 2.02788e-09 A 3= 3.83950e-04 A 5=-2.40488e-06 A 7=-1.05512e-07 Page 32 K = 0.00000e+00 A 4=-2.12377e-04 A 6= 6.86746e-08 A 8= 1.09362e-09 A 3= 6.08988e-04 A 5= 1.23671e-05 A 7=-3.60005e-08 Various data Focal length 24.03 F-number 3.50 Half-angle (°): 41.99 Image height 21.64 Lens length: 140.00 BF 17.00 Mamax 5.62 Mbmax 5.50 Subject distance infinity 1000 d 6 5.74 6.28 d 9 9.37 8.84 Lens group data Group starting plane focal length 1 1 -18.16 2 7 68.34 3 10 98.32 4 17 72.88 5 20 68.16 6 23 -49.98 7 26 71.08 [Numerical Example 2] Unit: mm Surface data Face number rd nd νd 1 46.274 3.00 1.95375 32.3 2 34.756 7.26 3 46.343 2.50 1.80400 46.5 4 24.899 7.11 5 36.440 2.00 1.80400 46.5 6 20.041 6.16 7* 21.250 2.00 1.58313 59.4 8* 12.242 10.86 9 -61.238 1.96 1.43875 94.7 10 30.699 4.98 1.84666 23.8 11 117.313 (variable) 12 76.894 1.40 1.94594 18.0 13 27.914 8.03 1.72047 34.7 14 -56.810 (variable) 15 46.457 3.87 1.49700 81.5 16 -69.777 (variable) 17 -96.276 0.94 1.91082 35.2 18 22.979 3.65 1.80809 22.8 19 -59.204 0.95 20 (aperture) ∞ (variable) 21 -589.072 0.99 1.83481 42.7 22 24.645 6.21 1.49700 81.5 23 -20.029 0.90 2.00069 25.5 24 -44.797 (variable) 25 81.815 1.20 1.83481 42.7 26 40.257 9.31 1.49700 81.5 27* -45.928 (variable) 28 72.122 8.81 1.49700 81.5 29 -19.225 1.30 1.83400 37.2 30 -26.516 (variable) 31 -80.891 1.92 1.83400 37.2 32 -42.583 1.20 1.49700 81.5 33* 30.058 (variable) 34 53.165 6.62 1.49700 81.5 35 -61.317 1.40 1.90043 37.4 36 177.708 6.38 1.71736 29.5 37 -38.940 5.69 38* -46.021 2.00 1.85135 40.1 39 * 200.000 (variable) 40* 851.877 6.15 1.58313 59.4 41 -56.177 21.63 Image plane ∞ Aspherical data Side 7 K = 0.00000e+00 A 4=-3.91257e-05 A 6=-2.45554e-08 A 8=-4.43227e-11 A 3=-1.24741e-05 A 5= 8.56096e-07 A 7= 3.62196e-10 Side 8 K =-3.60222e+00 A 4= 2.84929e-04 A 6= 1.27240e-06 A 8= 3.03064e-10 A 3=-3.64342e-04 A 5=-2.82422e-05 A 7=-3.06052e-08 Page 27 K = 0.00000e+00 A 4= 7.74666e-06 A 6=-3.44800e-08 A 8=-5.28976e-11 A 3=-2.42088e-05 A 5=-1.20566e-07 A 7= 2.54055e-09 Page 33 K = 0.00000e+00 A 4=-3.15722e-05 A 6=-5.85259e-07 A 8=-7.65073e-10 A 3= 7.29842e-05 A 5= 5.41061e-06 A 7= 3.34618e-08 Page 38 K = 5.23380e+00 A 4=-6.18845e-05 A 6= 8.85482e-07 A 8= 1.39067e-09 A 3=-7.23536e-05 A 5=-2.60137e-07 A 7=-6.21654e-08 Page 39 K = 0.00000e+00 A 4=-1.31983e-04 A 6=-3.80892e-07 A 8= 1.01226e-10 A 3= 1.23465e-04 A 5= 1.29780e-05 A 7= 2.46060e-10 Page 40 K = 0.00000e+00 A 4=-3.08515e-05 A 6=-2.13049e-07 A 8=-1.07787e-10 A 3= 6.97166e-05 A 5= 3.77177e-06 A 7= 7.14470e-09 Various data Zoom ratio 1.33 Wide-angle, Medium, Telephoto Focal length 17.51 ​​20.15 23.30 F-number 4.10 4.10 4.10 Half-angle (°): 51.01, 47.04, 42.88 Image height 21.64 21.64 21.64 Lens length 186.00 186.00 186.00 BF 21.63 21.63 21.63 Mamax 2.56 2.60 2.72 Mbmax 2.68 2.68 2.69 Object distance: infinite d11 3.08 1.91 1.32 d14 16.66 10.87 3.99 d16 0.94 5.46 10.75 d20 5.79 4.70 3.36 d24 1.00 1.00 1.00 d27 1.00 1.00 1.00 d30 3.00 3.00 3.00 d33 5.14 5.14 5.14 d39 1.01 4.53 8.05 Object distance: 1000mm d11 3.34 2.17 1.58 d14 16.41 10.61 3.73 d16 0.94 5.46 10.75 d20 5.79 4.70 3.36 d24 1.00 1.00 1.00 d27 1.00 1.00 1.00 d30 3.00 3.00 3.00 d33 5.14 5.14 5.14 d39 1.01 4.53 8.05 Lens group data Group Starting surface Focal length 1 1 -13.91 2 12 60.20 3 15 56.74 4 17 6854.60 5 21 -56.49 6 25 80.05 7 28 48.85 8 31 -52.48 9 34 2041.59 10 40 90.60 [Numerical Example 3] Unit: mm Surface data Face number rd nd νd 1 95.496 2.50 1.72916 54.7 2 22.225 8.06 3 35.557 2.00 1.72916 54.7 4* 17.812 6.92 5* 49.450 2.00 1.58313 59.4 6* 23.188 10.70 7 -28.673 1.20 1.72916 54.7 8 447.161 0.20 9 88.104 5.19 1.59270 35.3 10 -47.653 -0.01 11 126.711 1.20 1.89286 20.4 12 31.255 7.88 1.69895 30.1 13 -43.591 (variable) 14 37.160 3.39 1.48749 70.2 15 -113.656 (variable) 16 -124.741 0.97 1.83481 42.7 17 19.864 4.71 1.72151 29.2 18 -52.673 (variable) 19 (aperture) ∞ 2.85 20 -43.857 0.88 2.00069 25.5 21 99.532 3.34 1.49700 81.5 22 -30.507 (variable) 23* 157.747 1.50 1.60342 38.0 24 61.629 6.29 1.49700 81.5 25 -80.316 (variable) 26 28.660 4.53 1.43875 94.7 27 -34.423 0.98 1.96300 24.1 28 96.594 1.62 29 -282.726 2.69 1.80810 22.8 30 -34.171 (variable) 31 -85.046 2.86 1.95375 32.3 32 -45.821 1.47 1.49700 81.5 33 41.907 (Variable) 34 26.010 5.57 1.92286 20.9 35 -131.600 1.67 36 -82.255 1.20 2.00069 25.5 37 16.571 9.22 1.49700 81.5 38 -38.353 (variable) 39* -29.733 1.20 1.85400 40.4 40* -413.147 (variable) 41* 248.716 6.62 1.53110 56.0 42* -36.590 0.29 43 ∞ 1.30 1.51633 64.1 44 ∞ 14.96 Image plane ∞ Aspherical data Side 4 K =-1.71993e-02 A 4=-8.05114e-06 A 6= 5.00335e-08 A 8=-1.20729e-10 5th page K = 0.00000e+00 A 4= 6.16937e-05 A 6=-1.04127e-07 A 8= 2.41461e-11 Side 6 K = 1.65426e-01 A 4= 5.59864e-05 A 6=-1.60853e-07 A 8=-1.75503e-10 Page 23 K = 0.00000e+00 A 4=-5.11159e-07 A 6=-2.44689e-09 A 8= 6.71623e-12 A10 = -6.28115e-15 Page 39 K = 0.00000e+00 A 4= 1.69238e-05 A 6= 4.20804e-08 A 8=-1.76040e-10 Page 40 K = 0.00000e+00 A 4= 2.16465e-05 A 6= 3.71801e-08 A 8=-1.59834e-10 Page 41 K = 0.00000e+00 A 4=-2.74157e-05 A 6=-4.25327e-07 A 8=-3.54799e-10 A 3= 1.74796e-04 A 5= 4.92399e-06 A 7= 1.93150e-08 Page 42 K =-1.85411e+00 A 4=-1.04953e-04 A 6=-1.21486e-06 A 8=-7.64973e-10 A 3= 5.38689e-04 A 5= 1.58300e-05 A 7= 4.75875e-08 Various data Zoom ratio 1.33 Wide-angle, Medium, Telephoto Focal length 17.51 ​​20.32 23.30 F-number 4.00 4.00 4.00 Half-angle (°): 51.02, 46.79, 42.88 Image height 21.64 21.64 21.64 Lens length 165.00 165.00 165.00 BF 14.96 14.96 14.96 Mamax 6.18 6.65 6.39 Mbmax 4.97 5.31 5.32 Infinite subject distance d13 14.30 7.50 0.97 d15 0.96 4.96 8.65 d18 4.45 3.19 1.97 d22 0.99 0.99 0.99 d25 0.99 0.99 0.99 d30 2.95 2.95 2.95 d33 4.73 4.73 4.73 d38 2.73 1.92 1.57 d40 4.94 9.81 14.22 Subject distance: 1000mm d13 14.30 7.50 0.97 d15 0.96 4.96 8.65 d18 4.45 3.19 1.97 d22 0.99 0.99 0.99 d25 0.99 0.99 0.99 d30 2.95 2.95 2.95 d33 4.73 4.73 4.73 d38 3.00 2.23 1.92 d40 4.66 9.50 13.87 Lens group data Group starting plane focal length 1 1 -35.60 2 14 57.87 3 16 556.95 4 19 -95.63 5 23 121.72 6 26 84.73 7 31 -76.05 8 34 58.69 9 39 -37.57 10 41 60.55 The values ​​of equations (1) to (11) in numerical examples 1 to 3 are summarized in Table 1 below. The optical systems in numerical examples 1 to 3 satisfy all the conditions of equations (1) to (11).

[0073] [Table 1]

[0074] Figures 15, 18, and 23 show cross-sections of the optical systems of Examples 4 to 6, respectively. The optical systems of Examples 5 and 6 are zoom lenses capable of zooming between the wide-angle and telephoto ends. The optical systems of each example have multiple lens groups, including a shift lens group. The lens groups, the shift direction of the shift lens groups, and each cross-sectional view are described above.

[0075] Next, the characteristic configurations of the optical systems in Examples 4 to 6 will be described. The optical system of each example has a first shift lens group LA that is movable in the shift direction, and a second shift lens group LB that is positioned on the image side of the first shift lens group LA and is also movable in the shift direction. This configuration suppresses the amount of movement of the first and second shift lens groups LA and LB, enabling rapid shift imaging.

