Optical system and imaging device

Abstract

To provide a compact optical system capable of high-speed focusing. [Solution] The optical system is composed of a front lens group Lf with negative refractive power, an intermediate lens group Lm with negative refractive power, and a rear lens group Lr with positive refractive power, arranged in order from the object side to the image side, and the spacing between adjacent lens groups changes during focusing. When focusing from infinity to near, the intermediate lens group moves towards the object side. The front group has at least two negative lenses Ln1, Ln2 and at least one positive lens Lp. When the focal length of the optical system is f, the maximum half-angle of view of the optical system is ω, the length TTL is the distance on the optical axis from the lens surface closest to the object to the lens surface closest to the image to the optical system plus the air equivalent distance on the optical axis from the lens surface closest to the image to the image plane, and the focal length of the intermediate lens group is fm, the conditions 1.0 ≤ TTL / (f × tanω) ≤ 9.0 and 0.5 ≤ -fm / f ≤ 9.0 are satisfied.

Description

Technical Field

[0001] The present invention relates to an optical system used for imaging and the like.

Background Art

[0002] For an optical system used for imaging, faster focusing (weight reduction of the focus lens group) is required. In Patent Document 1, an optical system is disclosed that is composed of, in order from the object side, a first lens group with a negative refractive power, a second lens group that moves during focusing, and a third lens group that has a positive refractive power and includes an aperture stop.

Prior Art Documents

Patent Documents

[0003] [[ID=?]](此处原文序号重复,推测为笔误,翻译时保留原文格式) Japanese Patent Application Laid-Open No. 2023-167728

Summary of the Invention

Problems to be Solved by the Invention

[0004] There is a need for an optical system that is smaller and capable of faster focusing than conventional ones. <00000?]](此处原文序号重复,推测为笔误,翻译时保留原文格式)

Means for Solving the Problems

[0005] <?]](此处原文序号重复,推测为笔误,翻译时保留原文格式) ​One aspect of the present invention is an optical system composed of a front group with negative refractive power including at least one lens group, an intermediate lens group with negative refractive power, and a rear group with positive refractive power including at least one lens group, arranged sequentially from the object side to the image side, wherein the spacing between adjacent lens groups changes during focusing. When focusing from infinity to near, the intermediate lens group moves towards the object side. The front group has at least two negative lenses and at least one positive lens. When the focal length of the optical system is f, the maximum half-angle of view of the optical system is ω, the length TTL is the distance along the optical axis from the lens surface closest to the object to the lens surface closest to the image to the optical system plus the air-equivalent distance along the optical axis from the lens surface closest to the image to the image plane, and the focal length of the intermediate lens group is fm, 1.0 ≤ TTL / (f × tanω) ≤ 9.0 0.5 ≤ -fm / f ≤ 9.0 It is characterized by satisfying the following conditions. Furthermore, an imaging device equipped with the above optical system also constitutes another aspect of the present invention. [Effects of the Invention]

[0006] According to the present invention, it is possible to provide a compact optical system capable of high-speed focusing. [Brief explanation of the drawing]

[0007] [Figure 1] This is a cross-sectional view of the optical system of Example 1. [Figure 2] This is an aberration diagram of the optical system in Example 1. [Figure 3] This is a cross-sectional view of the optical system of Example 2. [Figure 4] This is an aberration diagram of the optical system in Example 2. [Figure 5] This is a cross-sectional view of the optical system of Example 3. [Figure 6] This is an aberration diagram of the optical system in Example 3. [Figure 7] This is a cross-sectional view of the optical system of Example 4. [Figure 8] This is an aberration diagram of the optical system in Example 4. [Figure 9]It is a cross-sectional view of the optical system of Example 5. [Figure 10] It is an aberration diagram of the optical system of Example 5. [Figure 11] It is a cross-sectional view of the optical system of Example 6. [Figure 12] It is an aberration diagram of the optical system of Example 6. [Figure 13] It is a cross-sectional view of the optical system of Example 7. [Figure 14] It is an aberration diagram of the optical system of Example 7. [Figure 15] It is a cross-sectional view of the optical system of Example 8. [Figure 16] It is an aberration diagram of the optical system of Example 8. [Figure 17] It is a cross-sectional view of the optical system of Example 9. [Figure 18] It is an aberration diagram of the optical system of Example 9. [Figure 19] It is a cross-sectional view of the optical system of Example 10. [Figure 20] It is an aberration diagram of the optical system of Example 10. [Figure 21] It is a cross-sectional view of the optical system of Example 11. [Figure 22] It is an aberration diagram of the optical system of Example 11. [Figure 23] It is a cross-sectional view of the optical system of Example 12. [Figure 24] It is an aberration diagram of the optical system of Example 12. [Figure 25] It is a cross-sectional view of the optical system of Example 13. [Figure 26] It is an aberration diagram of the optical system of Example 13. [Figure 27] It is a cross-sectional view of the optical system of Example 14. [Figure 28] It is an aberration diagram of the optical system of Example 14. [Figure 29] It is a cross-sectional view of the optical system of Example 15. [Figure 30] It is an aberration diagram of the optical system of Example 15. [Figure 31] It is a cross-sectional view of the optical system of Example 16. [Figure 32] It is an aberration diagram of the optical system of Example 16. [Figure 33] This is a cross-sectional view of the optical system of Example 17. [Figure 34] This is an aberration diagram of the optical system in Example 17. [Figure 35] This is a cross-sectional view of the optical system of Example 18. [Figure 36] This is an aberration diagram of the optical system in Example 18. [Figure 37] This is a cross-sectional view of the optical system of Example 19. [Figure 38] This is an aberration diagram of the optical system in Example 19. [Figure 39] This is a cross-sectional view of the optical system of Example 20. [Figure 40] This is an aberration diagram of the optical system in Example 20. [Figure 41] This is a cross-sectional view of the optical system of Example 21. [Figure 42] This is an aberration diagram of the optical system in Example 21. [Figure 43] This figure shows an imaging device equipped with the optical systems of Examples 1 to 21. [Modes for carrying out the invention]

[0008] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0009] Figures 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, and 41 show cross-sections of the optical systems of Examples 1 to 21, respectively. In each figure, the left side is the object side (front side), and the right side is the image side (back side).

