Optical system and imaging device

Abstract

To provide an optical system that is small-sized even though having a large diameter, has high optical performance, and can perform high-speed focusing.SOLUTION: An optical system is composed of a front group Lf with positive refractive power that includes at least one lens group, an intermediate lens group Lm with positive refractive power, and a rear group Lr with negative refractive power that includes at least one lens group, which are arranged in order from an object side to an image side. The intermediate lens group moves toward the object side during focusing from infinity to a close distance. The front group includes at least two positive lenses Lp1, Lp2 and at least one negative lens Ln. The rear group includes at least one aspherical lens La, Lb that has an aspherical surface with a pole away from an optical axis.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] Patent Document 1 discloses an optical system that is compact despite its large aperture, has high optical performance, and is capable of focusing. The optical system is composed of, arranged in this order from the object side to the image side, a front group having positive refractive power, an aperture stop, and a rear group having positive refractive power. In this optical system, the front group moves during focusing. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 2019-148680 Summary of the Invention [Problem to be solved by the invention]

[0004] In large-aperture optical systems, it tends to be difficult to correct various aberrations. Furthermore, if the focus lens group is made lighter to achieve faster autofocusing, it becomes difficult to suppress aberration fluctuations during focusing. The optical system of Patent Document 1 corrects various aberrations by using multiple aspherical lenses, but the correction of sagittal coma flare is insufficient. Furthermore, since the front group, which is large in diameter and has a large number of lenses, must be moved during focusing, it is difficult to speed up autofocusing.

[0005] The present invention provides an optical system that is small in size despite its large aperture, has high optical performance, and is capable of high-speed focusing, and an imaging apparatus equipped with the same. [Means for solving the problem]

[0006] One aspect of the present invention provides an optical system that is composed of, arranged in order from the object side to the image side, a front group having positive refractive power and including at least one lens group, an intermediate lens group having positive refractive power, and a rear group having negative refractive power and including at least one lens group, and in which the spacing between adjacent lens groups changes during focusing. During focusing from infinity to close range, the intermediate lens group moves toward the object side. The front group includes at least two positive lenses and at least one negative lens. The rear group is characterized by including at least one aspherical lens having an aspherical surface with a pole point located away from the optical axis.

[0007] Another aspect of the present invention is an optical system that is composed of, arranged in order from the object side to the image side, a front group including at least one lens group, an intermediate lens group, and a rear group including at least one lens group, and the spacing between adjacent lens groups changes during focusing. The intermediate lens group moves during focusing from infinity to close range. The front group includes at least two positive lenses and at least two negative lenses. The rear group includes at least one aspherical lens having an aspherical surface with a pole point located away from the optical axis. Note that an imaging device equipped with 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 is large in diameter, compact, has high optical performance, and is capable of high-speed focusing. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a cross-sectional view of an optical system according to a first embodiment. [Figure 2] 4A and 4B are longitudinal and lateral aberration diagrams of the optical system of Example 1 in a state where the optical system is focused at infinity. [Figure 3] FIG. 10 is a cross-sectional view of the optical system of the second embodiment. [Figure 4] 10A and 10B are longitudinal and lateral aberration diagrams of the optical system of Example 2 in a state where the optical system is focused at infinity. [Figure 5] FIG. 10 is a cross-sectional view of the optical system of the third embodiment. [Figure 6] 10A and 10B are longitudinal and lateral aberration diagrams of the optical system of Example 3 in a state where the optical system is focused at infinity. [Figure 7] FIG. 10 is a cross-sectional view of the optical system of Example 4. [Figure 8] 10A and 10B are longitudinal and lateral aberration diagrams of the optical system of Example 4 in a state where the optical system is focused at infinity. [Figure 9] FIG. 10 is a cross-sectional view of an optical system according to a fifth embodiment. [Figure 10] 10A and 10B are longitudinal and lateral aberration diagrams of the optical system of Example 5 in a state where the optical system is focused at infinity. [Figure 11] FIG. 10 is a cross-sectional view of an optical system according to a sixth embodiment. [Figure 12] 13A and 13B are longitudinal and lateral aberration diagrams of the optical system of Example 6 in a state where the optical system is focused at infinity. [Figure 13] FIG. 13 is a cross-sectional view of the optical system of Example 7. [Figure 14] 13A and 13B are longitudinal and lateral aberration diagrams of the optical system of Example 7 in a state where the optical system is focused at infinity. [Figure 15] FIG. 13 is a cross-sectional view of the optical system of Example 8. [Figure 16] 13A and 13B are longitudinal and lateral aberration diagrams of the optical system of Example 8 in a state where the optical system is focused at infinity. [Figure 17] FIG. 13 is a cross-sectional view of the optical system of Example 9. [Figure 18] 13A and 13B are longitudinal and lateral aberration diagrams of the optical system of Example 9 in a state where the optical system is focused at infinity. [Figure 19] FIG. 20 is a cross-sectional view of the optical system of Example 10. [Figure 20] 13A and 13B are longitudinal and lateral aberration diagrams of the optical system of Example 10 when focused at infinity. [Figure 21] FIG. 1 is a diagram showing an imaging device equipped with an optical system according to Examples 1 to 10. DETAILED DESCRIPTION OF THE INVENTION

[0010] Examples of the present invention will be described below with reference to the drawings. Figures 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 show cross sections of optical systems of Examples 1 to 10, respectively. In each figure, the left side is the object side (front side) and the right side is the image side (rear side).

[0011] First, we will explain matters common to each of the embodiments before specifically explaining Examples 1 to 10. The optical system of each embodiment is used in various imaging devices such as digital video cameras, digital still cameras, broadcast cameras, cameras for silver halide film, and surveillance cameras.

[0012] The optical system in each embodiment is composed of multiple lens groups. From the object side to the image side, Lf is a front group including at least one lens group, Lm is an intermediate lens group, and Lr is a rear group including at least one lens group. A lens group is a group of one or more lenses that move or remain stationary as a unit during focusing. In other words, the spacing between adjacent lens groups changes during focusing.

[0013] Ln is a negative lens located in the front group Lf, and Lp1 and Lp2 are positive lenses located in the front group Lf. SP is the aperture stop. IP is the image plane (paraxial). The image plane IP is where the imaging surface (light-receiving surface) of a solid-state imaging device such as a CCD sensor or CMOS sensor, or the film surface (photosensitive surface) of a silver halide film, is located.

[0014] A glass block having no refractive power, such as a cover glass or an IR cut filter, may be disposed between the lens surface closest to the object side of the optical system and the image plane.

[0015] In the optical systems of each embodiment, the front lens group Lf has positive refractive power, the middle lens group Lm has positive refractive power, and the rear lens group Lr has negative refractive power. By adopting this telephoto power arrangement, the overall length is reduced. The refractive power of each lens group and lens represents the paraxial refractive power, which corresponds to the reciprocal of the focal length.

[0016] In addition, in the optical systems of each embodiment, the middle lens group Lm moves toward the object during focusing from infinity to a close distance. This is because the front group Lf converges the light beam, thereby reducing the diameter of the light beam incident on the middle lens group Lm and reducing the weight of the focusing mechanism that moves the middle lens group Lm. In each figure, dashed arrows below the lens groups that move during focusing indicate the direction of movement of those lens groups during focusing from infinity to a close distance.

[0017] Furthermore, in the optical system of each embodiment, the front group Lf has at least two positive lenses Lp1 and Lp2 and at least one negative lens Ln. This configuration effectively corrects chromatic aberration. Note that when two lenses are cemented together to form a cemented lens, the number of lenses is considered to be two.

[0018] Additionally, the rear group Lr includes at least one aspherical lens La (Lb) with an aspherical surface having a pole point at a position away from the optical axis (hereinafter referred to as the periphery). This aspherical lens effectively corrects sagittal coma flare by providing a difference in refractive power to the central light beam and the peripheral light beam.

[0019] In this case, the polar point is defined as a point on the lens surface within the effective diameter where the tangent plane of the lens surface intersects at right angles with the optical axis.

[0020] The optical system of each embodiment having the above configuration has a large aperture, is compact, has high optical performance, and is capable of high-speed focusing (autofocus).

[0021] In the optical system of each embodiment, the total optical length (hereinafter referred to as total lens length) is defined as the distance on the optical axis from the lens surface closest to the object (the frontmost surface) to the lens surface closest to the image (the final surface) plus the back focus. The back focus is the air-equivalent length on the optical axis from the final surface to the image plane IP. The focal length of the entire optical system is defined as f, and the half angle of view (°) is defined as ω. In this case, it is preferable that the optical system of each embodiment satisfy the condition of the following formula (1).