[0076] Let Sa be the eccentricity sensitivity of the first shift lens group LA, and Sb be the eccentricity sensitivity of the second shift lens group LB. The eccentricity sensitivity is as described above. Let Mamax be the maximum displacement of the first shift lens group LA in the shift direction relative to the optical axis, and Mbmax be the maximum displacement of the second shift lens group LB in the shift direction relative to the optical axis. The maximum displacement of each shift lens is the displacement of each shift lens group when the maximum shift effect in the optical system specifications is obtained. Let f be the focal length of the entire optical system, and let ω be the half-angle of view of the optical system in the non-shifted state when the first and second shift lens groups LA and LB are not moving in the shift direction relative to the optical axis. In this case, it is preferable that the following condition of equation (12) is satisfied.

[0077] 0.3 ≤ |Mamax × Sa + Mbmax × Sb| / (f × tanω) ≤ 1.0 (12) The conditions in equation (12) indicate an appropriate ratio of the shift effect generated by the movement of the first and second shift lens groups LA and LB. If the amount of movement of the first and second shift lens groups LA and LB is large enough that the value of equation (12) exceeds the upper limit, it becomes difficult to perform rapid shift imaging, which is undesirable. If the amount of movement of the first and second shift lens groups LA and LB is small enough that the value of equation (12) falls below the lower limit, a sufficient shift effect cannot be obtained, which is also undesirable.

[0078] Furthermore, it is more preferable to set the lower limit of equation (12) to 0.35. Also, it is more preferable to set the upper limit of equation (12) to 0.8, 0.7, or 0.6.

[0079] Furthermore, it is preferable that the optical system of each embodiment satisfies at least one of the following configurations and conditions.

[0080] In the optical system of each embodiment, it is preferable that the first shift lens group LA has a positive lens Lap and a negative lens Lan, and the second lens shift group LB has a positive lens Lbp and a negative lens Lbn. This allows for achromatic aberration to be performed by the positive and negative lenses of each shift lens group, thereby reducing chromatic aberration during tilt imaging.

[0081] Furthermore, the optical system of each embodiment preferably satisfies the following condition (13) when the focal length of the first shift lens group LA is fa.

[0082] 0.03 ≤ |Mamax / fa| ≤ 0.25 (13) The conditions in equation (13) indicate an appropriate relationship between the maximum movement of the first shift lens group LA and its focal length. If the focal length of the first shift lens group LA is too short, such that |Mamax / fa| exceeds the upper limit of equation (13), it becomes difficult to correct chromatic aberration and coma aberration caused by the movement of the first shift lens group LA, which is undesirable. If the maximum movement of the first shift lens group LA is too small, such that |Mamax / fa| falls below the lower limit of equation (13), a sufficient shift effect cannot be obtained, which is also undesirable.

[0083] Furthermore, it is more preferable to set the lower limit of equation (13) to 0.05 or 0.06. Also, it is more preferable to set the upper limit of equation (13) to 0.20, 0.15, or 0.12.

[0084] Furthermore, the optical system of each embodiment preferably satisfies the following condition (14) when the focal length of the second shift lens group LB is fb.

[0085] 0.03 ≤ |Mbmax / fb| ≤ 0.25 (14) The conditions in equation (14) indicate an appropriate relationship between the maximum movement of the second shift lens group LB and its focal length. If the focal length of the second shift lens group LB is too short, such that |Mbmax / fb| exceeds the upper limit of equation (14), it becomes difficult to correct chromatic aberration and coma aberration caused by the movement of the second shift lens group LB, which is undesirable. If the maximum movement of the second shift lens group LB is too small, such that |Mbmax / fb| falls below the lower limit of equation (14), a sufficient shift effect cannot be obtained, which is also undesirable.

[0086] Furthermore, it is more preferable to set the lower limit of equation (14) to 0.05, 0.08, or 0.10. Also, it is more preferable to set the upper limit of equation (14) to 0.20, 0.15, or 0.13.

[0087] Furthermore, in each embodiment, it is preferable that the optical system satisfies the following condition (15), where Rfa is the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group LA, and Rra is the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group LA.

[0088] -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 (15) The conditions in equation (15) indicate the appropriate shape of the first shift lens group LA. If the shape of the first shift lens group LA approaches a meniscus shape such that (Rfa + Rra) / (Rra - Rfa) exceeds the upper limit or falls below the lower limit of equation (15), it becomes difficult to maintain the refractive power of the first shift lens group LA, and a sufficient shift effect cannot be obtained, which is undesirable.

[0089] Furthermore, it is more preferable to set the lower limit of equation (15) to -0.6, -0.4, -0.2, or -0.1. Also, it is more preferable to set the upper limit of equation (15) to 0.7 or 0.65.

[0090] Furthermore, in each embodiment, it is preferable that the optical system satisfies the following condition (15), where Rfb is the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group LB, and Rrb is the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group LB.

[0091] -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 (16) The conditions in equation (16) indicate the appropriate shape of the second shift lens group LB. If the shape of the second shift lens group LB approaches a meniscus shape such that (Rfb + Rrb) / (Rrb - Rfb) exceeds the upper limit or falls below the lower limit of equation (16), it becomes difficult to maintain the refractive power of the second shift lens group LB, and a sufficient shift effect cannot be obtained, which is undesirable.

[0092] Furthermore, it is more preferable to set the lower limit of equation (16) to -0.6, -0.4, -0.2, or +0.1. Also, it is more preferable to set the upper limit of equation (16) to 0.7 or 0.6.

[0093] Furthermore, it is preferable that the optical system of each embodiment satisfies the conditions of the following formula (17).

[0094] 1.0 < |fa| / f ≤ 10.0 (17) The conditions in equation (17) indicate an appropriate relationship between the focal length of the first shift lens group LA and the focal length of the entire optical system. If the focal length of the first shift lens group LA is too long, such that |fa| / f exceeds the upper limit of equation (17), the refractive power of the first shift lens group LA becomes too small, and a sufficient shift effect cannot be obtained, which is undesirable. If the focal length of the first shift lens group LA is too short, such that |fa| / f falls below the lower limit of equation (17), the refractive power of the first shift lens group LA becomes too large, and chromatic aberration during shift imaging becomes large, which is also undesirable.

[0095] Furthermore, it is more preferable to set the lower limit of equation (17) to 1.5, 2.0, or 2.5. Also, it is more preferable to set the upper limit of equation (17) to 9.0, 8.0, or 7.5.

[0096] Furthermore, it is preferable that the optical system of each embodiment satisfies the conditions of the following formula (18).

[0097] 1.0 < |fb| / f ≤ 10.0 (18) The conditions in equation (18) indicate an appropriate relationship between the focal length of the second shift lens group LB and the focal length of the entire optical system. If the focal length of the second shift lens group LB is too long, such that |fb| / f exceeds the upper limit of equation (18), the refractive power of the second shift lens group LB becomes too small, and a sufficient shift effect cannot be obtained, which is undesirable. If the focal length of the second shift lens group LB is too short, such that |fb| / f falls below the lower limit of equation (18), the refractive power of the second shift lens group LB becomes too large, and chromatic aberration during shift imaging becomes large, which is also undesirable.

[0098] Furthermore, it is more preferable to set the lower limit of equation (18) to 1.5 or 2.0. Also, it is more preferable to set the upper limit of equation (18) to 9.0, 8.0, 6.0, or 5.0.

[0099] Furthermore, in the optical system of each embodiment, it is preferable that the first shift lens group LA has a positive refractive power. In this case, when Dai is the distance along the optical axis from the lens surface closest to the object of the first shift lens group LA to the image plane IP, and TTL is the total distance along the optical axis from the lens surface closest to the object of the optical system to the image plane IP, it is preferable that the following condition of equation (19) is satisfied.

[0100] 0.1 ≤ Dai / TTL ≤ 0.7 (19) Equation (19) indicates the appropriate position of the first shift lens group LA. If the first shift lens group LA is positioned on the object side such that Dai / TTL exceeds the upper limit of equation (19), the convergence of off-axis rays will be insufficient and the diameter of the first shift lens group LA will increase, which is undesirable. If the first shift lens group LA is positioned on the image side such that Dai / TTL falls below the lower limit of equation (8), it will be difficult to secure the necessary back focus, which is also undesirable.

[0101] Furthermore, it is more preferable to set the lower limit of equation (19) to 0.2 or 0.3. Also, it is more preferable to set the upper limit of equation (19) to 0.65 or 0.6.

[0102] Furthermore, in the optical system of each embodiment, when the second shift lens group LB is composed of a positive lens Lbp and a negative lens Lbn, the Abbe number with respect to the d line of the positive lens Lbp is denoted as νbp, and the Abbe number with respect to the d line of the negative lens Lbn is denoted as νbn. In this case, it is preferable that the following condition of equation (20) is satisfied.

[0103] 10 ≤ |νbp - νbn| ≤ 70 (20) The conditions in equation (20) indicate an appropriate Abbe number difference for achromatic aberration between the positive and negative lenses of the second shift lens group LB. If the Abbe number difference is large such that |νbp-νbn| exceeds the upper limit of equation (20), it means that a low-dispersion material with a low refractive index will be used for either the positive or negative lens, making it difficult to maintain the refractive power of the second shift lens group LB, which is undesirable. If the Abbe number difference is small such that |νbp-νbn| falls below the lower limit of equation (20), it is undesirable because it becomes difficult to correct chromatic aberration.

[0104] Furthermore, it is more preferable to set the lower limit of formula (20) to 20, 30, or 35. Also, it is more preferable to set the upper limit of formula (20) to 60, 55, or 50.

[0105] Furthermore, in the optical system of each embodiment, when the first shift lens group LA is composed of a positive lens Lap and a negative lens Lan, the Abbe number with respect to the d line of the positive lens Lap is denoted as νap, and the Abbe number with respect to the d line of the negative lens Lan is denoted as νan. In this case, it is preferable that the following condition of equation (21) is satisfied.

[0106] 10 ≤ |νap - νan| ≤ ​​70 (21) The conditions in equation (21) indicate an appropriate Abbe number difference for achromaticity correction between the positive and negative lenses of the first shift lens group LA. If the Abbe number difference is large such that |νap-νan| exceeds the upper limit of equation (21), it means that a low-dispersion material with a low refractive index will be used for either the positive or negative lens, making it difficult to maintain the refractive power of the first shift lens group LA, which is undesirable. If the Abbe number difference is small such that |νap-νan| falls below the lower limit of equation (21), it is undesirable because it becomes difficult to correct chromatic aberration.

[0107] Furthermore, it is more preferable to set the lower limit of formula (21) to 20, 30, or 35. Also, it is more preferable to set the upper limit of formula (21) to 60, 55, or 50.

[0108] Furthermore, in the optical systems of each embodiment, it is preferable to suppress an increase in the diameter of the second shift lens group LB by having a negative refractive power.

[0109] Furthermore, in the optical system of each embodiment, it is preferable to place an intermediate lens group with positive refractive power between the first shift lens group LA and the second shift lens group LB. This allows the light beam incident on the second shift lens group LB to be focused, making it possible to increase the negative refractive power of the second shift lens group LB. As a result, the shift effect of the second shift lens group LB can be enhanced. In this case, when the focal length of the intermediate lens group is fi, it is preferable to satisfy the condition of the following equation (22).

[0110] 1.0 ≤ fi / f ≤ 10.0 (22) The conditions in equation (22) indicate the appropriate range of focal lengths for the intermediate lens group. If the focal length of the intermediate lens group is too long, such that fi / f exceeds the upper limit of equation (22), the convergence of the light beam incident on the second shift lens group LB will be insufficient, making it difficult to increase the negative refractive power of the second shift lens group LB, which is undesirable. If the focal length of the intermediate lens group is too short, such that fi / f falls below the lower limit of equation (22), the convergence of the light beam incident on the second shift lens group LB will be too strong, making it difficult to correct coma aberration during shift imaging, which is also undesirable.