[0010] First, before providing a detailed description of Examples 1 to 21, we will explain the points common to each example. The optical systems of each example can be used in various imaging devices such as digital video cameras, digital still cameras, broadcast cameras, silver halide film cameras, and surveillance cameras.

[0011] The optical system of each embodiment consists of a front group Lf including at least one lens group, an intermediate lens group Lm, and a rear group Lr including at least one lens group, arranged sequentially from the object side to the image side. A lens group is a collection of one or more lenses that move or remain stationary as a single unit during focusing. That is, the spacing between adjacent lens groups changes during focusing.

[0012] SP is the aperture diaphragm and is included in the rear group Lr. IP is the paraxial 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.

[0013] Furthermore, a glass block without refractive power, such as a cover glass or an IR cut filter, may be placed between the lens surface closest to the image plane and the image plane of the optical system.

[0014] In the optical system of each embodiment, the front lens group Lf has a negative refractive power as a whole, and the intermediate lens group Lm has a negative refractive power as a whole. The rear lens group Lr has a positive refractive power as a whole. By adopting this retrofocus type power arrangement, the optical system is widened. Note that the refractive power of the lens groups and lenses represents the refractive power in the paraxial direction and corresponds to the reciprocal of the focal length.

[0015] Furthermore, in the optical systems of each embodiment, the intermediate lens group Lm moves toward the object when focusing from infinity to near. By moving the intermediate lens group Lm, which is located in the intermediate part where the light beam does not spread widely, the weight of the intermediate lens group Lm as a focusing lens group is reduced. In each figure, the direction of movement of the lens group when focusing from infinity to near is indicated by a dashed arrow above the lens group that moves during focusing.

[0016] Furthermore, in the optical system of each embodiment, the front group Lf has at least two negative lenses Ln1 and Ln2 and at least one positive lens Lp. The first negative lens Ln1 is positioned on the object side of the front group Lf. This configuration effectively corrects distortion and chromatic aberration. The second negative lens Ln2 is positioned on the image side of the first negative lens Ln1. The positive lens Lp is positioned on the image side or object side of the second negative lens Ln2. Note that when two lenses are joined to form a cemented lens, the number of lenses is considered to be 2.

[0017] Let f be the focal length of the entire optical system, ω be the maximum half-angle of view of the optical system, and TTL be the length (total optical length) which is the distance along the optical axis from the lens surface closest to the object to the lens surface closest to the image, plus the back focus. In this case, it is preferable that the optical system of each embodiment satisfies the following condition (1). The back focus is the air-equivalent distance along the optical axis from the lens surface closest to the image to the image plane. If the optical system is a zoom lens capable of variable magnification, the focal length f is the focal length at the wide-angle end.

[0018] 1.0 ≤ TTL / (f × tanω) ≤ 9.0 (1) The conditions in equation (1) indicate an appropriate relationship between the total optical length and image height of the optical system. If TTL / (f×tanω) exceeds the upper limit of equation (1), the total optical length increases, making the optical system larger, which is undesirable. If the total optical length is shortened so that TTL / (f×tanω) falls below the lower limit of equation (1), the refractive power of each lens constituting the optical system increases, making it difficult to correct distortion and chromatic aberration, which is also undesirable.

[0019] Furthermore, it is more preferable to set the lower limit of equation (1) to 1.5, 2.0, 2.5, 3.0, or 3.4. Also, it is more preferable to set the upper limit of equation (1) to 8.5, 8.0, 7.5, or 7.0.

[0020] In each embodiment, the optical system preferably satisfies the following conditions (2) when the focal length of the intermediate lens group Lm is fm (f>0, fm<0).

[0021] 0.5 ≤ -fm / f ≤ 9.0 (2) The conditions in equation (2) indicate an appropriate relationship between the intermediate lens group Lm and the focal length of the entire optical system. If the refractive power of the intermediate lens group Lm is weakened so that -fm / f exceeds the upper limit of equation (2), the amount of movement of the intermediate lens group Lm during focusing increases, and the overall optical length increases, which is undesirable. If the refractive power of the intermediate lens group Lm is strengthened so that -fm / f falls below the lower limit of equation (2), the aberration fluctuations associated with focusing increase, which is also undesirable.

[0022] Furthermore, it is more preferable to set the lower limit of equation (2) to 0.7, 1.0, 1.2, or 1.3. Also, it is more preferable to set the upper limit of equation (2) to 8.5, 8.0, 7.5, or 7.0.

[0023] By satisfying the above configuration and at least one of the conditions in equations (1) and (2), it is possible to realize an optical system that is compact yet possesses high optical performance and enables high-speed focusing.

[0024] Furthermore, it is preferable that the optical system of each embodiment satisfies at least one of the following conditions (3) to (12).

[0025] In each embodiment, it is desirable that the optical system satisfies the following equation (3), where R11 is the radius of curvature of the object-side lens surface of the first negative lens Ln1 and R12 is the radius of curvature of the image-side lens surface of the first negative lens Ln1.