[0022] 3.0≦TTL / (f×tanω)≦10.0 (1) The condition in equation (1) indicates the appropriate relationship between the overall lens length and image height of an optical system. If TTL / (f×tanω) exceeds the upper limit of equation (1), the overall lens length becomes too long, which is undesirable. If the overall lens length becomes so short that TTL / (f×tanω) falls below the lower limit of equation (1), the refractive power of each lens becomes too strong, making it difficult to correct field curvature and distortion, which is also undesirable.

[0023] The optical system of each embodiment preferably satisfies the condition of the following formula (2), where PNdave is the average value of the refractive index at the d-line (wavelength 587.56 nm) of the material of all the positive lenses included in the optical system.

[0024] 1.50≦PNdave≦2.00 (2) The condition in formula (2) indicates the appropriate average refractive index of all positive lenses included in the optical system. If the average refractive index is high so that PNdave exceeds the upper limit of formula (2), chromatic dispersion will increase, making it difficult to correct axial chromatic aberration, which is undesirable. If the average refractive index is low so that PNdave falls below the lower limit of formula (2), the Petzval sum of the entire system will increase, making it difficult to correct field curvature, which is also undesirable.

[0025] It is preferable that the optical system of each embodiment satisfies the condition of the following formula (3) when the back focus is sk.

[0026] 0.01≦sk / TTL≦0.50 (3) The condition of formula (3) indicates the appropriate relationship between the back focal length and the overall lens length. If sk / TTL exceeds the upper limit of formula (3), the overall lens length becomes too long, which is undesirable. If the back focal length is short so that sk / TTL falls below the lower limit of formula (3), the effective diameter of the lens arranged on the image side becomes large, which is undesirable as the optical system becomes large in the radial direction.

[0027] It is preferable that the optical system of each embodiment satisfies the condition of the following expression (4), where ff is the focal length of the front group Lf.

[0028] 2.0≦ff / sk≦10.0 (4) The condition of equation (4) indicates the appropriate relationship between the focal length of the front group Lf and the back focus. If the refractive power of the front group Lf becomes so strong that ff / sk falls below the lower limit of equation (4), the Petzval sum of the entire system increases, making it difficult to correct curvature of field and chromatic aberration, which is undesirable. If the refractive power of the front group Lf becomes so weak that ff / sk exceeds the upper limit of equation (4), the power arrangement deviates from that of a telephoto type, and the overall lens length increases, which is undesirable.

[0029] In the optical system of each embodiment, it is preferable to satisfy the condition of the following formula (5), where fm is the focal length of the intermediate lens unit Lm and fr is the focal length of the rear lens unit Lr.

[0030] 0.1≦-fm / fr≦1.0 (5) The condition of equation (5) indicates the appropriate relationship between the focal length of the intermediate lens group Lm and the focal length of the rear lens group Lr. If the refractive power of the rear lens group Lr is weakened so that -fm / fr falls below the lower limit of equation (5), this deviates from the telephoto power arrangement and increases the overall lens length, which is undesirable. If the refractive power of the rear lens group Lr is strengthened so that -fm / fr exceeds the upper limit of equation (5), the angle of incidence of off-axial rays on the image plane increases, resulting in noticeable peripheral light falloff known as shading, which is also undesirable.

[0031] In the optical system of each embodiment, it is preferable that the following condition (6) be satisfied, where Df is the distance on the optical axis between the front lens unit Lf and the intermediate lens unit Lm.

[0032] 0.1≦Df / f≦1.0 (6) The condition of formula (6) indicates the appropriate relationship between the distance between the front group Lf and the intermediate lens group Lm and the focal length of the entire system. If Df is small, so that Df / f is below the lower limit of formula (6), the amount of movement of the intermediate lens group Lm during focusing becomes too small, making close-up imaging difficult, which is undesirable. If Df is large, so that Df / f is above the upper limit of formula (6), the overall lens length becomes long, which is undesirable.

[0033] It is preferable that the optical system of each embodiment satisfies the condition of the following expression (7).

[0034] 0.1≦-ff / fr≦2.0 (7) The condition of equation (7) indicates the appropriate relationship between the focal length of the front group Lf and the focal length of the rear group Lr. If the refractive power of the rear group Lr is weakened so that -ff / fr falls below the lower limit of equation (7), the lens will deviate from the telephoto power arrangement and the overall lens length will increase, which is undesirable. If the refractive power of the rear group Lr is strengthened so that -ff / fr exceeds the upper limit of equation (7), the angle of incidence of off-axial rays on the image plane will increase, resulting in significant shading, which is also undesirable.

[0035] In the optical system of each embodiment, when the positive lens Lp1 has the largest Abbe number referenced to the d-line among all the positive lenses included in the front group Lf and the Abbe number of the positive lens Lp1 referenced to the d-line is νdp1, it is preferable that the condition of the following formula (8) be satisfied:

[0036] 55≦νdp1≦97 (8) The condition of formula (8) indicates an appropriate range for the Abbe number of the positive lens Lp1. If the Abbe number of the positive lens Lp1 becomes small so that νdp1 falls below the lower limit of formula (8), color dispersion increases, making it difficult to correct chromatic aberration, which is undesirable. If the Abbe number of the positive lens Lp1 becomes large so that νdp1 exceeds the upper limit of formula (8), the number of glass materials that can be selected becomes limited, which is undesirable.

[0037] In the optical system of each embodiment, when the positive lens Lp2 has the smallest Abbe number based on the d-line among all the positive lenses included in the front group Lm, and the Abbe number of the positive lens Lp2 based on the d-line is νdp2, it is preferable that the condition of the following formula (9) be satisfied:

[0038] 15≦νdp2≦40 (9) Equation (9) shows the appropriate range of the Abbe number of the positive lens Lp2. If the Abbe number of the positive lens Lp2 becomes small so that νdp2 falls below the lower limit of equation (9), the number of glass materials that can be selected becomes limited, which is not preferable. If the Abbe number of the positive lens Lp2 becomes large so that νdp2 exceeds the upper limit of equation (9), the anomalous partial dispersion becomes too small, making it difficult to correct chromatic aberration on the short wavelength side, which is also not preferable.

[0039] In the optical system of each embodiment, it is desirable that the condition of the following formula (10) be satisfied, where Ln is the negative lens that is located closest to the object among all the negative lenses included in the front group Lm, and νdn is the Abbe number of the negative lens Ln based on the d-line.

[0040] 15≦νdn≦40 (10) The condition of formula (10) indicates an appropriate range for the Abbe number of the negative lens Ln. If the Abbe number of the negative lens Ln becomes small so that νdn falls below the lower limit of formula (10), the number of glass materials that can be selected becomes limited, which is undesirable. If the Abbe number of the negative lens Ln becomes large so that νdn exceeds the upper limit of formula (10), it becomes difficult to correct chromatic aberration, which is undesirable.

[0041] In the optical system of each embodiment, it is preferable that the negative lens Ln included in the front group Lf has a biconcave shape in order to effectively correct spherical aberration.

[0042] In the optical systems of the respective embodiments, in order to effectively correct curvature of field and distortion, it is preferable to satisfy the condition of the following formula (11), where Ra1 is the paraxial radius of curvature of the lens surface on the object side of the aspherical lens La and Ra2 is the paraxial radius of curvature on the image side.

[0043] 0 <Ra1 / f 0 <Ra2 / f (11) In the optical systems of the respective embodiments, in order to effectively correct curvature of field and chromatic aberration, it is preferable to satisfy the condition of the following formula (12), where Nda is the refractive index at the d-line of the aspherical lens La.

[0044] 1.44≦Nda≦1.77 (12) In the optical systems of each embodiment, in order to effectively correct curvature of field and distortion, it is preferable that an aspherical lens Lb be provided in the rear group Lr, and that the condition of the following equation (13) be satisfied, where Rb1 is the paraxial radius of curvature of the object-side lens surface of aspherical lens Lb, and Rb2 is the paraxial radius of curvature of the image-side lens surface of aspherical lens Lb:

[0045] Rb1 / f<0 Rb2 / f<0 (13) In the optical systems of the respective embodiments, it is preferable that the aspherical lens Lb has a pole point in the peripheral portion in order to effectively reduce sagittal coma flare.