[0111] Furthermore, it is more preferable to set the lower limit of equation (22) to 1.5, 1.7, or 1.8. Also, it is more preferable to set the upper limit of equation (22) to 8.0, 6.0, or 5.0.

[0112] Furthermore, it is preferable that the optical system of each embodiment has a first lens group with negative refractive power closest to the object. By adopting this retrofocus type power arrangement, the necessary back focus can be secured.

[0113] Furthermore, it is preferable that the optical system of each embodiment includes a first lens group with negative refractive power, a first shift lens group LA with positive refractive power, an intermediate lens group with positive refractive power, and a second shift lens group LB with negative refractive power, all arranged in order from the object side to the image side.

[0114] Furthermore, it is preferable that the optical system of each embodiment satisfies the following condition (23), where Ma is the amount of movement in the shift direction relative to the optical axis of the first shift lens group LA, and Mb is the amount of movement in the shift direction relative to the optical axis of the second shift lens group LB.

[0115] 0.0 <Ma×Sa / Mb×Sb≦3.0 (23) The conditions in equation (23) represent the appropriate relationship between the shift effects caused by the movement of the first and second shift lens groups LA and LB, respectively. If the ratio of the shift effect caused by the movement of the first shift lens group LA is large, such that Ma×Sa / Mb×Sb exceeds the upper limit of equation (23), the amount of movement of the first lens group LA becomes too large, making rapid shift imaging difficult, which is undesirable. If Ma×Sa / Mb×Sb falls below the lower limit of equation (23), the shift effects caused by the movement of the first and second shift lens groups LA and LB cancel each other out, and a sufficient shift effect cannot be obtained, which is also undesirable. It is preferable to always satisfy the conditions in equation (23) during shift imaging.

[0116] Furthermore, it is more preferable to set the lower limit of equation (23) to 0.2, 0.5, or 0.7. Also, it is more preferable to set the upper limit of equation (23) to 2.0, 1.5, or 1.1.

[0117] Furthermore, it is preferable that the optical system of each embodiment satisfies the following condition (24), where ωs is the half-angle of view when the first and second shift lens groups LA and LB are in their maximum shift state (during maximum shift imaging), and ω is the half-angle of view when the first and second shift lens groups LA and LB are in their non-shift state (during normal imaging), as described above.

[0118] 1.4 ≤ tanωs / tanω ≤ 4.0 (24) The conditions in equation (24) indicate an appropriate relationship between the field of view during maximum shift imaging and the field of view during normal imaging. If the shift effect is large enough that tanωs / tanω exceeds the upper limit of equation (24), the amount of movement of the first and second shift lens groups LA and LB becomes too large, making rapid shift imaging difficult, which is undesirable. If tanωs / tanω falls below the lower limit of equation (24), a sufficient shift effect cannot be obtained, which is also undesirable.

[0119] Furthermore, it is more preferable to set the lower limit of equation (24) to 1.5, 1.6, or 1.7. Also, it is more preferable to set the upper limit of equation (24) to 3.5, 3.0, or 2.7.

[0120] Furthermore, if the optical system of each embodiment is a zoom lens, it is preferable that the conditions of equation (12) and at least one of the conditions of equations (13) to (24) are satisfied at all zoom positions from the wide-angle end to the telephoto end.

[0121] Furthermore, in the optical system of each embodiment, the first shift lens group LA and the second shift lens group LB may move to opposite sides of each other in the shift direction, or they may move to the same side.

[0122] The optical systems of Examples 4 to 6 will be described in detail below. After Example 6, numerical examples 4 to 6 corresponding to each of Examples 4 to 6 are shown. [Examples]

[0123] The optical system of Embodiment 4 (Numerical Example 4) shown in Figure 15 consists of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, an aperture diaphragm SP, a fourth lens group with positive refractive power, a fifth lens group with positive refractive power, a sixth lens group with negative refractive power, and a seventh lens group with positive refractive power, arranged in order from the object side to the image side.

[0124] The second lens group is a focusing lens group that moves toward the image side when focusing from infinity to close. The fifth lens group corresponds to the first shift lens group LA and consists of a negative lens Lan and a positive lens Lap arranged in order from the object side. The fourth lens group corresponds to the intermediate lens group. The sixth lens group corresponds to the second shift lens group LB and consists of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0125] Figure 16 shows the longitudinal aberration of the optical system of numerical example 4 in the infinity focus state. Figure 17 shows the lateral aberration of the optical system of numerical example 4 during maximum shift imaging at a subject distance of 1m. Here, the lateral aberration is shown when the focus shift caused by the movement of the first and second shift lens groups LA and LB is corrected by the movement of the focus lens group. The explanation of the longitudinal and lateral aberration diagrams is as described above. [Examples]

[0126] The optical system of Embodiment 5 (Numerical Example 5) shown in Figure 18 is a zoom lens. This optical system is composed of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, a fourth lens group with negative refractive power, an aperture diaphragm SP, a fifth lens group with negative refractive power, a sixth lens group with positive refractive power, a seventh lens group with positive refractive power, an eighth lens group with negative refractive power, a ninth lens group with positive refractive power, a tenth lens group with negative refractive power, and an eleventh lens group with positive refractive power, arranged in order from the object side to the image side.

[0127] The second lens group is a focusing lens group that moves toward the image side when focusing from infinity to close. The sixth lens group corresponds to the first shift lens group LA and consists of a negative lens Lan and a positive lens Lap arranged in order from the object side. The seventh lens group corresponds to the intermediate lens group. The eighth lens group corresponds to the second shift lens group LB and consists of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0128] Figures 19 and 20 show the longitudinal aberrations of the optical system of numerical example 5 at the wide-angle and telephoto ends in an infinity focus state, respectively. Figures 21 and 22 show the lateral aberrations of the optical system of numerical example 5 at the wide-angle and telephoto ends at a subject distance of 1 m during maximum shift imaging, respectively. [Examples]

[0129] The optical system of Embodiment 6 (Numerical Example 6) shown in Figure 23 is a zoom lens. This optical system is composed of a first lens group with negative refractive power, a second lens group with positive refractive power, a third lens group with positive refractive power, a fourth lens group with negative refractive power including an aperture diaphragm SP, a fifth lens group with positive refractive power, a sixth lens group with positive refractive power, a seventh lens group with negative refractive power, an eighth lens group with positive refractive power, a ninth lens group with negative refractive power, and a tenth lens group with positive refractive power, arranged in order from the object side to the image side.

[0130] The ninth lens group is a focus lens group that moves toward the image side during focusing from infinity to the closest distance. The fifth lens group corresponds to the first shift lens group LA and is composed of a negative lens Lan and a positive lens Lap arranged in order from the object side. The sixth lens group corresponds to the intermediate lens group. The seventh lens group corresponds to the second shift lens group LB and is composed of a positive lens Lbp and a negative lens Lbn arranged in order from the object side.

[0131] FIG. 24 and FIG. 25 respectively show the longitudinal aberration in the infinity focus state at the wide-angle end and the telephoto end of the optical system of Numerical Example 6. FIG. 26 and FIG. 27 respectively show the lateral aberration at the maximum shift imaging at a subject distance of 1 m at the wide-angle end and the telephoto end of the optical system of Numerical Example 6.

[0132] Hereinafter, Numerical Examples 4 to 6 are shown. The explanations of the numerical values shown in each numerical example are as described above.