[0026] -1.0≦(R12-R11) / (R11+R12)<0.0 (3) The conditions in equation (3) indicate the appropriate shape (shape factor) of the first negative lens Ln1. If the shape factor of the first negative lens Ln1 exceeds the upper limit of equation (3), the object side of the first negative lens Ln1 becomes concave, making it difficult to achieve both field curvature and distortion, which is undesirable. If the shape factor of the first negative lens Ln1 falls below the lower limit of equation (3), the radius of curvature of the image-side lens surface of the first negative lens Ln1 becomes too small, making it difficult to achieve both field curvature and distortion, which is also undesirable.

[0027] Furthermore, it is preferable to set the lower limit of equation (3) to -0.9, -0.8, or -0.7. Also, it is preferable to set the upper limit of equation (3) to -0.05 or -0.1.

[0028] In each embodiment, the optical system preferably satisfies the following condition (4), where R21 is the radius of curvature of the object-side lens surface of the second negative lens Ln2 and R22 is the radius of curvature of the image-side lens surface of the second negative lens Ln2.

[0029] -1.0≦(R21+R22) / (R22-R21)≦1.0 (4) The conditions in equation (4) indicate the appropriate shape (shape factor) of the second negative lens Ln2. If the shape factor of the second negative lens Ln2 exceeds the upper limit or falls below the lower limit in equation (4), the second negative lens Ln2 will have a meniscus shape, making it difficult to correct chromatic aberration and therefore undesirable.

[0030] Furthermore, it is preferable to set the lower limit of equation (4) to -0.9, -0.8, or -0.7. Also, it is preferable to set the upper limit of equation (4) to 0.5, 0.3, or 0.2.

[0031] In each embodiment, the optical system preferably satisfies the following condition (5), where Rp1 is the radius of curvature of the object-side lens surface of the positive lens Lp, and Rp2 is the radius of curvature of the image-side lens surface of the positive lens Lp.

[0032] -1.0≦(Rp1+Rp2) / (Rp2-Rp1)≦30.0 (5) Equation (5) shows the appropriate shape factor for the positive lens Lp. If the shape factor of the positive lens Lp exceeds the upper limit of equation (5), the image side of the positive lens Lp becomes a concave surface with a small radius of curvature, making it difficult to correct chromatic aberration, which is undesirable. If the shape factor of the positive lens Lp falls below the lower limit of equation (5), the object side of the positive lens Lp becomes a concave surface, making it difficult to correct axial chromatic aberration and spherical aberration, which is also undesirable.

[0033] Furthermore, it is preferable to set the lower limit of equation (5) to -0.8, -0.5, 0.0, or 0.1. Also, it is preferable to set the upper limit of equation (5) to 25.0, 20.0, 15.0, or 10.0.

[0034] In each embodiment, the optical system preferably satisfies the following condition (6) when the lateral magnification in the state where the intermediate lens group Lm is in focus on an object at infinity (hereinafter referred to as the infinity focus state) is βm.

[0035] 0.0 < βm ≤ 1.0 (6) The conditions in equation (6) indicate the appropriate lateral magnification of the intermediate lens group Lm. If the negative refractive power of the intermediate lens group Lm weakens so that βm exceeds the upper limit of equation (6), the amount of movement of the intermediate lens group Lm during focusing increases, and the overall optical length increases, which is undesirable. If the negative refractive power of the intermediate lens group Lm strengthens so that βm falls below the lower limit of equation (6), the aberration fluctuations during focusing increase, which is also undesirable.

[0036] Furthermore, it is more preferable to set the lower limit of equation (6) to 0.02, 0.03, or 0.04. Also, it is more preferable to set the upper limit of equation (6) to 0.95, 0.9, or 0.85.

[0037] In each embodiment, the optical system preferably satisfies the following condition (7), where νdn is the average value of the Abbe numbers of all negative lenses included in the front group Lf.

[0038] 40 ≤ νdn ≤ 90 (7) The conditions in equation (7) indicate the appropriate Abbe number for all negative lenses in the front group Lf. If νdn exceeds the upper limit of equation (7), the refractive index of the usable glass material becomes lower, the radius of curvature of each negative lens becomes smaller, and it becomes difficult to correct coma and astigmatism, which is undesirable. If νdn falls below the lower limit of equation (7), the dispersion of chromatic aberration increases, and it becomes difficult to correct lateral chromatic aberration, which is also undesirable.

[0039] Furthermore, it is more preferable to set the lower limit of equation (7) to 42, 45, 48, or 50. Also, it is more preferable to set the upper limit of equation (7) to 88, 85, 82, or 80.

[0040] In each embodiment, the optical system preferably satisfies the following condition (8), where Rm1 is the radius of curvature of the lens surface closest to the object in the intermediate lens group Lm, and Rm2 is the radius of curvature of the lens surface closest to the image in the intermediate lens group Lm.

[0041] 0.5≦(Rm1+Rm2) / (Rm2-Rm1)≦30.0 (8) Equation (8) shows the appropriate shape factor for the intermediate lens group Lm. If the shape factor of the intermediate lens group Lm exceeds the upper limit of equation (8), the radii of curvature of the object-side lens surface and the image-side lens surface of the intermediate lens group Lm become closer together, and the negative refractive power weakens. Also, the amount of movement of the intermediate lens group Lm during focusing becomes too large, which is undesirable. If the shape factor of the intermediate lens group Lm falls below the lower limit of equation (8), the image-side lens surface of the intermediate lens group Lm becomes a concave surface with a small radius of curvature, and the fluctuation of spherical aberration during focusing becomes large, which is undesirable.

[0042] Furthermore, it is more preferable to set the lower limit of equation (8) to 0.6, 0.7, or 0.8. Also, it is more preferable to set the upper limit of equation (8) to 25.0, 20.0, 15.0, 10.0, or 8.0.