[0046] It is more preferable that the numerical ranges of the formulas (1) to (13) are as follows:

[0047] 4.0≦TTL / (f×tanω)≦7.0 (1a) 1.60≦PNdave≦1.90 (2a) 0.05≦sk / TTL≦0.30 (3a) 3.0≦ff / sk≦8.0 (4a) 0.3≦-fm / fr≦0.7 (5a) 0.2≦Df / f≦0.5 (6a) 0.5≦-ff / fr≦1.5 (7a) 60≦νdp1≦96 (8a) 16≦νdp2≦30 (9a) 18≦νdn≦30 (10a) 0.5≦Ra1 / f≦10.0 0.2≦Ra2 / f≦10.0 (11a) 1.500≦Nda≦1.728 (12a) -10.0≦Rb1 / f≦-0.1 -10.0≦Rb2 / f≦-0.1 (13a) Furthermore, it is more preferable to set the numerical ranges of the formulas (1) to (13) as follows:

[0048] 5.0≦TTL / (f×tanω)≦6.0 (1b) 1.70≦PNdave≦1.85 (2b) 0.09≦sk / TTL≦0.15 (3b) 4.0≦ff / sk≦7.0 (4b) 0.40≦-fm / fr≦0.60 (5b) 0.3≦Df / f≦0.4 (6b) 0.7≦-ff / fr≦1.0 (7b) 65≦νdp1≦95 (8b) 17≦νdp2≦25 (9b) 20≦νdn≦28 (10b) 8≦Ra1 / f≦2.0 0.4≦Ra2 / f≦0.5 (11b) 1.55≦Nda≦1.70 (12b) -1.0≦Rb1 / f≦-0.2 -1.0≦Rb2 / f≦-0.2 (13b) The optical systems of Examples 1 to 10 will now be described in detail.

[0049] In the optical system of Example 1, the front group Lm is composed of a first lens group L1. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens Ln, a positive lens, a positive lens LP2, a cemented lens of a positive lens and a negative lens, and a cemented lens of the positive lens LP1 and a negative lens. An aperture stop SP is arranged between the first lens group L1 and the second lens group L2, which serves as the intermediate lens group Lm.

[0050] The second lens group L2 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of the third lens group L3. The third lens group L3 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb, an aspherical lens La, and a positive lens.

[0051] In the optical systems of Examples 2, 3, 4, and 6, the front group Lm is composed of a first lens group L1. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens Ln, a positive lens LP2, a cemented lens of a positive lens and a negative lens, and a cemented lens of the positive lens LP1 and a negative lens. An aperture stop SP is arranged between the first lens group L1 and the second lens group L2, which serves as the intermediate lens group Lm.

[0052] The second lens group L2 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of the third lens group L3. The third lens group L3 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb, an aspherical lens La, and a positive lens.

[0053] In the optical system of Example 5, the front group Lm is composed of a first lens group L1 and a second lens group L2. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens group Ln, a positive lens group LP2, and a cemented lens of a positive lens and a negative lens. The second lens group L2 is composed of a cemented lens of a positive lens group LP1 and a negative lens. The second lens group L2 moves toward the image side during focusing from infinity to a close distance. An aperture stop SP is disposed between the second lens group L2 and the third lens group L3, which serves as the intermediate lens group Lm.

[0054] In the optical system of Example 5, the front group Lm is composed of a first lens group L1 and a second lens group L2. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens group Ln, a positive lens group LP2, and a cemented lens of a positive lens and a negative lens. The second lens group L2 is composed of a positive lens group LP1 and a cemented lens of a negative lens. An aperture stop SP is disposed between the second lens group L2 and a third lens group L3 serving as an intermediate lens group Lm.

[0055] The third lens group L3 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of the fourth lens group L4. The fourth lens group L4 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb, an aspherical lens La, and a positive lens.

[0056] In the optical system of Example 7, the front group Lm is composed of a first lens group L1. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens Ln, a positive lens LP2, a cemented lens of a positive lens and a negative lens, and a cemented lens of the positive lens LP1 and a negative lens. An aperture stop SP is arranged between the first lens group L1 and the second lens group L2, which serves as the intermediate lens group Lm.

[0057] The second lens group L2 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of a third lens group L3 and a fourth lens group L4. The third lens group L3 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb and an aspherical lens La. The third lens group L3 moves toward the image side during focusing from infinity to close range. The fourth lens group L4 is composed of a positive lens.

[0058] In the optical systems of Examples 8 and 9, the front group Lm is composed of a first lens group L1. The first lens group L1 is composed of, arranged in order from the object side to the image side, a positive lens, a biconcave negative lens Ln, a positive lens, a positive lens LP2, a cemented lens of a positive lens and a negative lens, and a cemented lens of the positive lens LP1 and a negative lens. An aperture stop SP is disposed between the first lens group L1 and the second lens group L2 serving as the intermediate lens group Lm.

[0059] The second lens group L2 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of the third lens group L3. The third lens group L3 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb and an aspherical lens La.

[0060] In the optical system of Example 10, the front group Lm is composed of a first lens group L1. The first lens group L1 is composed of, arranged in order from the object side to the image side, a biconcave negative lens Ln, a positive lens, a positive lens LP2, a cemented lens of a positive lens and a negative lens, and a cemented lens of the positive lens LP1 and a negative lens. An aperture stop SP is arranged between the first lens group L1 and the second lens group L2, which serves as the intermediate lens group Lm.

[0061] The second lens group L2 is composed of, arranged in order from the object side to the image side, a cemented lens of a negative lens and a positive lens, and a cemented lens of a positive lens and a negative lens. The rear group Lr is composed of the third lens group L3. The third lens group L3 is composed of, arranged in order from the object side to the image side, an aspherical lens Lb, an aspherical lens La, and a negative lens.

[0062] In the above Examples 1 to 10, the front and intermediate lens groups have positive refractive power and the rear group has negative refractive power. However, the front group may have negative refractive power, or the intermediate lens group may have negative refractive power. The rear group may have positive refractive power. In other words, the combination of positive and negative refractive powers of the front, intermediate, and rear groups is not limited. In addition, in Examples 1 to 10, the intermediate lens group moves toward the object side during focusing from infinity to close range, but it may also move toward the image side. In other words, the direction of movement of the intermediate lens group is not limited. Furthermore, the front group may include at least two positive lenses and at least two negative lenses. In these cases, it is preferable to satisfy at least one of the conditions of formulas (1) to (13).

[0063] Numerical Examples 1 to 10 corresponding to Examples 1 to 10 are shown below. In the surface data of each example, surface number m indicates the order of the surface when counted from the object side. r is the radius of curvature (mm) of the mth surface, and d (mm) is the distance on the optical axis between the mth surface and the (m+1)th surface. nd is the refractive index at the d-line (wavelength 587.56 nm) of the optical material between the mth surface and the (m+1)th surface, and vd is the Abbe number of the optical material based on the d-line. The Abbe number vd based on the d-line is given by Nd, NF, and NC, respectively, where Nd, NF, and NC are the refractive indices at the d-line (wavelength 587.56 nm), F-line (wavelength 486.13 nm), and C-line (wavelength 656.27 nm) of the Fraunhofer lines. νd=(Nd-1) / (NF-NC) The effective diameter (mm) indicates the diameter of the area through which light rays that contribute to image formation on the optical surface pass.

[0064] In each numerical example, the focal length (mm), F-number, and half angle of view (°) are all values when the optical system is focused on an object at infinity. BK and the total lens length correspond to the back focus sk and the total optical length (total lens length) TTL, respectively.

[0065] An "*" next to a 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 vertex of the surface in the optical axis direction, H is the height from the optical axis in a direction perpendicular to the optical axis, the direction of light travel is positive, R is the paraxial radius of curvature, K is the conic constant, and A3 to A14 are aspherical coefficients. The conic constant and the aspherical coefficients "e±x" are expressed as "×10 ±x " means.

[0066]

number

[0067] Figures 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 respectively show the longitudinal aberration (spherical aberration, astigmatism, distortion, and chromatic aberration) and transverse aberration of the optical systems of Numerical Examples 1 to 10 when focused at infinity. In the spherical aberration diagrams, Fno indicates the F-number, the solid line indicates the spherical aberration for the d-line (wavelength 587.6 nm), and the two-dot chain line indicates the spherical aberration for the g-line (wavelength 435.8 nm). In the astigmatism diagrams, the solid line S indicates the astigmatism at the sagittal image plane, and the dashed line M indicates the astigmatism at the meridional image plane. The distortion diagrams show distortion for the d-line. The chromatic aberration diagrams show the chromatic aberration of magnification at the g-line. ω is the half angle of view (°).