[0133] [Numerical Example 4] Unit: mm Surface data Surface number r d nd νd 1 62.323 2.00 1.59349 67.0 2 26.420 3.05 3 28.981 2.00 1.53110 56.0 4* 18.095 10.73 5 617.690 1.50 1.69680 55.5 6 28.345 (variable) 7 -3930.073 1.40 1.94594 18.0 8 20.279 8.95 2.00069 25.5 9 -100.110 (variable) 10 -38.048 0.99 1.59282 68.6 11 23.481 4.14 1.80810 22.8 12 -44.823 1.61 13 47.721 4.11 1.48749 70.2 14 -23.122 0.89 1.85478 24.8 15 -125.017 1.98 16 (Aperture) ∞ 1.99 17 62.406 1.50 1.74951 35.3 18 32.581 8.81 1.49700 81.5 19* -44.829 1.00 20 -215.264 4.39 1.49700 81.5 21 -17.231 1.00 1.84666 23.8 22 -27.640 2.84 23 -55.824 3.87 1.83481 42.7 24 -31.110 1.50 1.49700 81.5 25* 33.671 3.10 26* 19.487 7.10 1.49700 81.5 27 -529.565 0.14 28 71.145 1.40 1.85150 40.8 29 14.176 10.00 1.49700 81.5 30 82.229 6.12 31* -79.510 1.80 1.85135 40.1 32* ∞ 2.18 33 66.057 6.09 1.84666 23.8 34 -181.212 16.58 Image plane ∞ Aspherical data The 4th surface K = -1.02791e+00 A4 = 2.87563e-05 A6 = 1.76253e-07 A8 = 5.81404e-11 A3 = -7.67385e-05 A5 = -2.58218e-06 A7 = -5.57148e-09 The 19th surface K = 0.00000e+00 A 4= 1.34632e-05 A 6= 1.01153e-07 A 8= 5.35855e-11 A 3=-2.12859e-05 A 5=-1.37529e-06 A 7=-3.71642e-09 Page 25 K = 0.00000e+00 A 4=-2.09474e-05 A 6=-2.58019e-07 A 8=-2.01123e-10 A 3= 4.01914e-05 A 5= 2.89892e-06 A 7= 1.15784e-08 Page 26 K = 0.00000e+00 A 4=-6.91598e-06 A 6= 2.58033e-09 A 8=-5.98011e-11 Page 31 K = 1.51318e+01 A 4=-1.42712e-04 A 6= 1.44376e-06 A 8= 1.69744e-09 A 3= 4.26045e-04 A 5=-3.26106e-06 A 7=-9.46959e-08 Page 32 K = 0.00000e+00 A 4=-2.00721e-04 A 6= 1.23012e-07 A 8= 8.11833e-10 A 3= 6.21577e-04 A 5= 1.04687e-05 A 7=-3.09960e-08 Various data Focal length 24.04 F-number 3.50 Half-angle (°): 41.99 Image height 21.64 Lens length: 140.00 BF 16.58 Mamax 6.97 Mbmax -6.50 Subject distance infinity 1000 d 6 6.01 6.59 d 9 9.24 8.66 Lens group data Group start surface Focal length 1 1 -18.48 2 7 80.99<> 3 10 72.21 4 17 66.54 5 20 117.96 6 23 -52.54 7 26 65.40 [Numerical example 5] Unit: mm Surface data Surface number r d nd νd 1 49.771 3.00 1.95375 32.3 2 29.828 5.77 3 35.702 2.50 1.80400 46.5 4 24.263 6.45 5 33.506 2.00 1.80400 46.5 6 20.237 6.19 7* 22.283 2.00 1.58313 59.4 8* 13.004 11.08 9 -42.205 1.89 1.43875 94.7 10 38.9s15 5.27 1.84666 23.8 11 -1377.815 (Variable) 12 181.657 1.40 1.94594 18.0 13 40.510 6.71 1.72047 34.7 14 -59.865 (Variable) 15 49.683 3.70 1.49700 81.5 16 -87.826 (Variable) 17 -2468.761 0.89 1.91082 35.2 18 26.342 3.18 1.80809 22.8 19 -304.946 1.00 20 (aperture) ∞ (variable) 21 50.666 0.88 1.83481 42.7 22 21.288 4.99 1.49700 81.5 23 -33.813 0.79 2.00069 25.5 24 -746.177 1.00 25 66.678 1.20 1.83481 42.7 26 41.908 10.29 1.49700 81.5 27* -73.515 1.00 28 43.676 8.75 1.49700 81.5 29 -37.466 1.30 1.83400 37.2 30 -39.024 3.00 31 -93.529 2.16 1.83400 37.2 32 -47.762 1.20 1.49700 81.5 33* 37.379 3.44 34 37.449 7.84 1.49700 81.5 35 -59.715 1.40 1.90043 37.4 36 26.680 8.59 1.71736 29.5 37 -76.351 3.84 38* -46.734 2.00 1.85135 40.1 39* ∞ (Variable) 40* -552.309 5.88 1.58313 59.4 41* -41.246 19.07 Image plane ∞ Aspherical data Side 7 K = 0.00000e+00 A 4=-1.72149e-04 A 6=-1.40079e-06 A 8=-9.26033e-10 A 3= 2.56934e-04 A 5= 1.99314e-05 A 7= 5.46818e-08 Page 8 K =-4.50875e+00 A 4= 1.88449e-04 A 6= 1.16661e-07 A 8=-9.55466e-10 A 3=-1.46047e-04 A 5=-1.45036e-05 A 7= 2.78305e-08 Page 27 K = 0.00000e+00 A 4= 3.77519e-06 A 6= 3.40621e-09 A 8=-1.31787e-12 A 3=-8.89474e-06 A 5=-1.34205e-07 A 7= 1.68813e-11 Page 33 K = 0.00000e+00 A 4=-2.09615e-05 A 6=-3.79478e-07 A 8=-3.16456e-10 A 3= 4.21648e-05 A 5= 4.00403e-06 A 7= 1.76673e-08 Page 38 K = 5.90098e+00 A 4=-4.21519e-05 A 6= 1.40143e-06 A 8= 1.79315e-09 A 3=-3.98848e-04 A 5=-5.05087e-06 A 7=-8.58334e-08 Page 39 K = 0.00000e+00 A 4=-1.44200e-04 A 6=-4.44040e-07 A 8= 2.58731e-11 A 3=-8.95073e-05 A 5= 1.39501e-05 A 7= 4.08101e-09 Page 40 K = 0.00000e+00 A 4=-3.46404e-05 A 6=-1.81092e-07 A 8=-5.33452e-11 A 3= 2.08609e-04 A 5= 3.37807e-06 A 7= 4.39433e-09 Page 41 K = 0.00000e+00 A 4=-6.98276e-06 A 6= 6.69788e-09 A 8= 3.04358e-11 A 3= 1.67424e-04 A 5= 5.53596e-07 A 7=-2.31344e-09 Various data Zoom ratio 1.33 Wide-angle, Medium, Telephoto Focal length 17.51 ​​20.05 23.30 F-number 4.10 4.10 4.10 Half-angle (°): 51.01, 47.18, 42.88 Image height 21.64 21.64 21.64 Lens length 186.00 186.00 186.00 BF 19.07 19.07 19.07 Mamax 8.00 7.65 7.40 Mbmax -8.00 -8.00 -8.00 Infinite subject distance d11 1.73 1.32 1.77 d14 20.11 13.80 5.27 d16 0.87 5.60 12.70 d20 10.82 9.17 6.53 d39 0.84 4.47 8.11 Subject distance: 1000mm d11 2.10 1.70 2.14 d14 19.73 13.43 4.89 d16 0.87 5.60 12.70 d20 10.82 9.17 6.53 d39 0.84 4.47 8.11 Lens group data Group starting plane focal length 1 1 -15.60 2 12 85.71 3 15 64.42 4 17 -625.33 5 21 -78.90 6 25 90.74 7 28 43.69 8 31 -65.61 9 34 107.53 10 38 -54.89 11 40 76.12 [Numerical Example 6] Unit: mm Surface data Face number rd nd νd 1 91.967 2.50 1.72916 54.7 2 21.953 8.28 3 36.762 2.00 1.72916 54.7 4* 16.955 6.40 5* 40.707 2.00 1.58313 59.4 6* 22.334 10.41 7 -29.747 1.20 1.72916 54.7 8 2658.657 0.20 9 83.659 5.20 1.59270 35.3 10 -51.823 -0.02 11 128.892 1.20 1.89286 20.4 12 31.822 7.99 1.69895 30.1 13 -44.113 (variable) 14 39.742 3.34 1.48749 70.2 15 -105.677 (variable) 16 -172.087 0.99 1.83481 42.7 17 19.932 4.57 1.72151 29.2 18 -57.017 (variable) 19 (aperture) ∞ 2.82 20 -44.447 0.88 2.00069 25.5 21 81.304 3.18 1.49700 81.5 22 -34.422 0.99 23* 288.001 1.50 1.60342 38.0 24 64.410 6.66 1.49700 81.5 25 -66.796 1.00 26 29.881 4.35 1.43875 94.7 27 -43.585 0.98 1.96300 24.1 28 89.913 1.75 29 249.718 2.98 1.80810 22.8 30 -41.331 3.08 31 -143.839 2.65 1.95375 32.3 32 -67.142 1.48 1.49700 81.5 33* 41.497 4.77 34 26.209 5.62 1.92286 20.9 35 -127.653 0.86 36 -90.923 1.20 2.00069 25.5 37 16.401 9.64 1.49700 81.5 38 -35.816 (variable) 39* -30.339 1.20 1.85400 40.4 40 * 365.933 (variable) 41* 920.791 7.14 1.53110 56.0 42* -33.683 0.29 43 ∞ 1.30 1.51633 64.1 44 ∞ 15.73 Image plane ∞ Aspherical data Side 4 K =-9.82973e-02 A 4=-4.26494e-06 A 6= 5.89442e-08 A 8=-1.67134e-10 Page 5 K = 0.00000e+00 A 4= 6.70799e-05 A 6=-9.52149e-08 A 8=-9.42175e-11 Page 6 K = 2.79900e-01 A 4= 5.59413e-05 A 6=-1.66810e-07 A 8=-2.99467e-10 Page 23 K = 0.00000e+00 A 4=-1.00297e-06 A 6=-6.12250e-10 A 8= 2.66311e-12 A10 = -3.71951e-15 Page 33 K = 0.00000e+00 A 4=-2.07259e-07 A 6=-9.51258e-11 A 8= 9.58683e-13 A10 = 1.09043e-15 Page 39 K = 0.00000e+00 A 4= 1.24500e-05 A 6=-4.71307e-11 A 8=-1.42144e-10 Page 40 K = 0.00000e+00 A 4= 2.22248e-05 A 6=-5.72825e-09 A 8=-1.04066e-10 Page 41 K = 0.00000e+00 A 4=-3.27945e-05 A 6=-4.15749e-07 A 8=-3.22149e-10 A 3= 2.12035e-04 A 5= 5.04660e-06 A 7= 1.83460e-08 Page 42 K =-1.33928e+00 A 4=-1.04003e-04 A 6=-1.17545e-06 A 8=-7.13821e-10 A 3= 4.89581e-04 A 5= 1.51886e-05 A 7= 4.59374e-08 Various data Zoom ratio 1.33 Wide-angle, Medium, Telephoto Focal length 17.51 ​​20.32 23.30 F-number 4.00 4.00 4.00 Half-angle (°): 51.02, 46.80, 42.88 Image height 21.64 21.64 21.64 Lens length 165.00 165.00 165.00 BF 15.37 15.37 15.37 Mamax 10.08 9.43 8.65 Mbmax -10.15 -9.63 -8.96 Infinite subject distance d13 14.51 7.62 0.98 d15 1.14 5.14 8.76 d18 4.28 3.07 1.99 d38 2.54 1.88 1.57 d40 4.59 9.36 13.77 Subject distance: 1000mm d13 14.51 7.62 0.98 d15 1.14 5.14 8.76 d18 4.28 3.07 1.99 d38 2.77 2.13 1.86 d40 4.36 9.10 13.48 Lens group data Group starting plane focal length 1 1 -36.85 2 14 59.69 3 16 401.39 4 19 -75.15 5 23 127.27 6 26 66.15 7 31 -84.40 8 34 57.22 9 39 -32.76 10 41 61.34 The values ​​of equations (12) to (24) in numerical examples 4 to 6 are summarized in Table 2 below. The optical systems in numerical examples 4 to 6 satisfy all the conditions of equations (12) to (24).

[0134] [Table 2]

[0135] Figures 28(A), (B), 31(A), (B), and 34(A), (B) show cross-sections of the optical system L0 of Examples 7 to 9, respectively. The optical system L0 of Examples 7 to 9 is a zoom lens capable of zooming between the wide-angle end and the telephoto end, with each Figure (A) showing a cross-section at the wide-angle end and each Figure (B) showing a cross-section at the telephoto end. The optical system L0 of each example has multiple lens groups, including a shift lens group. The lens groups, the shift direction of the shift lens group, and each cross-sectional view are described above.

[0136] Next, the characteristic configurations of the optical system L0 in Examples 7 to 9 will be described. The optical system L0 in each example has a first shift lens group LA that can move in a direction perpendicular to the optical axis (shift direction), and a second shift lens group LB that is positioned on the image side of the first shift lens group LA and can move in the shift direction. By moving these first and second shift lens groups LA and LB in the shift direction, a tilt effect is obtained. In this case, correction of image distortion due to optical eccentricity (shift) of the lenses can be performed by moving just one shift lens group, but by moving two shift lens groups, it becomes possible to correct the composition shift that occurs when correcting image distortion, making it easier to perform tilt imaging with a small amount of composition shift. Furthermore, by correcting image distortion by moving two shift lens groups, it is possible to effectively correct various aberrations such as coma aberration and chromatic aberration caused by the movement, and to facilitate tilt imaging for objects that require a large amount of image distortion correction.

[0137] Furthermore, the optical system L0 of each embodiment includes a focus lens group that moves along the optical axis during focusing, located on the image side of the second shift lens group LB. By positioning the focus lens group on the image side in this way, it becomes possible to correct image distortion required during tilt imaging before correcting focus fluctuations. Therefore, it is possible to simultaneously correct focus fluctuations due to changes in object distance and focus fluctuations due to the movement of the shift lens group. Moreover, among the various aberrations that occur when correcting image distortion due to the movement of the two shift lens groups, those that could not be corrected by each shift lens group, particularly astigmatism, can be corrected by the focus lens group. This makes it possible to easily perform tilt imaging with excellent optical performance.

[0138] In the optical system L0 of each embodiment, the maximum amount of movement of the first shift lens group LA in the shift direction is denoted as Mamax, and the maximum amount of movement of the second shift lens group LB in the shift direction is denoted as Mbmax. Here, the direction in which the first shift lens group LA moves is considered positive, and the opposite direction is considered negative. The maximum amount of movement is the amount of movement of each shift lens group when the maximum tilt effect is obtained in the specifications of the optical system of each embodiment, and the direction of movement may be positive or negative. Also, let the focal length of the first shift lens group LA be fa, and the focal length of the second shift lens group LB be fb. In this case, it is preferable that the optical system L0 of each embodiment satisfies the conditions of the following equation (25).