[0043] Furthermore, let Df be the distance along the optical axis between the image-side lens surface of the front lens group Lf and the object-side lens surface of the intermediate lens group Lm when in focus at infinity, and let Dm be the distance along the optical axis between the image-side lens surface of the intermediate lens group Lm and the object-side lens surface of the rear lens group Lr when in focus at infinity. In this case, it is desirable that the optical system of each embodiment satisfies the following condition (9).

[0044] 0.01 ≤ Dm / Df ≤ 1.00 (9) The conditions in equation (9) indicate an appropriate relationship between the intermediate lens group Lm and the front lens group Lf and the rear lens group Lr. If Dm / Df exceeds the upper limit of equation (9), the distance between the front lens group Lf and the intermediate lens group Lm becomes small, making it difficult to secure sufficient movement of the intermediate lens group Lm during focusing, which is undesirable. If Dm / Df falls below the lower limit of equation (9), the distance between the front lens group Lf and the intermediate lens group Lm becomes large, increasing the overall optical length, which is also undesirable.

[0045] Furthermore, it is more preferable to set the lower limit of equation (9) to 0.03, 0.05, 0.07, or 0.10. Also, it is more preferable to set the upper limit of equation (9) to 0.90, 0.80, 0.70, or 0.60.

[0046] The optical system of each embodiment preferably satisfies the following condition (10) when the focal length of the front group Lf is ff (ff < 0).

[0047] -2.00 ≤ f / ff ≤ -0.01 (10) Equation (10) shows the appropriate relationship between the focal length of the front group Lf and the focal length of the entire optical system. If the negative refractive power of the front group Lf weakens so that f / ff exceeds the upper limit of equation (10), pincushion distortion increases due to the retrofocus type power arrangement, making it difficult to achieve both field curvature and distortion, which is undesirable. If the negative refractive power of the front group Lf strengthens so that f / ff falls below the lower limit of equation (10), the optical system approaches a telecentric type on the image side, and the overall optical length increases, which is undesirable.

[0048] Furthermore, it is preferable to set the lower limit of equation (10) to -0.18, -1.50, or -1.20. Also, it is preferable to set the upper limit of equation (10) to -0.02, -0.03, or -0.04.

[0049] The optical system of each embodiment preferably satisfies the following condition (11) when the focal length of the rear group Lr is fr (fr>0).

[0050] 0.1 ≤ fr / f ≤ 6.0 (11) The condition in equation (11) specifies the ratio of the focal length of the rear group Lr to the focal length of the entire optical system. If the refractive power of the rear group Lr is weak enough that fr / f exceeds the upper limit of equation (11), it is undesirable because it becomes difficult to correct pincushion distortion and suppress the angle of incidence on the image plane. If the refractive power of the rear group Lr is strong enough that fr / f falls below the lower limit of equation (11), it is undesirable because the optical system approaches a telecentric design on the image side, and the overall optical length increases.

[0051] Furthermore, it is more preferable to set the lower limit of equation (11) to 0.3, 0.5, 0.8, or 1.0. Also, it is more preferable to set the upper limit of equation (11) to 5.7, 5.5, 5.3, 5.0, or 4.7.

[0052] In each embodiment, the optical system preferably satisfies the following condition (12), where Fn is the minimum F-number when in focus at infinity.

[0053] 0.9 ≤ Fn ≤ 5.6 (12) The conditions in equation (12) indicate the appropriate minimum F-number for the optical system. If Fn falls outside the range of equation (12), it is undesirable because it is not possible to ensure adequate brightness for the optical system.

[0054] Furthermore, it is more preferable to set the lower limit of equation (12) to 1.0, 1.1, or 1.2. Also, it is more preferable to set the upper limit of equation (12) to 5.0, 4.5, 4.0, 3.5, or 3.2.

[0055] The optical system of each embodiment preferably satisfies at least one of the following configurations.

[0056] In order to approximate the power configuration of a retrofocus type optical system in each embodiment, it is preferable to place the first lens group L1 with negative refractive power closest to the object. In this case, in order to suppress the enlargement of the focusing mechanism, it is desirable to fix (immobilize) the first lens group L1 relative to the image plane during focusing.

[0057] In order to approximate the power configuration of a retrofocus type optical system in each embodiment, it is preferable to place the lens with positive refractive power closest to the image.

[0058] In order to reduce the size and weight of the intermediate lens group Lm, which serves as the focusing lens group, it is preferable that the optical system of each embodiment is composed of a single negative lens.

[0059] The optical systems of Examples 1 to 21 will be described in detail below.

[0060] In the optical systems of Examples 1 to 4 shown in Figures 1, 3, 5, and 7, the front lens group Lf (first lens group L1) is composed of a first negative lens Ln1, a negative lens, and a cemented lens of a second negative lens L2 and a positive lens Lp, arranged in order from the object side. The intermediate lens group Lm (second lens group L2) is composed of one negative lens. The rear lens group Lr is composed of one third lens group L3, which has a positive lens on the image side.

[0061] In the optical systems of Examples 5-11 shown in Figures 9, 11, 13, 15, 17, 19, and 21, Examples 13-16 shown in Figures 25, 27, 29, and 31, and Examples 19 and 20 shown in Figures 37 and 39, the front group Lf (first lens group L1) is composed of a first negative lens Ln1, a negative lens, a second negative lens L2, and a positive lens Lp, arranged in order from the object side. The intermediate lens group Lm (second lens group L2) is composed of one negative lens. The rear group Lr is composed of one third lens group L3, which has a positive lens on the image side.

[0062] In the optical system of Embodiment 12 shown in Figure 23, the front group Lf (first lens group L1) consists of a first negative lens Ln1, a negative lens, a negative lens, a positive lens Lp, and a second negative lens L2, arranged in order from the object side. The intermediate lens group Lm (second lens group L2) consists of one negative lens. The rear group Lr consists of one third lens group L3, with a positive lens on the image side.