[0068] The lateral aberration diagram shows the amount of lateral aberration for the d-line, with the solid line M showing the amount of lateral aberration in the meridional section and the dashed line S showing the amount of lateral aberration in the sagittal section. [Numerical example 1] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -52.482 1.40 1.92286 20.9 38.96 2 108.023 4.86 41.65 3 181.785 7.77 1.95375 32.3 47.68 4 -69.829 0.14 48.50 5 72.841 6.56 1.95906 17.5 50.00 6 -743.568 0.20 49.53 7 134.931 11.26 1.71700 47.9 47.84 8 -43.452 1.31 1.78880 28.4 46.66 9 -117.176 0.10 44.15 10 226.380 5.10 1.43875 94.7 40.17 11 -77.993 1.33 1.85478 24.8 38.59 12 83.028 3.86 35.67 13 (Aperture) ∞ (Variable) 34.56 14 -28.935 1.34 1.78880 28.4 29.20 15 27.835 10.19 2.00100 29.1 31.49 16 -60.921 0.20 32.76 17* 96.206 11.76 1.76385 48.5 34.02 18 -24.110 2.02 1.84666 23.8 34.98 19 -44.071 (variable) 36.85 20* -13.205 3.55 1.53500 56.0 36.20 21* -12.550 3.37 34.67 22* 56.432 4.06 1.63560 23.9 34.98 23* 21.754 4.20 37.83 24 -96.183 1.39 1.92286 20.9 38.00 25 -96.519 38.50 Image plane ∞ Aspheric data Page 17 K = 0.00000e+00 A 4= 5.37646e-05 A 6= 1.55863e-06 A 8= 6.05348e-09 A10 = 1.82198e-12 A 3=-1.65820e-04 A 5=-1.24402e-05 A 7=-1.24659e-07 A 9=-1.62280e-10 Page 20 K =-4.27441e+00 A 4= 1.78716e-05 A 6=-6.05510e-06 A 8=-2.51039e-08 A10=-6.98524e-12 A 3= 5.33362e-04 A 5= 3.06426e-05 A 7= 5.26407e-07 A 9= 6.44512e-10 Page 21 K =-4.40654e+00 A 4= 6.44848e-04 A 6= 9.25388e-06 A 8= 2.81051e-08 A10 = 9.86621e-12 A 3=-3.46691e-04 A 5=-9.85179e-05 A 7=-6.15848e-07 A 9=-7.80055e-10 Page 22 K = 0.00000e+00 A 4= 5.80061e-04 A 6= 7.76706e-06 A 8=-6.95980e-08 A10=-1.91328e-10 A12=-1.81766e-14 A 3=-1.22295e-04 A 5=-1.17096e-04 A 7= 1.86177e-07 A 9= 5.23501e-09 A11= 3.30660e-12 Page 23 K = 0.00000e+00 A 4=-2.19737e-04 A 6=-1.00699e-05 A 8=-1.69644e-07 A10=-4.30350e-10 A12=-9.61000e-14 A 3= 7.95396e-04 A 5= 3.69643e-05 A 7= 1.67386e-06 A 9= 1.08448e-08 A11= 9.72341e-12 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens total length 113.00 BF 11.92 Object distance / magnification infinite 0.154x d13 13.27 7.22 d19 1.84 7.88 Entrance pupil position 25.90 Exit pupil position -51.59 Front principal point position 37.37 Back principal point position -36.58 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 76.33 43.88 13.83 -10.43 2 14 40.71 25.52 14.32 2.58 3 20 -85.30 16.57 4.32 -8.00 [Numerical example 2] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -57.005 1.44 1.80810 22.8 38.96 2 90.515 5.96 41.28 3 97.899 8.21 1.94594 18.0 49.02 4 -101.934 0.20 49.50 5 94.495 13.00 1.80400 46.5 49.39 6 -45.449 1.40 1.92286 20.9 48.73 7 -106.941 0.20 47.88 8 67.455 10.47 1.43875 94.7 42.80 9 -48.750 1.40 1.58144 40.8 40.94 10 73.537 4.19 36.35 11 (Aperture) ∞ (Variable) 35.23 12 -32.143 1.39 1.74077 27.8 29.89 13 26.064 12.76 2.00100 29.1 31.39 14 -75.863 0.20 31.13 15* 89.351 11.05 1.69680 55.5 31.04 16 -22.410 2.79 1.69895 30.1 31.97 17 -51.399 (variable) 33.67 18* -13.515 3.76 1.53500 56.0 33.53 19* -13.485 2.83 32.58 20* 60.099 4.26 1.61550 25.8 33.16 21* 21.080 3.13 36.83 22 -240.533 2.28 2.00069 25.5 37.26 23 -119.912 37.80 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 3.32972e-05 A 6= 1.11752e-06 A 8= 4.14369e-09 A10= 1.04564e-12 A 3=-1.00111e-04 A 5=-8.89535e-06 A 7=-8.84820e-08 A 9=-1.04206e-10 Side 18 K =-5.88757e+00 A 4=-2.71472e-04 A 6=-1.48622e-05 A 8=-5.67023e-08 A10=-1.61539e-11 A 3= 7.95535e-04 A 5= 9.96883e-05 A 7= 1.20415e-06 A 9= 1.46692e-09 Page 19 K =-3.35640e+00 A 4= 6.15817e-04 A 6= 1.66019e-06 A 8=-8.55019e-09 A10=-5.05019e-14 A 3=-1.43247e-04 A 5=-6.16012e-05 A 7= 1.05295e-07 A 9= 1.76563e-10 Page 20 K = 0.00000e+00 A 4= 6.51831e-04 A 6= 1.02975e-05 A 8=-7.77252e-08 A10=-3.25677e-10 A12=-6.51157e-14 A 3=-4.72892e-04 A 5=-1.34367e-04 A 7= 3.46845e-08 A 9= 7.21992e-09 A11= 7.39708e-12 Page 21 K = 0.00000e+00 A 4=-2.90800e-04 A 6=-1.41705e-05 A 8=-2.40217e-07 A10=-6.85583e-10 A12=-1.74180e-13 A 3= 6.44304e-04 A 5= 5.83963e-05 A 7= 2.30041e-06 A 9= 1.62058e-08 A11= 1.65507e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens length 117.51 BF 11.92 Object distance / magnification infinite 0.156x d11 12.75 6.75 d17 1.91 7.91 Entrance pupil position 27.93 Exit pupil position -54.47 Front principal point position 41.00 Back principal point position -36.58 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 76.03 46.48 17.85 -8.91 2 12 41.75 28.19 14.63 0.71 3 18 -93.30 16.26 0.79 -10.96 [Numerical example 3] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -57.655 1.44 1.80810 22.8 38.96 2 90.921 6.16 41.23 3 100.032 7.98 1.94594 18.0 49.04 4 -104.726 0.20 49.50 5 96.854 12.67 1.80400 46.5 49.50 6 -46.640 1.40 1.92286 20.9 48.90 7 -105.961 0.20 48.14 8 65.321 10.84 1.43875 94.7 43.01 9 -47.982 1.40 1.58144 40.8 41.08 10 72.990 4.20 36.46 11 (Aperture) ∞ (Variable) 35.37 12 -32.736 1.43 1.74077 27.8 29.98 13 26.135 12.01 2.00100 29.1 31.44 14 -78.540 0.50 31.18 15* 89.297 11.03 1.69680 55.5 31.05 16 -22.527 2.44 1.69895 30.1 31.99 17 -51.670 (variable) 33.63 18* -13.497 3.74 1.53500 56.0 33.52 19* -13.289 2.82 32.56 20* 62.834 4.43 1.61550 25.8 33.11 21* 21.077 3.19 36.86 22 -245.008 2.29 2.00069 25.5 37.26 23 -117.939 (variable) 37.80 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 3.33689e-05 A 6= 1.12024e-06 A 8= 4.13811e-09 A10= 1.04675e-12 A 3=-9.89037e-05 A 5=-8.92891e-06 A 7=-8.85418e-08 A 