[0139] (Mamax × fa) / (Mbmax × fb) < 0 (25) The condition in equation (1) indicates an appropriate relationship between the composition shift generated by the first shift lens group LA and the composition shift generated by the second shift lens group B. Satisfying the condition in equation (1) results in the direction of the composition shift caused by the movement of the first shift lens group LA and the direction of the composition shift caused by the movement of the second shift lens group LB being opposite directions, so as to cancel each other out. If the value in equation (25) exceeds the upper limit, the directions of the composition shifts become the same and do not cancel each other out, making it undesirable as it would only allow tilt imaging with a large composition shift.

[0140] Furthermore, it is more preferable to set the upper limit of equation (26) to -0.1, -0.2, -0.3, or -0.4.

[0141] Furthermore, it is preferable that the optical system L0 of each embodiment satisfies at least one of the following conditions.

[0142] 0.05 ≤ |fa / f| ≤ 3.00 (26) 0.05 ≤ |fb / f| ≤ 3.00 (27) 0.4 ≤ |Pa| + |Pb| ≤ 12.0 (28) 0 <Lbk / f≦0.90 (29) 0.3 ≤ |f / fbw| ≤ 10.0 (30) 0.1 ≤ |fLfobj / fb| ≤ 2.0 (31) 0.01 ≤ |Mamax / fa| ≤ 0.30 (32) 0.01 ≤ |Mbmax / fb| ≤ 0.30 (33) -8.00≦(Rfa+Rra) / (Rra-Rfa)≦8.00 (34) -8.00≦(Rfb+Rrb) / (Rrb-Rfb)≦8.00 (35) 0.10 ≤ Dfc / TTL ≤ 0.70 (36) 0 <Dbw / TTL≦0.40 (37) In equations (26) to (37), let f be the focal length of the entire optical system at the wide-angle end, fa be the focal length of the first shift lens group LA, and fb be the focal length of the second shift lens group LB. Let fbw be the focal length of the intermediate lens group LBW, which is positioned between the first shift lens group LA and the second shift lens group LB and does not move in the shift direction. Let fLfobj be the focal length of the focusing lens group closest to the object among at least one focusing lens group. Let Pa be the Petzval sum of the first shift lens group LA, and Pb be the Petzval sum of the second shift lens group LB. Let Lbk be the back focus of the optical system at the wide-angle end. The back focus is the air-equivalent distance on the optical axis from the image-side lens surface to the image plane. Let Rfa be the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group LA, Rra be the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group LA, Rfb be the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group LB, and Rrb be the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group LB. At the wide-angle end and in focus at infinity, let Dfc be the distance along the optical axis from the lens surface closest to the image in the object-side focusing lens group to the image plane, and TTL be the distance along the optical axis from the lens surface closest to the object in the optical system to the image plane (total lens length) at the wide-angle end. At the wide-angle end and in focus at infinity, let Dbw be the distance along the optical axis from the lens surface closest to the image in the second shift lens group LB to the lens surface closest to the object in the object-side focusing lens group.

[0143] The conditions in equation (26) indicate an appropriate relationship between the focal length of the entire optical system L0 and the focal length of the first shift lens group LA. If |fa / f| falls below the lower limit of equation (26), the amount of eccentric aberration per unit movement of the first shift lens group LA increases, making it difficult to maintain good optical performance during tilt imaging, which is undesirable. If |fa / f| exceeds the upper limit of equation (26), a large amount of movement and a large lens diameter of the first shift lens group LA are required to tilt the object plane in focus significantly, resulting in a larger optical system, which is also undesirable.

[0144] Furthermore, it is more preferable to set the lower limit of equation (26) to 0.10, 0.20, 0.30, or 0.50. Also, it is more preferable to set the upper limit of equation (26) to 2.50, 2.00, or 1.80.

[0145] The conditions in equation (27) indicate an appropriate relationship between the focal length of the entire optical system L0 and the focal length of the second shift lens group LB. If |fb / f| falls below the lower limit of equation (27), the amount of eccentric aberration per unit movement of the second shift lens group LB increases, making it difficult to maintain good optical performance during tilt imaging, which is undesirable. If |fb / f| exceeds the upper limit of equation (27), a large amount of movement and a large lens diameter of the second shift lens group LB are required to tilt the object plane in focus significantly, resulting in a larger optical system, which is also undesirable.

[0146] Furthermore, it is more preferable to set the lower limit of equation (27) to 0.10, 0.20, or 0.30. Also, it is more preferable to set the upper limit of equation (27) to 2.50 or 2.30.

[0147] The condition in equation (28) represents an appropriate sum of the Petzval sum of the first shift lens group LA and the Petzval sum of the second shift lens group LB. The Petzval sum P of the shift lens groups is defined by the following equation.

[0148]

number

[0149] rν: radius of paraxial curvature of the ν-th surface Nν: Refractive index at the d-line of the incident medium on the ν-plane N′ν: Refractive index at the d-line of the ejection-side medium on the ν-plane f: focal length of the entire optical system If |Pa|+|Pb| falls below the lower limit of equation (28), a large amount of movement and a large lens diameter are required for each shift lens group in order to significantly tilt the object plane that is in focus during tilt imaging, which is undesirable because it increases the size of the optical system. If |Pa|+|Pb| exceeds the upper limit of equation (28), the amount of eccentric aberration per unit movement of each shift lens group increases, making it difficult to maintain good optical performance during tilt imaging, which is also undesirable.

[0150] Furthermore, it is more preferable to set the lower limit of equation (28) to 0.45, 0.5, or 0.55. Also, it is more preferable to set the upper limit of equation (28) to 10.0, 8.0, 6.0, or 4.0.

[0151] The conditions in equation (29) indicate an appropriate relationship between the focal length and back focus of the entire optical system L0. By positioning the lens at a high height from the optical axis to satisfy these conditions, image field curvature can be easily corrected, and good optical performance can be achieved. If Lbk / f exceeds the upper limit of equation (29), the overall length of the lens becomes long, which is undesirable. If Lbk / f falls below the lower limit of equation (29), the lens surface closest to the image will come into contact with the image sensor or silver halide film placed on the image plane, which is also undesirable.

[0152] Furthermore, it is more preferable to set the lower limit of equation (29) to 0.05 or 0.10. Also, it is more preferable to set the upper limit of equation (29) to 0.85 or 0.83.

[0153] The conditions in equation (30) indicate an appropriate relationship between the focal length of the intermediate lens group LBW and the focal length of the entire optical system L0. If |f / fbw| falls below the lower limit of equation (30), the refractive power of the intermediate lens group LBW becomes too weak, making it difficult to suppress the height of off-axis rays incident on the second shift lens group LB, and the second shift lens group LB becomes larger, which is undesirable. If |f / fbw| exceeds the upper limit of equation (30), the refractive power of the intermediate lens group LBW becomes too strong, making it difficult to correct the various aberrations occurring in the intermediate lens group LBW, which is also undesirable.

[0154] Furthermore, it is more preferable to set the lower limit of equation (30) to 0.4, 0.45, or 0.5. Also, it is more preferable to set the upper limit of equation (30) to 9.0, 8.0, or 7.0.

[0155] The conditions in equation (31) indicate an appropriate relationship between the focal length of the second shift lens group LB and the focal length of the focusing lens group closest to the object. If |fLfobj / fb| exceeds the upper limit of equation (31), the refractive power of the focusing lens group closest to the object becomes too weak, increasing the amount of movement required for focusing. This is undesirable because it makes it difficult to miniaturize the entire system. If |fLfobj / fb| falls below the lower limit of equation (31), the refractive power of the focusing lens group closest to the object becomes too strong, increasing the amount of aberrations that occur during focusing. This is undesirable because it makes it difficult to correct aberrations that could not be corrected by each shift lens group and to maintain good optical performance.

[0156] Furthermore, it is more preferable to set the lower limit of equation (31) to 0.2, 0.3, 0.4, or 0.5. Also, it is more preferable to set the upper limit of equation (31) to 1.5, 1.2, or 1.0.

[0157] The conditions in equation (32) indicate an appropriate relationship between the focal length of the first shift lens group LA and the maximum displacement of the first shift lens group LA. If |Mamax / fa| falls below the lower limit of equation (32), the displacement of the first shift lens group LA becomes small, and sufficient image drift cannot be obtained during tilt imaging. This is undesirable because it becomes difficult to significantly tilt the object plane in focus. If |Mamax / fa| exceeds the upper limit of equation (32), the refractive power of the first shift lens group LA becomes too strong, increasing the amount of eccentric aberration per unit displacement, making it difficult to maintain good optical performance during tilt imaging, which is also undesirable.

[0158] Furthermore, it is more preferable to set the lower limit of equation (32) to 0.015 or 0.20. Also, it is more preferable to set the upper limit of equation (32) to 0.20, 0.10, or 0.05.

[0159] The conditions in equation (33) indicate an appropriate relationship between the focal length of the second shift lens group LB and the maximum displacement of the second shift lens group LB. If |Mbmax / fb| falls below the lower limit of equation (33), the displacement of the second shift lens group LB becomes small, and sufficient image drift cannot be obtained during tilt imaging. This is undesirable because it becomes difficult to significantly tilt the object plane in focus. If |Mbmax / fb| exceeds the upper limit of equation (33), the refractive power of the second shift lens group LB becomes too strong, increasing the amount of eccentric aberration per unit displacement, making it difficult to maintain good optical performance during tilt imaging, which is also undesirable.

[0160] Furthermore, it is more preferable to set the lower limit of formula (33) to 0.015 or 0.02. Also, it is more preferable to set the upper limit of formula (33) to 0.20, 0.10, or 0.05.

[0161] The conditions in equation (34) indicate the appropriate shape factors for the lens surface closest to the object and the lens surface closest to the image in the first shift lens group LA. When the shape of the first shift lens group LA approaches a meniscus shape such that the shape factor exceeds the upper limit or falls below the lower limit of equation (34), the refractive power of the first shift lens group LA decreases. As a result, the amount of image distortion decreases, making it difficult to tilt the object plane in focus significantly, which is undesirable.

[0162] Furthermore, it is more preferable to set the lower limit of equation (34) to -6.0, -5.0, 0.0, or +0.3. Also, it is more preferable to set the upper limit of equation (34) to 6.0, 5.0, 2.0, or 1.5.

[0163] The conditions in equation (35) indicate the appropriate shape factors for the lens surface closest to the object and the lens surface closest to the image in the second shift lens group LB. When the shape of the second shift lens group LB approaches a meniscus shape such that the shape factor exceeds the upper limit or falls below the lower limit of equation (35), the refractive power of the second shift lens group LB decreases. As a result, the amount of image distortion decreases, making it difficult to tilt the object plane in focus significantly, which is undesirable.

[0164] Furthermore, it is more preferable to set the lower limit of equation (35) to -6.0, -5.0, or 0.0. Also, it is more preferable to set the upper limit of equation (35) to 7.0, 6.0, or 5.0.

[0165] The conditions in equation (36) indicate an appropriate relationship between the total length of the lens and the distance from the image-side lens surface to the image plane of the focusing lens group closest to the object. If Dfc / TTL falls below the lower limit of equation (36), it becomes difficult to secure the amount of movement necessary for focusing the focusing lens group closest to the object, making it impossible to focus on nearby objects, which is undesirable. If Dfc / TTL exceeds the upper limit of equation (36), the focusing lens group closest to the object is too far from the image plane, resulting in the focusing lens group being positioned at a low height from the optical axis for off-axis rays. As a result, it becomes difficult for the focusing lens group to correct various aberrations, especially astigmatism, that could not be corrected by each shift lens group during tilt imaging, which is undesirable.