[0063] In the optical system of Embodiment 17 shown in Figure 33, the front group Lf (first lens group L1) consists of a first negative lens Ln1, a negative lens, a second negative lens L2, and a positive lens Lp, arranged in order from the object side. The intermediate lens group Lm (second lens group L2) consists of one negative lens. The rear group Lr consists of a third lens group L3, a fourth lens group L4, and a fifth lens group L5, with the positive lens closest to the image. The fourth lens group L4 moves towards the object side when focusing from infinity to near.

[0064] In the optical system of Embodiment 18 shown in Figure 35, the front group Lf is composed of a first lens group L1 consisting of a first negative lens Ln1, a second lens group L2 consisting of a negative lens, and a third lens group L3 consisting of the second negative lens L2 and a positive lens Lp, arranged in order from the object side. The second lens group L2 moves towards the object side when focusing from infinity to near. The intermediate lens group Lm (fourth lens group L2) is composed of one negative lens. The rear group Lr is composed of one fifth lens group L5, which has a positive lens on the image side.

[0065] In the optical system of Embodiment 21 shown in Figure 41, the front group Lf (first lens group L1) consists of a first negative lens Ln1, a negative lens, a second negative lens L2, and a positive lens Lp, arranged in order from the object side. The intermediate lens group Lm (second lens group L2) consists of a cemented lens of a negative lens and a positive lens. The rear group Lr consists of one third lens group L3, with the positive lens closest to the image.

[0066] The following shows numerical examples 1 to 21 corresponding to each of Examples 1 to 21. In the surface data of each numerical example, surface number i indicates the order of the optical surfaces counted from the object side. r is the radius of curvature of the i-th surface (mm), and d is the lens thickness or air gap on the optical axis between the i-th surface and the (i+1)-th surface (mm). Also, nd is the refractive index of the optical element at the d-line between the i-th surface and the (i+1)-th surface, and νd is the Abbe number of the optical element 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 Fraunhofer lines d-line (587.56 nm), F-line (486.13 nm), and C-line (656.27 nm) are Nd, NF, and NC, respectively. νd = (Nd-1) / (NF-NC) It is expressed as follows: The effective diameter is the diameter (mm) of the region on the i-th lens surface through which the light rays contributing to image formation pass.

[0067] Note that the focal length (mm), F-number, and half-angle of view (°) are all values ​​for the optical system in the infinity focus state for each example. The half-angle of view is the maximum half-angle of view of the optical system. The total lens length is the optical total length TTL (mm) mentioned above, and BF is the back focus (mm) mentioned above.

[0068] 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 direction of the optical axis, 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 A14 are the aspherical coefficients. The cone constant and aspherical coefficients "e±x" are multiplied by 10. ±x It means...

[0069]

number

[0070] It is expressed by the formula shown. * indicates a surface with an aspherical shape. "ex" is 10 -x It means that.