9=-1.03939e-10 Page 18 K =-5.59343e+00 A 4=-2.48212e-04 A 6=-1.44824e-05 A 8=-5.60354e-08 A10=-1.60139e-11 A 3= 7.60344e-04 A 5= 9.56402e-05 A 7= 1.18371e-06 A 9= 1.45357e-09 Page 19 K =-3.18771e+00 A 4= 6.12209e-04 A 6= 1.74522e-06 A 8=-7.07541e-09 A10= 8.53125e-13 A 3=-1.41291e-04 A 5=-6.14094e-05 A 7= 8.77888e-08 A 9= 1.17866e-10 Page 20 K = 0.00000e+00 A 4= 6.38602e-04 A 6= 9.77458e-06 A 8=-7.78300e-08 A10=-3.15421e-10 A12=-6.15155e-14 A 3=-4.51554e-04 A 5=-1.30558e-04 A 7= 6.85395e-08 A 9= 7.07611e-09 A11= 7.08707e-12 Page 21 K = 0.00000e+00 A 4=-2.90901e-04 A 6=-1.42728e-05 A 8=-2.38720e-07 A10=-6.76314e-10 A12=-1.71301e-13 A 3= 6.33038e-04 A 5= 5.91833e-05 A 7= 2.29968e-06 A 9= 1.60352e-08 A11= 1.62948e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens length 117.18 BF 11.92 Object distance / magnification infinite 0.156x d11 12.99 6.69 d17 1.90 7.98 Entrance pupil position 27.96 Exit pupil position -54.62 Front principal point position 41.11 Back principal point position -36.58 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 76.81 46.48 18.00 -8.82 2 12 42.39 27.41 14.35 0.58 3 18 -96.89 16.48 0.87 -11.04 [Numerical example 4] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -57.677 1.43 1.78472 25.7 39.40 2 84.118 6.81 41.25 3 95.377 8.63 1.92286 18.9 50.03 4 -101.009 0.20 50.50 5 97.881 12.70 1.72916 54.7 50.26 6 -48.085 1.38 1.92286 18.9 49.65 7 -91.921 0.20 49.21 8 78.154 11.23 1.43875 94.7 44.03 9 -43.858 1.41 1.56732 42.8 42.12 10 80.566 4.10 37.43 11 (Aperture) ∞ (Variable) 36.39 12 -30.774 1.45 1.74077 27.8 31.49 13 27.703 12.38 2.00100 29.1 34.07 14 -75.431 0.20 33.99 15* 72.163 12.61 1.64000 60.1 32.32 16 -21.799 1.49 1.63980 34.5 33.34 17 -47.877 (variable) 34.89 18* -16.619 3.96 1.53500 56.0 34.57 19* -17.356 3.05 32.98 20* 43.533 5.14 1.63560 23.9 33.38 21* 21.080 4.00 36.60 22 -113.628 2.42 1.95906 17.5 36.82 23 -91.080 37.63 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 5.41546e-05 A 6= 1.45093e-06 A 8= 4.26187e-09 A10= 7.39216e-13 A 3=-1.76505e-04 A 5=-1.24650e-05 A 7=-1.03377e-07 A 9=-9.14957e-11 Page 18 K =-8.40074e+00 A 4=-1.58789e-04 A 6=-7.00442e-06 A 8=-1.79131e-08 A10=-2.32428e-12 A 3= 7.86549e-04 A 5= 5.33971e-05 A 7= 4.78090e-07 A 9= 3.38563e-10 Page 19 K =-5.78545e+00 A 4= 6.52084e-04 A 6= 1.00083e-05 A 8= 3.62759e-08 A10= 1.40337e-11 A 3=-3.20449e-04 A 5=-1.00889e-04 A 7=-7.25492e-07 A 9=-1.07937e-09 Page 20 K = 0.00000e+00 A 4= 4.05205e-04 A 6= 6.56796e-06 A 8=-7.47369e-08 A10=-3.30628e-10 A12=-8.87165e-14 A 3=-2.22625e-04 A 5=-8.95434e-05 A 7= 1.59019e-07 A 9= 6.92079e-09 A11= 8.35416e-12 Page 21 K = 0.00000e+00 A 4=-4.71817e-04 A 6=-1.58142e-05 A 8=-1.99245e-07 A10=-5.19029e-10 A12=-1.29054e-13 A 3= 1.07100e-03 A 5= 8.81324e-05 A 7= 2.12198e-06 A 9= 1.26705e-08 A11= 1.23288e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens length 122.03 BF 11.99 Object distance / magnification infinite 0.156x d11 13.33 7.46 d17 1.91 7.77 Entrance pupil position 28.24 Exit pupil position -54.31 Front principal point position 41.26 Back principal point position -36.51 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 81.69 48.09 20.54 -7.04 2 12 42.09 28.13 14.97 0.97 3 18 -87.55 18.59 3.74 -9.69 [Numerical example 5] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -57.108 1.44 1.78472 25.7 39.14 2 84.051 6.64 41.29 3 93.607 8.71 1.92286 18.9 50.03 4 -100.238 0.20 50.50 5 97.808 12.90 1.72916 54.7 50.19 6 -47.012 1.40 1.92286 18.9 49.56 7 -90.310 (variable) 49.10 8 93.968 10.78 1.43875 94.7 44.20 9 -43.311 1.43 1.56732 42.8 42.41 10 102.979 (variable) 38.05 11 (Aperture) ∞ (Variable) 36.61 12 -30.758 1.45 1.74077 27.8 31.46 13 27.429 12.62 2.00100 29.1 33.93 14 -79.278 0.20 33.79 15* 71.392 12.51 1.64000 60.1 32.22 16 -21.821 1.65 1.63980 34.5 33.22 17 -46.886 (variable) 34.79 18* -15.051 3.91 1.53500 56.0 34.44 19* -15.900 3.00 32.81 20* 43.280 5.32 1.63560 23.9 33.30 21* 21.127 3.73 36.61 22 -131.817 2.30 1.95906 17.5 36.84 23 -106.190 37.58 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 5.74684e-05 A 6= 1.51200e-06 A 8= 4.35527e-09 A10= 7.22714e-13 A 3=-1.85812e-04 A 5=-1.30857e-05 A 7=-1.06798e-07 A 9=-9.20134e-11 Side 18 K =-7.08229e+00 A 4=-1.68119e-04 A 6=-8.97552e-06 A 8=-2.78675e-08 A10=-5.45973e-12 A 3= 8.44342e-04 A 5= 6.28773e-05 A 7= 6.68687e-07 A 9= 6.12342e-10 Page 19 K =-4.64706e+00 A 4= 7.60583e-04 A 6= 1.02069e-05 A 8= 3.24402e-08 A10= 1.24833e-11 A 3=-4.38725e-04 A 5=-1.12557e-04 A 7=-6.78666e-07 A 9=-9.55775e-10 Page 20 K = 0.00000e+00 A 4= 5.18854e-04 A 6= 8.60317e-06 A 8=-7.51418e-08 A10=-3.34287e-10 A12=-8.49540e-14 A 3=-4.04452e-04 A 5=-1.11096e-04 A 7= 7.12499e-08 A 9= 7.09873e-09 A11= 8.23498e-12 Page 21 K = 0.00000e+00 A 4=-4.61864e-04 A 6=-1.56818e-05 A 8=-1.99763e-07 A10=-5.20986e-10 A12=-1.28244e-13 A 3= 1.04929e-03 A 5= 8.66417e-05 A 7= 2.11760e-06 A 9= 1.27305e-08 A11= 1.23271e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens length 122.18 BF 12.21 Object distance / magnification infinite 0.158x d 7 0.20 0.78 d10 4.29 3.71 d11 13.36 7.54 d17 1.91 7.74 Entrance pupil position 28.09 Exit pupil position -53.58 Front principal point position 40.84 Back principal point position -36.28 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 64.06 31.30 24.03 9.68 2 8 -285.48 12.21 19.60 10.46 3 12 42.34 28.42 15.26 1.20 4 18 -84.85 18.26 3.75 -9.24 [Numerical example 6] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -58.898 