[0166] Furthermore, it is more preferable to set the lower limit of equation (36) to 0.20 or 0.30. Also, it is more preferable to set the upper limit of equation (36) to 0.60 or 0.50.

[0167] The conditions in equation (37) indicate an appropriate relationship between the total lens length and the distance from the image-side lens surface of the second shift lens group LB to the object-side lens surface of the object-side focusing lens group. If Dbw / TTL exceeds the upper limit of equation (37), the distance between the second shift lens group LB and the object-side focusing lens group becomes too large. This is undesirable because it becomes difficult for the focusing lens group to correct aberrations, especially astigmatism, that could not be corrected by each shift lens group during tilt imaging. If Dbw / TTL falls below the lower limit of equation (37), the second shift lens group LB and the object-side focusing lens group come into contact, which is also undesirable.

[0168] Furthermore, it is more preferable to set the lower limit of equation (37) to 0.01 or 0.02. Also, it is more preferable to set the upper limit of equation (37) to 0.30 or 0.20.

[0169] In the optical system of each embodiment, which is a zoom lens, it is preferable that the conditions of equation (25) and at least one of the conditions of equations (26) to (37) are satisfied at all zoom positions from the wide-angle end to the telephoto end.

[0170] Furthermore, in the optical system L0 of each embodiment, it is preferable that the first shift lens group LA has a positive refractive power. Having a positive refractive power in the first shift lens group LA causes the on-axial light beam to converge, making it possible to reduce the diameter of the second shift lens group LB, which is positioned on the image side of the first shift lens group LA.

[0171] The optical systems of Examples 7 to 9 will be described in detail below. After Example 9, numerical examples 7 to 9 corresponding to each of Examples 7 to 9 are shown. [Examples]

[0172] The optical system L0 of Embodiment 7 (Numerical Example 7) shown in Figures 28(A) and (B) consists of a front group LF including a first lens group with positive refractive power, a second lens group with negative refractive power, and a third lens group with positive refractive power, arranged in order from the object side to the image side; an intermediate group LM including a fourth lens group with positive refractive power, an aperture diaphragm SP, a fifth lens group with negative refractive power, and a sixth lens group with positive refractive power; and a rear group LR including a seventh lens group with positive refractive power, an eighth lens group with negative refractive power, a ninth lens group with positive refractive power, and a tenth lens group with negative refractive power.

[0173] The fourth lens group corresponds to the first shift lens group LA and consists of one positive lens. The fifth lens group corresponds to the intermediate lens group LBW. The sixth lens group corresponds to the second shift lens group LB and consists of two positive lenses and one negative lens arranged in order from the object side. The eighth lens group is the focusing lens group and moves towards the image side when focusing from infinity to close. The focusing lens group also corrects aberrations that cannot be corrected by each shift lens group, especially astigmatism. This is the same in other embodiments described later.

[0174] Figure 30(A) shows the longitudinal aberration of the optical system L0 of numerical example 7 during normal imaging at the wide-angle end and in focus at infinity (non-shifted state of each shift lens group). Figure 30(B) shows the longitudinal aberration of the optical system L0 of numerical example 7 during normal imaging at the telephoto end and in focus at infinity. Figure 31(A) shows the lateral aberration in tilt imaging 1 of the optical system L0 of numerical example 7 at the wide-angle end and with the object plane at a distance of approximately 5000 mm on the optical axis from the lens plane closest to the object tilted at approximately 70° with respect to a plane perpendicular to the optical axis. Figure 31(B) shows the lateral aberration in tilt imaging 2 of the optical system L0 of numerical example 7 at the telephoto end and with the object plane at a distance of approximately 20000 mm on the optical axis from the lens plane closest to the object tilted at approximately 70° with respect to a plane perpendicular to the optical axis. The explanation of the longitudinal aberration diagrams and lateral aberration diagrams is as described above. [Examples]

[0175] The optical system L0 of Embodiment 8 (Numerical Example 8) shown in Figures 31(A) and (B) is composed of a front group LF including a first lens group with negative refractive power, arranged in order from the object side to the image side; an intermediate group LM including a second lens group with positive refractive power, a third lens group with negative refractive power including an aperture diaphragm SP, and a fourth lens group with negative refractive power; and a rear group LR including a fifth lens group with positive refractive power, a sixth lens group with negative refractive power, a seventh lens group with negative refractive power, and an eighth lens group with positive refractive power.

[0176] The second lens group corresponds to the first shift lens group LA and consists of one positive lens. The third lens group corresponds to the intermediate lens group LBW. The fourth lens group corresponds to the second shift lens group LB and consists of one negative lens and one positive lens arranged in order from the object side. The sixth lens group is the focusing lens group and moves towards the image side when focusing from infinity to close.

[0177] Figure 32(A) shows the longitudinal aberration during normal imaging at the wide-angle end and in focus at infinity for optical system L0 of numerical example 8. Figure 32(B) shows the longitudinal aberration during normal imaging at the telephoto end and in focus at infinity for optical system L0 of numerical example 8. Figure 33(A) shows the lateral aberration in tilt imaging 1 at the wide-angle end of optical system L0 of numerical example 8, with the object plane at a distance of approximately 875 mm on the optical axis from the lens plane closest to the object tilted at approximately 60° with respect to a plane perpendicular to the optical axis. Figure 33(B) shows the lateral aberration in tilt imaging 2 at the telephoto end of optical system L0 of numerical example 8, with the object plane at a distance of approximately 1625 mm on the optical axis from the lens plane closest to the object tilted at approximately 60° with respect to a plane perpendicular to the optical axis. [Examples]

[0178] The optical system L0 of Embodiment 9 (Numerical Example 9) shown in Figures 34(A) and (B) consists of a front group LF including a first lens group with positive refractive power, a second lens group with negative refractive power, and a third lens group with positive refractive power, arranged in order from the object side to the image side; an intermediate group LM including a fourth lens group with positive refractive power, an aperture diaphragm SP, a fifth lens group with negative refractive power, and a sixth lens group with positive refractive power; and a rear group LR including a seventh lens group with positive refractive power, an eighth lens group with negative refractive power, a ninth lens group with negative refractive power, a tenth lens group with positive refractive power, and an eleventh lens group with negative refractive power.

[0179] The fourth lens group corresponds to the first shift lens group LA and consists of one negative lens and one positive lens arranged in order from the object side. The fifth lens group corresponds to the intermediate lens group LBW. The sixth lens group corresponds to the second shift lens group LB and consists of two positive lenses and one negative lens arranged in order from the object side. The eighth and ninth lens groups are focusing lens groups; when focusing from infinity to close, the eighth lens group moves towards the image side and the ninth lens group moves towards the object side.

[0180] Figure 35(A) shows the longitudinal aberration during normal imaging at the wide-angle end and in focus at infinity for optical system L0 of numerical example 9. Figure 35(B) shows the longitudinal aberration during normal imaging at the telephoto end and in focus at infinity for optical system L0 of numerical example 9. Figure 36(A) shows the lateral aberration in tilt imaging 1 at the wide-angle end of optical system L0 of numerical example 9, with the object plane at a distance of approximately 10,000 mm on the optical axis from the lens plane closest to the object tilted at approximately 70° with respect to a plane perpendicular to the optical axis. Figure 36(B) shows the lateral aberration in tilt imaging 2 at the telephoto end of optical system L0 of numerical example 9, with the object plane at a distance of approximately 25,000 mm on the optical axis from the lens plane closest to the object tilted at approximately 70° with respect to a plane perpendicular to the optical axis.

[0181] Numerical examples 7-9 are shown below. The explanation for the numbers shown in each example is as described above. [Numerical Example 7] Unit: mm Surface data Face number rd nd νd 1 234.114 8.00 1.49700 81.5 2 -1561.673 0.20 3 159.245 3.00 1.61340 44.3 4 97.016 12.00 1.43875 94.7 5 796.722 (variable) 6 382.039 1.50 1.59381 39.4 7 94.755 4.31 8 -102.009 1.49 1.51377 71.1 9 65.024 2.87 1.83500 24.2 10 113.551 (variable) 11 75.635 7.12 1.49700 81.5 12 -85.236 0.20 13 142.977 5.66 1.59270 35.3 14 -65.295 1.80 2.00100 29.1 15 666.296 (variable) 16 81.444 3.02 1.79408 48.5 17 -3854.328 3.00 18 (aperture) ∞ 5.29 19 -58.433 1.10 1.76885 50.7 20 49.134 2.63 21 79.545 3.69 1.78774 26.3 22 -106.114 2.00 23* 9480.302 2.18 1.58313 59.4 24 -120.323 1.30 1.85250 23.8 25 121.810 2.00 26 58.608 4.96 1.51677 78.3 27 -47.194 (variable) 28 163.182 2.72 1.73871 29.9 29 -73.001 1.20 1.74671 52.8 30 42.368 (variable) 31 104.573 2.00 1.84658 23.8 32 61.318 5.47 1.50293 80.8 33 -65.018 (variable) 34 178.122 3.99 1.72047 34.7 35 -109.975 1.40 1.43875 94.7 36 52.597 5.27 37 -52.603 1.40 1.60237 66.9 38 2159.365 (variable) Image plane ∞ Aspherical data Page 23 K = 0.00000e+00 A 4=-1.22481e-06 A 6= 6.88762e-10 A 8=-2.41637e-12 Various data Zoom ratio 3.77 Wide-angle, Medium, Telephoto Focal length 103.00 200.00 388.00 F-numbers: 4.64, 5.69, 5.77 Half-angle (°): 11.86 6.17 3.19 Image height 21.64 21.64 21.64 Lens length: 252.25, 300.76, 342.25 BF 21.40 51.67 66.85 Figure 3(A) shows the aberration diagram for tilt imaging 1 in numerical example 1, and Figure 3(B) shows the aberration diagram for tilt imaging 2.