[0071] [Numerical Example 1] Unit: mm Surface data Face number rd nd νd Effective diameter 1 65.261 1.80 1.72916 54.7 49.89 2 22.391 3.55 37.56 3* 22.501 2.00 1.53110 55.9 36.80 4* 10.890 13.42 29.87 5 -53.904 1.30 1.49700 81.7 29.50 6 31.665 7.26 2.00100 29.1 28.06 7 -170.929 (variable) 26.65 8 -27.852 0.95 1.59551 39.2 19.62 9 -150.734 (variable) 18.96 10 139.988 4.24 1.85150 40.8 18.12 11 -65.064 8.86 18.24 12 (aperture) ∞ 2.50 19.44 13 18.966 5.08 1.49700 81.7 20.12 14 302.519 0.20 19.37 15 36.344 2.38 1.90043 37.4 18.79 16 253.349 1.68 18.14 17 -249.226 1.00 1.72342 38.0 16.87 18 10.762 11.88 1.59282 68.6 15.28 19 -14.861 1.00 1.92286 20.9 17.56 20 -55.116 2.99 19.24 21* -40.771 1.70 1.53110 55.9 20.52 22* -192.389 5.14 23.82 23 373.650 8.30 1.94594 18.0 33.95 24 -32.440 35.68 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4=-6.63796e-06 A 6=-6.70307e-08 A 8= 1.62682e-10 A10 = -2.22192e-13 Side 4 K =-1.26367e+00 A 4= 5.39505e-05 A 6=-1.58869e-07 A 8= 3.69399e-10 A10 = -4.45172e-13 Page 21 K = 0.00000e+00 A 4=-9.21608e-05 A 6= 2.28848e-07 A 8=-7.30417e-10 Page 22 K = 0.00000e+00 A 4=-1.90938e-05 A 6= 3.36972e-07 A 8=-8.12350e-10 Various data Focal length 14.42 F-number 1.85 Half-angle (°): 56.32 Image height 21.64 Lens length: 108.50 BF 12.62 Object distance / magnification infinite 0.14x d 7 7.67 4.37 d 9 1.00 4.29 Entrance pupil position 18.88 Exit pupil position -149.28 Front principal point position 32.02 Back principal point position -1.80 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -41.18 29.32 -4.78 -36.15 2 8 -57.54 0.95 -0.14 -0.73 3 10 34.79 56.93 38.91 -52.31 [Numerical Example 2] Unit: mm Surface data Face number rd nd νd Effective diameter 1 47.171 1.87 1.80400 46.5 46.08 2 22.711 2.31 36.70 3* 24.162 2.02 1.53110 55.9 35.89 4* 12.024 12.89 29.05 5 -55.245 1.30 1.49700 81.7 28.59 6 30.384 4.93 2.00100 29.1 26.66 7 -575.600 (Variable) 25.86 8 -32.636 0.97 1.60342 38.0 16.39 9 -99.430 (variable) 16.94 10 -237.710 1.52 1.80400 46.5 18.31 11 -66.734 4.42 18.59 12 (aperture) ∞ 2.44 19.92 13 19.221 5.76 1.49700 81.7 21.41 14 480.236 3.21 20.70 15 27.344 2.83 1.91082 35.3 18.86 16 177.325 2.22 18.10 17 -101.556 1.00 1.72047 34.7 16.40 18 13.782 10.26 1.59282 68.6 17.00 19 -12.917 1.00 1.92286 20.9 17.08 20 -64.308 1.37 19.13 21* -55.861 1.92 1.53110 55.9 19.45 22* -1766.888 4.62 22.85 23 163.791 7.11 1.94594 18.0 33.28 24 -37.534 34.54 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 3.21743e-06 A 6=-6.08657e-08 A 8= 2.18972e-10 A10 = -1.82457e-13 A 3= 2.70657e-04 A 5=-7.24404e-07 A 7=-9.38783e-10 Side 4 K =-1.35961e+00 A 4= 4.88728e-05 A 6=-2.44638e-07 A 8= 4.21747e-10 A10 = 2.57357e-13 A 3= 3.28781e-04 A 5= 1.88670e-06 A 7=-3.21714e-09 Page 21 K = 2.02073e+01 A 4=-2.05627e-04 A 6= 9.51957e-07 A 8= 1.59827e-09 A 3= 6.16949e-04 A 5= 2.29044e-06 A 7=-6.20542e-08 Page 22 K =-3.30434e+07 A 4=-9.21712e-05 A 6= 1.17033e-06 A 8=-4.97083e-10 A 3= 4.50423e-04 A 5=-3.81127e-06 A 7=-3.26512e-08 Various data Focal length 15.97 F-number 1.85 Half-angle (°): 53.56 Image height 21.64 Lens length: 103.50 BF 14.90 Object distance / magnification infinite 0.14x d 7 9.65 4.03 d 9 3.00 8.62 Entrance pupil position 19.31 Exit pupil position -100.70 Front principal point position 33.08 Back principal point position -1.08 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -40.22 25.33 -1.67 -26.15 2 8 -80.95 0.97 -0.30 -0.91 3 10 29.84 49.66 25.64 -37.89 [Numerical Example 3] Unit: mm Surface data Face number rd nd νd Effective diameter 1 54.263 1.80 1.71038 29.4 40.25 2 18.693 1.72 30.92 3* 18.123 1.99 1.53110 55.9 30.35 4* 12.853 10.76 27.04 5 -36.937 1.30 1.49700 81.7 26.58 6 32.558 5.05 2.01394 26.4 25.27 7 -133.408 (variable) 24.57 8 -21.968 0.94 1.59500 44.8 17.96 9 -68.163 (variable) 18.98 10 -145.204 2.39 1.65685 60.8 20.35 11 -35.095 2.99 20.82 12 (aperture) ∞ 1.99 21.98 13 18.463 7.07 1.49700 81.7 23.57 14 -139.008 0.20 22.70 15 43.437 2.81 2.00427 29.4 21.38 16 -838.306 1.19 20.56 17 -70.276 1.00 1.68831 31.0 19.77 18 14.014 6.00 1.63980 62.6 17.15 19 1299.454 1.30 15.48 20 -75.836 5.09 1.49503 83.2 15.82 21 -12.046 0.90 1.79356 25.7 16.56 22 -73.430 1.97 18.59 23* -73.662 1.84 1.53110 55.9 19.08 24* -10000.000 6.17 22.21 25 169.020 7.10 1.96302 24.1 35.04 26 -41.181 36.16 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4=-2.16302e-05 A 6= 4.33290e-08 A 8=-1.46860e-10 A10 = -1.04000e-13 Side 4 K =-4.09435e-01 A 