1.43 1.77830 23.9 38.97 2 79.559 7.50 40.39 3 87.680 8.91 1.92286 18.9 50.10 4 -102.220 0.20 50.50 5 107.165 13.39 1.83481 42.7 49.86 6 -42.832 1.41 1.92286 20.9 49.12 7 -113.183 0.18 47.89 8 86.599 10.32 1.43875 94.7 43.18 9 -44.859 1.41 1.62004 36.3 41.26 10 89.938 3.85 37.13 11 (Aperture) ∞ (Variable) 36.10 12 -30.631 1.44 1.74077 27.8 31.26 13 28.100 12.53 2.00100 29.1 33.80 14 -72.348 0.20 33.75 15* 73.399 12.66 1.61997 63.9 32.38 16 -21.651 1.49 1.63980 34.5 33.39 17 -45.432 (variable) 35.07 18* -22.765 4.76 1.58313 59.4 34.77 19* -23.663 2.23 32.99 20* 41.144 5.56 1.63560 23.9 33.26 21* 21.025 3.97 36.50 22 -106.173 2.31 2.00069 25.5 36.71 23 -89.769 37.52 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 4.78352e-05 A 6= 1.37566e-06 A 8= 4.44487e-09 A10= 9.60554e-13 A 3=-1.57093e-04 A 5=-1.14446e-05 A 7=-1.02173e-07 A 9=-1.03240e-10 Page 18 K =-1.29274e+01 A 4=-1.45405e-04 A 6=-4.67476e-06 A 8=-9.99426e-09 A10=-9.34234e-13 A 3= 6.80273e-04 A 5= 4.00711e-05 A 7= 2.91510e-07 A 9= 1.68767e-10 Page 19 K =-4.58640e+00 A 4= 5.12047e-04 A 6= 9.18831e-06 A 8= 3.85546e-08 A10= 1.55327e-11 A 3=-2.27546e-05 A 5=-8.37482e-05 A 7=-7.29744e-07 A 9=-1.17802e-09 Page 20 K = 0.00000e+00 A 4= 2.13459e-04 A 6= 4.17605e-06 A 8=-6.33667e-08 A10=-2.82786e-10 A12=-7.61168e-14 A 3= 1.18437e-04 A 5=-5.72546e-05 A 7= 1.81175e-07 A 9= 5.85598e-09 A11= 7.19340e-12 Page 21 K = 0.00000e+00 A 4=-5.43258e-04 A 6=-1.65813e-05 A 8=-1.96156e-07 A10=-5.22183e-10 A12=-1.34334e-13 A 3= 1.10691e-03 A 5= 1.00494e-04 A 7= 2.11678e-06 A 9= 1.25576e-08 A11= 1.26205e-11 Focal length 47.62 F-number 1.25 Half angle of view (°) 24.44 Image height 21.64 Lens length 122.90 BF 11.99 Object distance / magnification infinite 0.156x d11 13.27 7.38 d17 1.88 7.77 Entrance pupil position 27.70 Exit pupil position -54.18 Front principal point position 41.05 Back principal point position -35.62 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 81.42 48.60 20.83 -6.33 2 12 42.48 28.32 15.20 1.08 3 18 -90.71 18.84 4.67 -8.56 [Numerical example 7] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -59.271 1.45 1.77830 23.9 39.18 2 78.481 7.52 40.37 3 88.031 8.90 1.92286 18.9 50.10 4 -101.866 0.20 50.50 5 106.241 13.37 1.83481 42.7 49.88 6 -42.958 1.40 1.92286 20.9 49.16 7 -113.119 0.18 47.93 8 83.478 10.39 1.43875 94.7 43.12 9 -45.067 1.41 1.62004 36.3 41.17 10 84.082 3.95 36.95 11 (Aperture) ∞ (Variable) 35.94 12 -30.479 1.38 1.74077 27.8 31.30 13 28.090 12.57 2.00100 29.1 33.94 14 -72.239 0.20 33.91 15* 73.841 12.58 1.61997 63.9 32.26 16 -21.658 1.44 1.63980 34.5 33.29 17 -45.220 (variable) 34.98 18* -23.030 4.75 1.58313 59.4 34.73 19* -23.797 2.22 32.97 20* 39.989 5.42 1.63560 23.9 33.25 21* 21.003 (variable) 36.37 22 -116.422 2.24 2.00069 25.5 36.83 23 -99.610 37.59 Image plane ∞ Aspheric data Page 15 K = 0.00000e+00 A 4= 4.76767e-05 A 6= 1.37160e-06 A 8= 4.43564e-09 A10= 9.58782e-13 A 3=-1.56923e-04 A 5=-1.14141e-05 A 7=-1.01904e-07 A 9=-1.03065e-10 Page 18 K =-1.30224e+01 A 4=-1.40575e-04 A 6=-4.55413e-06 A 8=-9.60966e-09 A10=-8.15633e-13 A 3= 6.77762e-04 A 5= 3.90339e-05 A 7= 2.82929e-07 A 9= 1.58676e-10 Page 19 K =-4.48730e+00 A 4= 5.12069e-04 A 6= 9.26009e-06 A 8= 3.91727e-08 A10 = 1.58266e-11 A 3=-2.10974e-05 A 5=-8.39538e-05 A 7=-7.39122e-07 A 9=-1.19902e-09 Page 20 K = 0.00000e+00 A 4= 2.09225e-04 A 6= 4.13181e-06 A 8=-6.34547e-08 A10=-2.82812e-10 A12=-7.56848e-14 A 3= 1.21537e-04 A 5=-5.66474e-05 A 7= 1.83081e-07 A 9= 5.86021e-09 A11 = 7.18175e-12 Page 21 K = 0.00000e+00 A 4=-5.40859e-04 A 6=-1.63457e-05 A 8=-1.93607e-07 A10=-5.17563e-10 A12=-1.33696e-13 A 3= 1.09739e-03 A 5= 9.94067e-05 A 7= 2.08612e-06 A 9= 1.24198e-08 A11= 1.25353e-11 Focal length 47.60 F-number 1.25 Half angle of view (°) 24.44 Image height 21.64 Lens length 122.88 BF 12.09 Object distance / magnification infinite 0.155x d11 13.05 7.36 d17 1.84 8.10 d21 4.31 3.74 Entrance pupil position 27.88 Exit pupil position -54.12 Front principal point position 41.26 Back principal point position -35.50 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 82.25 48.78 20.64 -6.66 2 12 42.57 28.17 15.20 1.19 3 18 -79.60 12.40 6.69 -1.09 4 22 646.32 2.24 7.26 6.21 [Numerical example 8] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 1000.000 1.57 2.00100 29.1 38.96 2∞ 7.26 38.93 3 -64.570 1.40 1.84666 23.8 38.76 4 82.506 7.08 40.59 5 132.751 6.79 1.91082 35.3 48.05 6 -110.730 0.11 48.65 7 78.960 6.02 1.94594 18.0 50.00 8 -1068.515 0.20 49.62 9 86.214 11.02 1.76385 48.5 47.73 10 -52.439 1.27 1.85478 24.8 46.57 11 -163.604 0.11 44.29 12 124.478 4.88 1.43875 94.7 40.24 13 -122.423 1.29 1.85478 24.8 38.66 14 64.286 4.39 35.50 15 (Aperture) ∞ (Variable) 34.34 16 -27.994 1.29 1.78880 28.4 28.61 17 29.062 9.85 2.00100 29.1 31.19 18 -53.658 0.20 32.29 19* 94.813 11.85 1.76385 48.5 33.65 20 -23.639 1.45 1.85478 24.8 34.56 21 -45.440 (variable) 36.28 22* -14.039 3.99 1.58313 59.4 35.82 23* -12.405 2.92 34.63 24* 78.180 3.57 1.68948 31.0 34.95 25* 21.567 38.00 Image plane ∞ Aspheric data Page 19 K = 0.00000e+00 A 4= 6.32292e-05 A 6= 2.21434e-06 A 8= 9.48450e-09 A10= 3.09432e-12 A 3=-1.70963e-04 A 5=-1.62090e-05 A 7=-1.87106e-07 A 9=-2.64337e-10 Page 22 K =-3.43065e+00 A 4= 1.04387e-05 A 6=-9.73401e-06 A 8=-4.53649e-08 A10=-1.34370e-11 A 3= 4.90633e-04 A 5= 4.68535e-05 A 7= 9.01074e-07 A 9= 1.21136e-09 Page 23 K =-3.86397e+00 A 4= 8.03053e-04 A 6= 1.33760e-05 A 8= 4.37050e-08 