[0182] Wide-angle, Intermediate, Telephoto, Tilt imaging 1, Tilt imaging 2 d 5 2.00 50.51 92.00 2.00 92.00 d10 49.78 31.66 1.30 49.786 1.30 d15 5.00 23.11 53.48 5.00 53.48 d27 2.00 6.27 6.43 2.79 7.99 d30 28.25 16.89 17.23 27.46 15.67 d33 41.10 17.91 2.23 41.10 2.23 d38 21.40 51.67 66.85 21.40 66.85 Tilt imaging 1 Tilt imaging 2 Ma 1.98 1.48 Mb -2.65 -2.01 Lens group data Group starting plane focal length 1 1 251.97 2 6 -80.83 3 11 108.78 4 16 100.48 5 19 -34.56 6 21 113.70 7 26 51.41 8 28 -76.76 9 31 98.66 10 34 -75.32 [Numerical Example 8] Unit: mm Surface data Face number rd nd νd 1* 79.371 2.20 1.58313 59.4 2* 13.546 11.37 3 -53.682 1.00 1.49700 81.5 4 57.875 0.87 5 35.848 4.23 1.66607 42.7 6 -157.714 (variable) 7 36.329 2.68 1.83512 44.5 8 -126.914 0.99 9 (aperture) ∞ 1.36 10 -59.134 0.99 1.94674 31.2 11 10.767 4.19 1.89346 29.1 12 242.548 2.69 13 -50.968 0.99 1.59546 39.6 14 51.185 1.99 1.83469 42.7 15 57.022 (Variable) 16 17.273 0.90 1.63456 46.3 17 12.189 6.41 1.49700 81.5 18 -49.155 0.20 19* 33.177 6.86 1.49700 81.5 20* -24.530 (variable) 21 47.342 1.00 1.65522 61.3 22 16.354 (Variable) 23 57.360 1.60 1.85400 40.4 24 * 38.398 (variable) 25 -13481.460 3.87 1.49700 81.5 26 -90.892 16.73 Image plane ∞ Aspherical data Front page K = 0.00000e+00 A 4=-2.10776e-06 A 6= 3.37878e-09 A 8=-9.33388e-11 A10= 4.09217e-13 A12=-7.32138e-16 A14= 4.99326e-19 2nd side K =-3.55374e-01 A 4=-5.89741e-06 A 6=-7.88985e-08 A 8= 6.33293e-10 A10=-7.85129e-12 A12= 3.18317e-14 A14=-5.22383e-17 Page 19 K = 0.00000e+00 A 4=-5.54838e-05 A 6=-4.56699e-08 A 8=-6.57734e-11 A10= 4.55079e-12 A12= 4.25204e-14 Page 20 K = 0.00000e+00 A 4= 2.12635e-05 A 6= 5.35516e-08 A 8=-1.27211e-10 A10= 1.93396e-12 A12= 9.78814e-14 Page 24 K = 0.00000e+00 A 4=-5.24079e-06 A 6=-2.86738e-08 A 8=-4.11376e-11 Various data Zoom ratio 1.65 Wide-angle, Medium, Telephoto Focal length 20.61 31.15 33.94 F-number 4.12 4.12 4.12 Half-angle (°): 44.45, 34.59, 32.51 Image height 21.64 21.64 21.64 Lens length: 113.98mm, 107.21mm, 107.29mm BF 16.73 16.73 16.73 Wide-angle, Intermediate, Telephoto, Tilt imaging 1, Tilt imaging 2 d 6 22.25 4.76 2.02 22.25 2.02 d15 2.01 1.99 1.96 2.01 1.96 d20 2.42 2.10 2.05 2.60 2.20 d22 8.97 9.28 9.34 8.79 9.18 d24 5.19 15.93 18.79 5.19 18.79 Tilt imaging 1 Tilt imaging 2 Ma 1.15 0.80 Mb 1.60 1.06 Lens group data Group starting plane focal length 1 1 -37.94 2 7 34.08 3 9 -40.19 4 13 -45.81 5 16 16.53 6 21 -38.63 7 23 -141.51 8 25 184.10 [Numerical Example 9] Unit: mm Surface data Face number rd nd νd 1 139.817 8.00 1.49700 81.5 2 -13406.368 0.20 3 131.919 3.00 1.61340 44.3 4 66.622 12.00 1.43875 94.7 5 236.562 (variable) 6 217.624 1.58 1.51709 78.4 7 73.685 4.44 8 -105.351 1.50 1.62108 64.9 9 58.740 3.26 1.88186 27.1 10 125.501 (variable) 11 53.379 7.21 1.49700 81.5 12 -133.527 8.53 13 79.857 5.72 1.59270 35.3 14 -65.264 1.80 2.00100 29.1 15 272.645 (variable) 16 74.775 1.80 1.65883 59.6 17 55.275 4.28 1.60939 48.6 18 9331.080 11.10 19 (aperture) ∞ 7.40 20 -55.468 2.52 1.94630 32.6 21 58.994 2.92 22 146.845 3.77 1.66079 32.8 23 -74.025 0.20 24* 150.948 2.98 1.58313 59.4 25 -113.853 1.32 1.88128 37.8 26 -1168.104 2.00 27 45.273 4.10 1.51711 52.5 28 -141.030 (variable) 29 168.151 3.03 1.73251 28.4 30 -53.714 1.20 1.82189 46.0 31 39.241 (variable) 32 187.927 2.00 1.91557 31.4 33 73.558 (Variable) 34 61.958 4.90 1.50506 65.4 35 -43.964 (variable) 36 241.200 3.94 1.72047 34.7 37 -85.469 1.40 1.43875 94.7 38 79.051 4.26 39 -47.471 1.42 1.54951 73.7 40 142.356 (variable) Image plane ∞ Aspherical data Page 24 K = 0.00000e+00 A 4=-3.43550e-07 A 6= 1.74952e-09 A 8=-2.14367e-11 A10= 1.52783e-13 A12=-3.90773e-16 Various data Zoom ratio 3.00 Wide-angle, Medium, Telephoto Focal length 194.00 350.00 582.00 F-numbers: 5.60, 6.84, 8.24 Half-angle (°): 6.36, 3.54, 2.13 Image height 21.64 21.64 21.64 Lens length: 260.20 x 314.07 x 350.20 BF 23.11 52.34 81.24 Wide-angle, Intermediate, Telephoto, Tilt imaging 1, Tilt imaging 2 d 5 9.43 63.31 99.43 9.43 99.43 d10 14.05 8.30 1.29 14.05 1.29 d15 5.42 11.17 18.18 5.42 18.18 d28 2.68 3.55 2.00 3.55 3.48 d31 9.69 14.42 20.28 8.38 18.80 d33 3.69 2.62 2.00 4.13 1.99 d35 68.35 34.59 2.01 68.35 2.01 d40 23.11 52.34 81.24 23.11 81.24 Tilt imaging 1 Tilt imaging 2 Ma 1.91 3.74 Mb -1.22 -2.79 Lens group data Group starting plane focal length 1 1 255.36 2 6 -74.86 3 11 87.13 4 16 127.20 5 20 -29.89 6 22 65.10 7 27 66.78 8 29 -55.42 9 32 -133.12 10 34 51.72 11 36 -69.25

[0183] [Table 3]

[0184] [Imaging device] Figure 37 shows a digital still camera (imaging device) 10 using the optical systems of each of the above embodiments. In Figure 37, 13 is the camera body, and 11 is the imaging optical system composed of one of the optical systems of Embodiments 1 to 9. 12 is an image sensor (photoelectric conversion element) such as a CCD sensor or CMOS sensor, which is built into the camera body 13 and captures (photoelectrically converts) the optical image formed by the imaging optical system 11, that is, it captures the subject through the imaging optical system 11.

[0185] The camera body 13 may be a single-lens reflex camera with a quick-turn mirror, or a mirrorless camera without a quick-turn mirror.

[0186] By using the optical systems of each embodiment in this way, it is possible to realize an imaging device that is compact yet provides good tilt and shift effects while reducing composition shift.

[0187] The above embodiments include the following configuration. (Composition 1) The optical system comprises a first shift lens group that can move in a direction perpendicular to the optical axis, and a second shift lens group positioned on the image side of the first shift lens group and also movable in a direction perpendicular to the optical axis. When the lateral magnifications of the first and second shift lens groups are βa and βb respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups are βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups are Sa = (1-βa) × βra and Sb = (1-βb) × βrb respectively, and the amount of movement of the first shift lens group relative to the optical axis is Ma, and the amount of movement of the second shift lens group relative to the optical axis is Mb, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 The following conditions are met: Furthermore, when the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, the maximum value of the movement amount Ma of the first shift lens group is Mamax, and the maximum value of the movement amount Mb of the second shift lens group is Mbmax, 0.03 ≤ |Mamax / fa| ≤ 0.25 0.03 ≤ |Mbmax / fb| ≤ 0.25 An optical system characterized by satisfying at least one of the following conditions. (Configuration 2) When the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group is Rfa, the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group is Rra, the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group is Rfb, and the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group is Rrb, In that case, -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 The optical system according to configuration 1, characterized in that it satisfies at least one of the following conditions. (Composition 3) When the focal length of the optical system is f, 1.0 < |fa| / f ≤ 10.0 1.0 < |fb| / f ≤ 10.0 The optical system according to configuration 1 or 2, characterized in that it satisfies at least one of the following conditions. (Composition 4) When Dbi is the distance along the optical axis from the lens surface closest to the object in the second shift lens group to the image plane, and TTL is the distance along the optical axis from the lens surface closest to the object in the optical system to the image plane, 0.1 ≤ Dbi / TTL ≤ 0.9 The optical system according to any one of claims 1 to 3, characterized in that it satisfies the following conditions. (Composition 5) The optical system according to any one of claims 1 to 4, characterized in that the second shift lens group is composed of a positive lens and a negative lens. (Composition 6) When the Abbe number with respect to the d line of the positive lens is νbp and the Abbe number with respect to the d line of the negative lens is νbn, 10 ≤ |νbp - νbn| ≤ 70 The optical system according to configuration 5, characterized by satisfying the following conditions. (Composition 7) The optical system according to configuration 1, characterized in that the first shift lens group is composed of a positive lens and a negative lens. (Composition 8) When the Abbe number with respect to the d line of the positive lens is νap and the Abbe number with respect to the d line of the negative lens is νan, 10 ≤ |νap - νan| ≤ ​​70 The optical system according to configuration 7, characterized by satisfying the following conditions. (Composition 9) The optical system according to any one of configurations 1 to 8, characterized in that the second shift lens group has a negative refractive power. (Composition 10) It has an intermediate lens group with positive refractive power positioned between the first shift lens group and the second shift lens group, When the focal length of the intermediate lens group is fi and the focal length of the optical system is f, 1.0 <fi / f≦10.0 An optical system described in any one of configurations 1 to 9 that satisfies the following conditions. (Composition 11) The aforementioned optical system is a zoom lens capable of zooming from the wide-angle end to the telephoto end. At all zoom positions from wide-angle to telephoto, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 The following conditions are met: 0.03 ≤ Mamax / |fa| ≤ 0.25 0.03 ≤ Mbmax / |fb| ≤ 0.25 An optical system according to any one of configurations 1 to 10, characterized in that it satisfies at least one of the following conditions. (Composition 12) The optical system according to any one of configurations 1 to 11, characterized in that the first shift lens group and the second shift lens group move toward the same side relative to the optical axis. (Composition 13) The optical system comprises a first shift lens group that can move in a direction perpendicular to the optical axis, and a second shift lens group positioned on the image side of the first shift lens group and also movable in a direction perpendicular to the optical axis. When the lateral magnifications of the first and second shift lens groups are βa and βb respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups are βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups are Sa = (1-βa) × βra and Sb = (1-βb) × βrb respectively, and the amount of movement of the first shift lens group relative to the optical axis is Ma, and the amount of movement of the second shift lens group relative to the optical axis is Mb, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 An optical system characterized by satisfying the following conditions. (Composition 14) The optical system comprises a first shift lens group that can move in a direction perpendicular to the optical axis, and a second shift lens group positioned on the image side of the first shift lens group and also movable in a direction perpendicular to the optical axis. When the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, the maximum displacement of the first shift lens group with respect to the optical axis is Mamax, and the maximum displacement of the second shift lens group with respect to the optical axis is Mbmax, 0.03 ≤ |Mamax / fa| ≤ 0.25 0.03 ≤ |Mbmax / fb| ≤ 0.25 An optical system characterized by satisfying at least one of the following conditions. (Composition 15) The optical system comprises a first shift lens group that can move in a direction perpendicular to the optical axis, and a second shift lens group positioned on the image side of the first shift lens group and also movable in a direction perpendicular to the optical axis. Let βa and βb be the respective lateral magnifications of the first and second shift lens groups, respectively; βra and βrb be the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups, respectively; Sa and Sb be the respective eccentricity sensitivities of the first and second shift lens groups, respectively: Sa = (1-βa) × βra and Sb = (1-βb) × βrb; Mamax be the maximum displacement of the first shift lens group relative to the optical axis; Mbmax be the maximum displacement of the second shift lens group relative to the optical axis; f be the focal length of the optical system; and ω be the half-angle of view of the optical system when the first and second shift lens groups are not moving relative to the optical axis. 0.3 ≤ |Mamax × Sa + Mbmax × Sb| / (f × tanω) ≤ 1.0 An optical system characterized by satisfying the following conditions. (Composition 16) The optical system according to configuration 15, characterized in that the first and second shift lens groups are each composed of a positive lens and a negative lens. (Composition 17) When the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group is Rfa, the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group is Rra, the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group is Rfb, and the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group is Rrb, -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 The optical system according to configuration 15 or 16, characterized in that it satisfies at least one of the following conditions. (Composition 18) When the focal length of the first shift lens group is fa and the focal length of the second shift lens group is fb, 0.05 ≤ |Mamax / fa| ≤ 0.25 0.05 ≤ |Mbmax / fb| ≤ 0.25 An optical system according to any one of configurations 15 to 17, characterized in that it satisfies at least one of the following conditions. (Composition 19) When the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, and the focal length of the optical system is f, 1.0 ≤ |fa| / f ≤ 10.0 1.0 ≤ |fb| / f ≤ 10.0 An optical system according to any one of configurations 15 to 18, characterized in that it satisfies at least one of the following conditions. (Composition 20) An optical system capable of zooming, The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. The second shift lens group has a focus lens group that moves along the optical axis during focusing, on the image side of the second shift lens group. When the maximum displacement of the first shift lens group with respect to the optical axis is Mamax, the maximum displacement of the second shift lens group with respect to the optical axis is Mbmax, the focal length of the first shift lens group is fa, and the focal length of the second shift lens group is fb, (Mamax × fa) / (Mbmax × fb) < 0 An optical system characterized by satisfying the following conditions. (Composition 21) When the focal length of the optical system at the wide-angle end is f, the focal length of the first shift lens group is fa, and the focal length of the second shift lens group is fb, 0.05 ≤ |fa / f| ≤ 3.00 0.05 ≤ |fb / f| ≤ 3.00 The optical system according to configuration 20, characterized in that it satisfies at least one of the following conditions. (Composition 22) When the Petzval sum of the first shift lens group is Pa and the Petzval sum of the second shift lens group is Pb, 0.4 ≤ |Pa| + |Pb| ≤ 12.0 The optical system according to configuration 20 or 21, characterized by satisfying the following conditions. (Composition 23) When f is the focal length of the optical system at its wide-angle end, and Lbk is the air-equivalent distance along the optical axis from the image-side lens surface to the image plane at the wide-angle end, 0 <Lbk / f≦0.90 An optical system according to any one of configurations 20 to 22, characterized by satisfying the following conditions. (Composition 24) The lens group comprises an intermediate lens group positioned between the first shift lens group and the second shift lens group, which does not move in a direction perpendicular to the optical axis, When the focal length at the wide-angle end of the optical system is f, and the focal length of the intermediate lens group is fbw, 0.3 ≤ |f / fbw| ≤ 10.0 An optical system according to any one of configurations 20 to 23, characterized by satisfying the following conditions. (Composition 25) The optical system described in any one of configurations 1 to 24, An imaging device characterized by having an image sensor that captures an image of a subject through the optical system.