4=-2.77194e-05 A 6= 1.77503e-10 A 8=-1.89719e-12 A10 = -1.57970e-12 Page 23 K = 0.00000e+00 A 4=-2.13465e-04 A 6= 8.40013e-07 A 8=-3.02689e-09 Page 24 K = 0.00000e+00 A 4=-1.27749e-04 A 6= 9.14292e-07 A 8=-1.70037e-09 Various data Focal length 19.40 F-number 1.85 Half-angle (°): 48.12 Image height 21.64 Lens length 98.50 BF 14.16 Object distance / magnification infinite 0.17x d 7 8.67 4.68 d 9 2.09 6.08 Entrance pupil position 18.25 Exit pupil position -90.25 Front principal point position 34.05 Back principal point position -5.24 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -48.71 22.62 -4.12 -26.39 2 8 -54.90 0.94 -0.28 -0.88 3 10 29.29 50.02 22.37 -44.52 [Numerical Example 4] Unit: mm Surface data Face number rd nd νd Effective diameter 1 46.684 3.00 1.80400 46.5 52.01 2 19.961 2.63 36.81 3* 20.782 2.00 1.53110 55.9 36.23 4* 12.821 14.86 31.40 5 -43.288 2.50 1.49700 81.7 30.82 6 37.873 12.88 2.00100 29.1 28.56 7 -141.631 (variable) 24.65 8 -25.816 0.95 1.60342 38.0 16.54 9 -107.799 (variable) 17.23 10 -98.804 1.96 1.80400 46.5 18.63 11 -34.798 5.68 19.00 12 (aperture) ∞ 5.39 20.20 13 21.022 6.62 1.49700 81.7 21.64 14 -6056.893 1.21 20.64 15 34.604 2.48 1.91082 35.3 19.52 16 156.936 3.28 18.84 17 -220.642 1.09 1.72047 34.7 16.82 18 13.063 11.25 1.59282 68.6 17.00 19 -13.388 1.00 1.92286 20.9 18.00 20 -67.956 1.53 20.99 21* -47.879 1.80 1.53110 55.9 21.30 22* 520.414 3.82 24.87 23 191.839 7.72 1.94594 18.0 33.29 24 -33.171 34.67 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.07891e-05 A 6=-5.19000e-07 A 8=-2.06626e-10 A10 = -1.35290e-13 A 3= 9.93172e-05 A 5= 2.31635e-06 A 7= 2.10795e-08 Side 4 K =-6.68875e-01 A 4= 4.59686e-05 A 6=-3.16799e-07 A 8= 4.67231e-10 A10 = -1.99855e-13 A 3= 6.73852e-05 A 5= 4.47768e-07 A 7=-4.47987e-10 Page 21 K = 1.35267e+01 A 4=-8.36963e-05 A 6= 1.69232e-06 A 8= 3.61017e-09 A 3= 1.68754e-04 A 5=-5.57535e-06 A 7=-1.19124e-07 Page 22 K = 0.00000e+00 A 4=-5.67603e-05 A 6= 8.23422e-07 A 8= 3.56174e-10 A 3= 2.00189e-04 A 5=-8.06247e-07 A 7=-4.06312e-08 Various data Focal length 14.81 F-number 1.85 Half-angle (°): 55.61 Image height 21.64 Lens length: 119.57 BF 14.96 Object distance / magnification infinite 0.15x d 7 7.92 4.10 d 9 3.04 6.86 Entrance pupil position 21.34 Exit pupil position -143.80 Front principal point position 34.77 Back principal point position 0.15 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -48.98 37.87 -5.82 -44.06 2 8 -56.50 0.95 -0.19 -0.78 3 10 32.81 54.84 31.78 -45.46 [Numerical Example 5] Unit: mm Surface data Face number rd nd νd Effective diameter 1 88.400 3.00 1.80400 46.5 54.15 2 26.895 3.00 41.48 3* 23.707 2.00 1.53110 55.9 39.40 4* 15.490 17.03 35.17 5 -38.413 2.50 1.49700 81.7 32.51 6 53.172 0.72 31.10 7 60.005 10.00 2.00100 29.1 31.12 8 -92.813 (variable) 29.49 9 -27.561 0.95 1.60342 38.0 19.66 10 -74.649 (variable) 20.46 11 -205.316 2.29 1.80400 46.5 22.04 12 -44.952 6.80 22.39 13 (aperture) ∞ 10.45 23.51 14 25.048 8.52 1.49700 81.7 25.39 15 242.025 0.63 23.82 16 38.517 3.10 1.91082 35.3 23.00 17 178.012 3.16 22.16 18 -1152.030 1.00 1.72047 34.7 21.86 19 13.310 16.78 1.59282 68.6 21.54 20 -15.376 1.00 1.92286 20.9 22.66 21 -170.190 2.42 25.31 22* -55.429 1.97 1.53110 55.9 25.63 23* 905.010 2.59 29.65 24 206.295 8.59 1.94594 18.0 35.60 25 -33.034 37.00 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.32628e-05 A 6=-4.47249e-07 A 8=-1.65015e-10 A10 = -8.58865e-14 A 3=-1.25279e-04 A 5= 2.68420e-06 A 7= 1.74739e-08 Side 4 K =-8.20898e-01 A 4= 3.42198e-05 A 6=-2.26513e-07 A 8= 5.67319e-10 A10 = -3.78508e-13 A 3=-1.72751e-04 A 5= 7.38748e-07 A 7=-2.52753e-09 Page 22 K = 1.26592e+01 A 4=-6.61153e-05 A 6= 1.67440e-06 A 8= 3.12852e-09 A 3= 9.52868e-05 A 5=-6.43242e-06 A 7=-1.13413e-07 Page 23 K = 0.00000e+00 A 4=-5.23370e-05 A 6= 7.79126e-07 A 8= 6.72532e-10 A 3= 1.31902e-04 A 5=-1.07771e-06 A 7=-4.31786e-08 Various data Focal length 16.93 F-number 1.85 Half-angle (°): 51.95 Image height 21.64 Lens length: 140.63 BF 17.66 Object distance / magnification infinite 0.22x d 8 11.48 4.65 d10 3.00 9.83 Entrance pupil position 23.18 Exit pupil position -344.14 Front principal point position 39.32 Back principal point position 0.73 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -52.01 38.24 -6.78 -48.71 2 9 -72.96 0.95 -0.35 -0.95 3 11 42.32 69.30 45.54 -59.56 [Numerical Example 6] Unit: mm Surface data Face number rd nd νd Effective diameter 1 42.159 1.80 1.80400 46.5 34.30 