A10= 1.68143e-11 A 3=-5.11667e-04 A 5=-1.34444e-04 A 7=-9.23043e-07 A 9=-1.26929e-09 Page 24 K = 0.00000e+00 A 4= 7.88845e-04 A 6= 1.55975e-05 A 8=-1.88494e-08 A10=-1.08563e-10 A12= 1.94811e-15 A 3=-2.01869e-04 A 5=-1.72721e-04 A 7=-5.58477e-07 A 9= 2.77439e-09 A11= 1.49300e-12 Page 25 K = 0.00000e+00 A 4=-2.37204e-04 A 6=-1.29810e-05 A 8=-2.21118e-07 A10=-5.61060e-10 A12=-1.26354e-13 A 3= 8.53219e-04 A 5= 4.46557e-05 A 7= 2.18381e-06 A 9= 1.41173e-08 A11= 1.27265e-11 Various data Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens total length 120.00 BF 16.33 Object distance / magnification infinite 0.152x d15 13.30 7.38 d21 1.84 7.77 Entrance pupil position 35.80 Exit pupil position -42.97 Front principal point position 44.63 Back principal point position -32.17 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 74.00 53.40 22.83 -11.03 2 16 39.93 24.64 13.63 2.24 3 22 -76.12 10.48 4.27 -2.45 [Numerical example 9] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 296.014 1.65 2.00100 29.1 38.96 2 419.137 7.26 38.86 3 -64.808 1.46 1.84666 23.8 38.71 4 73.123 6.27 40.63 5 135.172 6.15 1.91082 35.3 47.36 6 -129.521 0.16 48.02 7 97.022 6.19 1.94594 18.0 50.00 8 -276.153 0.20 49.85 9 71.468 12.40 1.76385 48.5 47.95 10 -49.479 1.39 1.85478 24.8 46.75 11 -139.704 0.11 44.51 12 156.547 3.74 1.43875 94.7 40.52 13 -239.478 1.41 1.85478 24.8 39.06 14 62.600 (variable) 36.03 15 (Aperture) ∞ (Variable) 34.82 16 -30.050 1.45 1.78880 28.4 28.83 17 27.513 9.61 2.00100 29.1 30.45 18 -69.975 0.20 31.92 19* 95.890 11.65 1.76385 48.5 33.19 20 -23.742 1.96 1.85478 24.8 34.25 21 -43.249 (variable) 36.18 22* -14.678 3.92 1.58313 59.4 35.73 23* -12.828 2.48 34.48 24* 74.622 4.66 1.68948 31.0 34.60 25* 21.555 38.00 Image plane ∞ Aspheric data Page 19 K = 0.00000e+00 A 4= 6.03791e-05 A 6= 2.21892e-06 A 8= 9.65989e-09 A10= 3.17596e-12 A 3=-1.55004e-04 A 5=-1.60217e-05 A 7=-1.89413e-07 A 9=-2.70138e-10 Page 22 K =-3.47418e+00 A 4= 2.64139e-05 A 6=-9.66133e-06 A 8=-4.51978e-08 A10=-1.34194e-11 A 3= 4.15841e-04 A 5= 4.56382e-05 A 7= 8.97296e-07 A 9= 1.20748e-09 Page 23 K =-4.22528e+00 A 4= 8.07011e-04 A 6= 1.37783e-05 A 8= 4.44833e-08 A10= 1.66680e-11 A 3=-5.47883e-04 A 5=-1.37042e-04 A 7=-9.49537e-07 A 9=-1.27441e-09 Page 24 K = 0.00000e+00 A 4= 7.63375e-04 A 6= 1.45509e-05 A 8=-1.86686e-08 A10=-1.08001e-10 A12=-8.56394e-16 A 3=-4.19469e-04 A 5=-1.61944e-04 A 7=-5.17042e-07 A 9= 2.70292e-09 A11= 1.60470e-12 Page 25 K = 0.00000e+00 A 4=-2.55253e-04 A 6=-1.37547e-05 A 8=-2.19520e-07 A10=-5.61626e-10 A12=-1.27978e-13 A 3= 5.92881e-04 A 5= 5.44466e-05 A 7= 2.19254e-06 A 9= 1.40493e-08 A11= 1.28176e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens total length 120.00 BF 16.20 Object distance / magnification infinite 0.159x d14 4.54 7.09 d15 13.02 7.05 d21 1.94 7.90 Entrance pupil position 35.11 Exit pupil position -41.54 Front principal point position 42.87 Back principal point position -32.30 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 71.61 48.37 23.57 -5.40 2 16 42.90 24.87 14.34 2.82 3 22 -80.40 11.06 5.49 -1.41 [Numerical example 10] Unit: mm Surface Data Surface number rd nd νd Effective diameter 1 -60.699 1.36 1.84666 23.8 38.96 2 82.970 6.43 41.15 3 2917.279 3.64 1.95375 32.3 46.06 4 -141.895 0.15 46.94 5 78.186 8.96 1.84666 23.8 52.04 6 -130.498 0.20 52.12 7 66.351 14.13 1.71700 47.9 50.02 8 -48.476 1.29 1.78880 28.4 48.70 9 -140.821 0.24 46.25 10 201.502 8.16 1.59282 68.6 42.39 11 -45.384 1.33 1.72047 34.7 40.65 12 82.183 3.80 35.80 13 (Aperture) ∞ (Variable) 34.49 14 -33.003 1.32 1.78880 28.4 28.47 15 27.217 8.49 2.00100 29.1 29.86 16 -101.028 0.20 30.93 17* 96.420 10.76 1.76385 48.5 32.05 18 -24.146 1.43 1.84666 23.8 33.30 19 -39.274 (variable) 34.94 20* -16.083 4.48 1.53500 56.0 34.70 21* -15.233 1.52 34.10 22* 52.399 5.41 1.63560 23.9 34.28 23* 21.359 2.78 37.93 24 -508.103 1.31 1.92286 20.9 38.37 25 1609.712 38.74 Image plane ∞ Aspheric data Page 17 K = 0.00000e+00 A 4= 7.62821e-05 A 6= 3.07168e-06 A 8= 1.45215e-08 A10= 5.06023e-12 A 3=-1.86315e-04 A 5=-2.10917e-05 A 7=-2.74094e-07 A 9=-4.18974e-10 Page 20 K =-6.88013e+00 A 4=-1.89303e-04 A 6=-1.02530e-05 A 8=-4.46873e-08 A10=-1.37534e-11 A 3= 6.85791e-04 A 5= 6.61195e-05 A 7= 8.87808e-07 A 9= 1.21558e-09 Page 21 K =-4.16417e+00 A 4= 1.08906e-03 A 6= 2.66900e-05 A 8= 9.56578e-08 A10= 3.41491e-11 A 3=-5.97375e-04 A 5=-2.26804e-04 A 7=-1.99988e-06 A 9=-2.69826e-09 Page 22 K = 0.00000e+00 A 4= 7.37075e-04 A 6= 2.16848e-05 A 8= 2.96573e-08 A10=-5.96693e-11 A12= 1.67586e-14 A 3=-3.44779e-04 A 5=-1.89748e-04 A 7=-1.29702e-06 A 9= 8.64156e-10 A11= 4.85021e-13 Page 23 K = 0.00000e+00 A 4=-5.61961e-04 A 6=-2.43268e-05 A 8=-3.21277e-07 A10=-8.07403e-10 A12=-1.87901e-13 A 3= 9.72704e-04 A 5= 1.25282e-04 A 7= 3.39021e-06 A 9= 2.01933e-08 A11= 1.85964e-11 Focal length 48.50 F-number 1.25 Half angle of view (°) 24.04 Image height 21.64 Lens total length 113.00 BF 10.71 Object distance / magnification infinite 0.159x d13 13.13 6.36 d19 1.75 8.53 Entrance pupil position 29.34 Exit pupil position -39.71 Front principal point position 31.18 Back principal point position -37.79 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 64.39 49.69 17.37 -10.09 2 14 44.02 22.21 13.41 2.90 3 20 -68.23 15.50 5.50 -4.86 Table 1 shows the values of formulas (1) to (12) in numerical examples 1 to 10. Each numerical example satisfies all of the conditions of formulas (1) to (12).