[0188] The embodiments described above are merely representative examples, and various modifications and changes can be made to each embodiment when implementing the present invention. [Explanation of symbols]

[0189] LA 1st Shift Lens Group LB 2nd Shift Lens Group IP image plane

Claims

1. The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. When the lateral magnifications of the first and second shift lens groups are βa and βb respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups are βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups are Sa = (1 - βa) × βra and Sb = (1 - βb) × βrb respectively, and the amount of movement of the first shift lens group relative to the optical axis is Ma, and the amount of movement of the second shift lens group relative to the optical axis is Mb, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 The following conditions are met: Furthermore, when the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, the maximum value of the movement amount Ma of the first shift lens group is Mamax, and the maximum value of the movement amount Mb of the second shift lens group is Mbmax, 0.03≦|Mamax / fa|≦0.25 0.03≦|Mbmax / fb|≦0.25 An optical system characterized by satisfying at least one of the following conditions.

2. When Rfa is the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group, Rra is the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group, Rfb is the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group, and Rrb is the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group, In that case, -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 The optical system according to claim 1, characterized in that it satisfies at least one of the following conditions.

3. When the focal length of the optical system is f, 1.0<|fa| / f≦10.0 1.0<|fb| / f≦10.0 The optical system according to claim 1, characterized in that it satisfies at least one of the following conditions.

4. When Dbi is the distance along the optical axis from the lens surface closest to the object in the second shift lens group to the image plane, and TTL is the distance along the optical axis from the lens surface closest to the object in the optical system to the image plane, 0.1 ≤ Dbi / TTL ≤ 0.9 The optical system according to claim 1, characterized in that it satisfies the following conditions.

5. The optical system according to claim 1, characterized in that the second shift lens group is composed of a positive lens and a negative lens.

6. When the Abbe number with respect to the d-line of the positive lens is νbp and the Abbe number with respect to the d-line of the negative lens is νbn, 10≦|νbp−νbn|≦70 The optical system according to claim 5, characterized in that it satisfies the following conditions.

7. The optical system according to claim 1, characterized in that the first shift lens group is composed of a positive lens and a negative lens.

8. When the Abbe number with respect to the d line of the positive lens is νap and the Abbe number with respect to the d line of the negative lens is νan, 10≦|νap−νan|≦70 The optical system according to claim 7, characterized in that it satisfies the following conditions.

9. The optical system according to claim 1, characterized in that the second shift lens group has a negative refractive power.

10. It has an intermediate lens group with positive refractive power positioned between the first shift lens group and the second shift lens group, When the focal length of the intermediate lens group is fi and the focal length of the optical system is f, 1.0<fi / f≦10.0 The optical system according to claim 1 that satisfies the following conditions.

11. The aforementioned optical system is a zoom lens capable of zooming from the wide-angle end to the telephoto end. At all zoom positions from wide-angle to telephoto, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 The following conditions are met: 0.03≦Mamax / |fa|≦0.25 0.03≦Mbmax / |fb|≦0.25 The optical system according to claim 1, characterized in that it satisfies at least one of the following conditions.

12. The optical system according to claim 1, characterized in that the first shift lens group and the second shift lens group move toward the same side relative to the optical axis.

13. The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. When the lateral magnifications of the first and second shift lens groups are βa and βb respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups are βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups are Sa = (1 - βa) × βra and Sb = (1 - βb) × βrb respectively, and the amount of movement of the first shift lens group relative to the optical axis is Ma, and the amount of movement of the second shift lens group relative to the optical axis is Mb, 0.5 ≤ -(Ma × Sa) / (Mb × Sb) ≤ 1.2 An optical system characterized by satisfying the following conditions.

14. The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. When the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, the maximum displacement of the first shift lens group with respect to the optical axis is Mamax, and the maximum displacement of the second shift lens group with respect to the optical axis is Mbmax, 0.03≦|Mamax / fa|≦0.25 0.03≦|Mbmax / fb|≦0.25 An optical system characterized by satisfying at least one of the following conditions.

15. The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. Let the lateral magnifications of the first and second shift lens groups be βa and βb, respectively, the combined lateral magnifications of all lens groups on the image side of the first and second shift lens groups be βra and βrb, the eccentricity sensitivities Sa and Sb of the first and second shift lens groups be Sa = (1 - βa) × βra and Sb = (1 - βb) × βrb, respectively, let Mamax be the maximum displacement of the first shift lens group relative to the optical axis, Mbmax be the maximum displacement of the second shift lens group relative to the optical axis, f be the focal length of the optical system, and ω be the half-angle of view of the optical system when the first and second shift lens groups are not moving relative to the optical axis. 0.3 ≤ |Mamax × Sa + Mbmax × Sb| / (f × tanω) ≤ 1.0 An optical system characterized by satisfying the following conditions.

16. The optical system according to claim 15, characterized in that the first and second shift lens groups are each composed of a positive lens and a negative lens.

17. When Rfa is the paraxial radius of curvature of the lens surface closest to the object in the first shift lens group, Rra is the paraxial radius of curvature of the lens surface closest to the image in the first shift lens group, Rfb is the paraxial radius of curvature of the lens surface closest to the object in the second shift lens group, and Rrb is the paraxial radius of curvature of the lens surface closest to the image in the second shift lens group, -0.8≦(Rfa+Rra) / (Rra-Rfa)≦0.8 -0.8≦(Rfb+Rrb) / (Rrb-Rfb)≦0.8 The optical system according to claim 15, characterized in that it satisfies at least one of the following conditions.

18. When the focal length of the first shift lens group is fa and the focal length of the second shift lens group is fb, 0.05≦|Mamax / fa|≦0.25 0.05≦|Mbmax / fb|≦0.25 The optical system according to claim 15, characterized in that it satisfies at least one of the following conditions.

19. When the focal length of the first shift lens group is fa, the focal length of the second shift lens group is fb, and the focal length of the optical system is f, 1.0≦|fa| / f≦10.0 1.0≦|fb| / f≦10.0 The optical system according to claim 15, characterized in that it satisfies at least one of the following conditions.

20. An optical system capable of zooming, The optical system comprises a first shift lens group that is movable in a direction perpendicular to the optical axis, and a second shift lens group that is positioned on the image side of the first shift lens group and is movable in a direction perpendicular to the optical axis. The second shift lens group has a focus lens group that moves along the optical axis during focusing, on the image side of the second shift lens group. When the maximum displacement of the first shift lens group with respect to the optical axis is Mamax, the maximum displacement of the second shift lens group with respect to the optical axis is Mbmax, the focal length of the first shift lens group is fa, and the focal length of the second shift lens group is fb, (Max × fa) / (Mbmax × fb) < 0 An optical system characterized by satisfying the following conditions.

21. When the focal length of the optical system at the wide-angle end is f, the focal length of the first shift lens group is fa, and the focal length of the second shift lens group is fb, 0.05≦|fa / f|≦3.00 0.05≦|fb / f|≦3.00 The optical system according to claim 20, characterized in that it satisfies at least one of the following conditions.

22. When the Petzval sum of the first shift lens group is Pa and the Petzval sum of the second shift lens group is Pb, 0.4≦|Pa|+|Pb|≦12.0 The optical system according to claim 20, characterized in that it satisfies the following conditions.

23. When f is the focal length of the optical system at its wide-angle end, and Lbk is the air-equivalent distance along the optical axis from the image-side lens surface to the image plane at the wide-angle end, 0<Lbk / f≦0.90 The optical system according to claim 20, characterized in that it satisfies the following conditions.

24. The lens group comprises an intermediate lens group positioned between the first shift lens group and the second shift lens group, which does not move in a direction perpendicular to the optical axis, When the focal length at the wide-angle end of the optical system is f, and the focal length of the intermediate lens group is fbw, 0.3≦|f / fbw|≦10.0 The optical system according to claim 20, characterized in that it satisfies the following conditions.

25. An optical system according to any one of claims 1 to 24, An imaging device characterized by having an image sensor that captures an image of a subject through the optical system.

Images