[0069] [Table 1]

[0070] [Imaging device] 21 shows a digital still camera as an imaging device that uses the optical system of Examples 1 to 10 as its imaging optical system. Reference numeral 20 denotes the camera body, and 21 denotes the imaging optical system configured using any of the optical systems of Examples 1 to 10. Reference numeral 22 denotes a solid-state imaging element such as a CCD sensor or CMOS sensor that is built into the camera body 20 and captures an optical image (subject image) formed by the imaging optical system 21. Reference numeral 23 denotes a recording unit that records image data generated by processing the imaging signal from the imaging element 22, and 24 denotes a rear display that displays the image data.

[0071] By using the optical system of each embodiment as an imaging optical system, a small camera with high optical performance can be obtained.

[0072] The camera may be a single-lens reflex camera with a quick-turn mirror, a mirrorless camera without a quick-turn mirror, or an integrated lens camera.

[0073] The above embodiment includes the following configurations.

[0074] (Configuration 1) An optical system comprising, arranged in order from the object side to the image side, a front group having positive refractive power including at least one lens group, an intermediate lens group having positive refractive power, and a rear group having negative refractive power including at least one lens group, wherein the spacing between adjacent lens groups changes during focusing, During focusing from infinity to close range, the intermediate lens group moves toward the object side, the front group includes at least two positive lens elements and at least one negative lens element; An optical system characterized in that the rear group includes at least one aspherical lens having an aspherical surface with a pole point located away from the optical axis. (Configuration 2) Let TTL be the length on the optical axis from the lens surface of the optical system closest to the object to the lens surface of the optical system closest to the image, plus the air-equivalent length on the optical axis from the lens surface closest to the image to the image plane, f be the focal length of the optical system, and ω be the half angle of view of the optical system. 3.0≦TTL / (f×tanω)≦10.0 The optical system according to configuration 1, characterized in that the following condition is satisfied: (Configuration 3) When the average refractive index of all the positive lenses included in the optical system at the d-line is PNdave, 1.50≦PNdave≦2.00 3. The optical system according to configuration 1 or 2, wherein the following condition is satisfied: (Configuration 4) Let TTL be the length on the optical axis from the lens surface closest to the object side of the optical system to the lens surface closest to the image side of the optical system plus the air-equivalent length on the optical axis from the lens surface closest to the image side to the image plane, and let sk be the air-equivalent length. 0.01≦sk / TTL≦0.50 4. The optical system according to any one of configurations 1 to 3, wherein the following condition is satisfied: (Configuration 5) When the focal length of the front group is ff, 2.0≦ff / sk≦10.0 5. The optical system according to any one of configurations 1 to 4, wherein the following condition is satisfied: (Configuration 6) When the focal length of the intermediate lens group is fm and the focal length of the rear lens group is fr, 0.1≦-fm / fr≦1.0 6. The optical system according to any one of configurations 1 to 5, wherein the following condition is satisfied: (Configuration 7) When the distance on the optical axis between the front lens group and the intermediate lens group is Df, 0.1≦Df / f≦1.0 7. The optical system according to any one of configurations 1 to 6, wherein the following condition is satisfied: (Configuration 8) When the focal length of the front group is ff and the focal length of the rear group is fr, 0.1≦-ff / fr≦2.0 8. The optical system according to any one of configurations 1 to 7, wherein the following condition is satisfied: (Configuration 9) When the Abbe number of the positive lens having the largest Abbe number based on the d-line among all the positive lenses included in the front group is denoted by νdp1, 55≦νdp1≦96 9. The optical system according to any one of configurations 1 to 8, wherein the following condition is satisfied: (Configuration 10) When the Abbe number of the positive lens having the smallest Abbe number based on the d-line among all the positive lenses included in the front group is denoted by νdp2, 15≦νdp2≦40 10. The optical system according to any one of configurations 1 to 9, wherein the following condition is satisfied: (Configuration 11) When the Abbe number of the negative lens located nearest to the object side among all the negative lenses included in the front lens group is νdn, the Abbe number is determined based on the d-line, 15≦νdn≦40 11. The optical system according to any one of configurations 1 to 10, wherein the following condition is satisfied: (Configuration 12) 12. The optical system according to claim 11, wherein the negative lens has a biconcave shape. (Configuration 13) When the paraxial radii of curvature of the object-side and image-side lens surfaces of the at least one aspherical lens are Ra1 and Ra2, respectively, 0 <Ra1 / f 0 <Ra2 / f 13. The optical system according to any one of configurations 1 to 12, comprising an aspherical lens that satisfies the following condition: (Configuration 14) When the refractive index of the at least one aspherical lens at the d-line is Nda, 1.44≦Nda≦1.77 2. The optical system according to claim 1, wherein the following condition is satisfied: (Configuration 15) When the paraxial radii of curvature of the object-side and image-side lens surfaces of the at least one aspherical lens are Rb1 and Rb2, respectively, Rb1 / f<0 Rb2 / f<0 14. The optical system according to claim 13, comprising an aspherical lens that satisfies the following condition: (Configuration 16) An optical system comprising, arranged in order from the object side to the image side, a front group including at least one lens group, an intermediate lens group, and a rear group including at least one lens group, wherein the spacing between adjacent lens groups changes during focusing, The intermediate lens group moves during focusing from infinity to close range, the front group includes at least two positive lenses and at least two negative lenses, The optical system is characterized in that the rear group includes at least one aspherical lens having an aspherical surface with a pole point at a position away from the optical axis (Configuration 17). The optical system according to any one of configurations 1 to 16; and an image sensor that captures an image of a subject through the optical system.

[0075] The embodiments described above are merely representative examples, and various modifications and alterations are possible to each embodiment when implementing the present invention. [Explanation of symbols]

[0076] Lf front group Lm intermediate lens group Lr rear group Lp1, Lp2 positive lenses Ln negative lens La, Lb aspherical lens

Claims

1. An optical system comprising, arranged in order from the object side to the image side, a front group having positive refractive power including at least one lens group, an intermediate lens group having positive refractive power, and a rear group having negative refractive power including at least one lens group, wherein the spacing between adjacent lens groups changes during focusing, During focusing from infinity to close range, the intermediate lens group moves toward the object side, the front group includes at least two positive lenses and at least one negative lens; An optical system characterized in that the rear group includes at least one aspherical lens having an aspherical surface with a pole point located away from the optical axis.

2. Let TTL be the length on the optical axis from the lens surface closest to the object side of the optical system to the lens surface closest to the image side of the optical system plus the air-equivalent length on the optical axis from the lens surface closest to the image side to the image plane, f be the focal length of the optical system, and ω be the half angle of view of the optical system. 3.0≦TTL / (f×tanω)≦10.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

3. When the average refractive index at the d-line of all the positive lenses included in the optical system is PNdave, 1.50≦PNdave≦2.00 2. The optical system according to claim 1, wherein the following condition is satisfied:

4. Let TTL be the length on the optical axis from the lens surface closest to the object side of the optical system to the lens surface closest to the image side of the optical system plus the air-equivalent length on the optical axis from the lens surface closest to the image side to the image plane, and let sk be the air-equivalent length. 0.01≦sk / TTL≦0.50 2. The optical system according to claim 1, wherein the following condition is satisfied:

5. When the focal length of the front group is ff, 2.0≦ff / sk≦10.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

6. When the focal length of the intermediate lens group is fm and the focal length of the rear lens group is fr, 0.1≦-fm / fr≦1.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

7. When the distance on the optical axis between the front lens group and the intermediate lens group is Df, 0.1≦Df / f≦1.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

8. When the focal length of the front group is ff and the focal length of the rear group is fr, 0.1≦-ff / fr≦2.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

9. When the Abbe number of the positive lens having the largest Abbe number based on the d-line among all the positive lenses included in the front group is denoted by νdp1, 55≦νdp1≦96 2. The optical system according to claim 1, wherein the following condition is satisfied:

10. When the Abbe number of the positive lens having the smallest Abbe number based on the d-line among all the positive lenses included in the front group is denoted by νdp2, 15≦νdp2≦40 2. The optical system according to claim 1, wherein the following condition is satisfied:

11. When the Abbe number of the negative lens located nearest to the object side among all the negative lenses included in the front group is νdn, the Abbe number based on the d-line is: 15≦νdn≦40 2. The optical system according to claim 1, wherein the following condition is satisfied:

12. The optical system according to claim 11 , wherein the negative lens has a biconcave shape.

13. When the paraxial radii of curvature of the object-side and image-side lens surfaces of the at least one aspherical lens are Ra1 and Ra2, respectively, 0<Ra1 / f 0<Ra2 / f 2. The optical system according to claim 1, further comprising an aspherical lens that satisfies the following condition:

14. When the refractive index of the at least one aspherical lens at the d-line is Nda, 1.44≦Nda≦1.77 2. The optical system according to claim 1, wherein the following condition is satisfied:

15. When the paraxial radii of curvature of the object-side and image-side lens surfaces of the at least one aspherical lens are Rb1 and Rb2, respectively, Rb1 / f<0 Rb2 / f<0 14. The optical system according to claim 13, further comprising an aspherical lens that satisfies the following condition:

16. An optical system comprising, arranged in order from the object side to the image side, a front group including at least one lens group, an intermediate lens group, and a rear group including at least one lens group, wherein the spacing between adjacent lens groups changes during focusing, The intermediate lens group moves during focusing from infinity to close range, the front group includes at least two positive lenses and at least two negative lenses; An optical system characterized in that the rear group includes at least one aspherical lens having an aspherical surface with a pole point located away from the optical axis.

17. An optical system according to any one of claims 1 to 16; and an image sensor that captures an image of a subject through the optical system.

Images