2 15.635 1.00 25.62 3* 15.795 2.00 1.53110 55.9 24.92 4* 10.401 7.84 21.35 5 -72.201 1.30 1.49700 81.7 20.75 6 30.766 0.20 18.79 7 30.369 2.96 2.00100 29.1 18.69 8 -2381.368 (variable) 17.84 9 -21.774 0.94 1.60342 38.0 12.13 10 -104.815 (variable) 12.73 11 174.598 1.84 1.80400 46.5 14.51 12 -47.339 2.80 14.78 13 (aperture) ∞ 1.90 15.45 14 17.388 4.31 1.49700 81.7 16.21 15 -314.744 0.20 15.73 16 31.502 2.10 1.91082 35.3 15.29 17 200.667 2.65 14.74 18 -136.250 1.00 1.72047 34.7 12.91 19 12.058 8.25 1.59282 68.6 12.22 20 -14.819 1.00 1.92286 20.9 14.55 21 -59.061 1.05 15.96 22* -89.100 1.80 1.53110 55.9 16.31 23* -174.036 2.67 18.92 24 147.125 3.69 1.94594 18.0 25.10 25 -62.964 26.17 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.99333e-05 A 6=-3.32477e-07 A 8= 3.13155e-10 A10 = -1.04099e-12 A 3= 7.75721e-06 A 5= 1.94024e-06 A 7=-1.78117e-10 Side 4 K =-4.78636e-01 A 4= 9.03911e-05 A 6= 4.94061e-07 A 8= 4.94492e-09 A10 = -1.35561e-11 A 3=-2.04635e-04 A 5=-4.78336e-06 A 7=-9.95991e-08 Page 22 K = 7.31323e+01 A 4=-1.81316e-04 A 6=-6.52451e-07 A 8=-7.59521e-09 A 3= 9.94772e-05 A 5= 2.70934e-06 A 7= 9.71306e-08 Page 23 K = 0.00000e+00 A 4=-1.13344e-04 A 6=-1.10833e-06 A 8=-3.43599e-09 A 3= 2.71180e-04 A 5= 8.99932e-06 A 7= 1.29577e-07 Various data Focal length 14.38 F-number 2.00 Half-angle (°): 56.39 Image height 21.64 Lens length: 75.72 BF 14.00 Object distance / magnification infinite 0.11x d 8 5.45 3.39 d10 2.99 5.05 Entrance pupil position 14.24 Exit pupil position -33.23 Front principal point position 24.24 Back principal point position -0.38 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -30.28 17.09 -0.13 -15.40 2 9 -45.74 0.94 -0.16 -0.75 3 11 19.04 35.25 10.17 -24.17 [Numerical Example 7] Unit: mm Surface data Face number rd nd νd Effective diameter 1 58.200 3.00 1.80400 46.5 48.66 2 22.035 7.09 36.10 3* 19.082 2.00 1.53110 55.9 30.80 4* 11.538 10.41 25.97 5 -49.619 2.50 1.49700 81.7 25.44 6 26.802 0.33 23.00 7 28.030 10.00 2.00100 29.1 22.98 8 -685.279 (variable) 19.40 9 -28.932 0.95 1.60342 38.0 16.67 10 -84.768 (variable) 17.29 11 642.558 1.87 1.80400 46.5 18.86 12 -67.606 2.84 19.12 13 (aperture) ∞ 4.29 19.77 14 19.125 5.84 1.49700 81.7 21.16 15 -245.150 0.48 20.41 16 31.844 2.50 1.91082 35.3 19.28 17 107.732 2.62 18.48 18 -94.741 1.00 1.72047 34.7 16.63 19 11.237 10.59 1.59282 68.6 14.78 20 -16.726 1.00 1.92286 20.9 17.18 21 -90.402 1.41 18.80 22* -157.835 2.29 1.53110 55.9 19.15 23* 179.479 4.13 22.67 24 233.929 6.10 1.94594 18.0 30.88 25 -37.236 32.07 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.67464e-05 A 6=-4.07892e-07 A 8= 1.25135e-10 A10 = -6.96454e-13 A 3=-2.30024e-04 A 5= 1.76413e-06 A 7= 1.44210e-08 Side 4 K =-5.19129e-01 A 4= 2.58673e-05 A 6=-8.12220e-08 A 8= 2.75080e-09 A10 = -3.84135e-12 A 3=-2.77971e-04 A 5= 1.10993e-07 A 7=-3.68275e-08 Page 22 K = 1.72765e+02 A 4=-1.72314e-04 A 6=-1.55352e-06 A 8=-5.72938e-09 A 3= 1.08937e-04 A 5= 8.23248e-06 A 7= 1.53959e-07 Page 23 K = 0.00000e+00 A 4=-1.14703e-04 A 6=-1.14958e-06 A 8=-3.83109e-09 A 3= 1.65854e-04 A 5= 8.20399e-06 A 7= 1.21240e-07 Various data Focal length 15.26 F-number 1.85 Half-angle (°): 54.80 Image height 21.64 Lens length: 110.14 BF 16.17 Object distance / magnification infinite 0.15x d 8 7.72 3.11 d10 3.00 7.62 Entrance pupil position 21.18 Exit pupil position -85.75 Front principal point position 34.16 Back principal point position 0.91 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -39.38 35.33 -0.21 -32.28 2 9 -73.26 0.95 -0.31 -0.91 3 11 28.64 46.97 22.24 -35.54 [Numerical Example 8] Unit: mm Surface data Face number rd nd νd Effective diameter 1 58.985 3.00 1.80400 46.5 48.86 2 22.105 6.51 36.22 3* 19.518 2.00 1.53110 55.9 31.67 4* 11.702 10.73 26.75 5 -50.694 2.50 1.49700 81.7 26.16 6 26.876 0.38 23.74 7 28.546 10.00 2.00100 29.1 23.74 8 -1356.889 (variable) 20.29 9 -30.208 0.95 1.59069 39.7 17.02 10 -69.774 (variable) 17.60 11 533.211 1.84 1.78921 47.5 19.12 12 -73.851 2.80 19.36 13 (aperture) ∞ 4.34 19.96 14 19.231 5.81 1.49700 81.7 21.28 15 -243.365 0.66 20.53 16 32.355 2.40 1.91082 35.3 19.29 17 105.214 2.67 18.52 18 -94.624 1.05 1.72047 34.7 16.64 19 11.292 10.61 1.59282 68.6 14.79 20 -16.613 1.01 1.92286 20.9 17.19 21 -99.294 1.70 18.85 22* -176.279 2.24 1.53110 55.9 19.42 23* 140.809 3.64 23.05 24 223.926 6.27 1.94594 18.0 30.72 25 -35.868 31.96 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.43844e-05 A 6=-4.10784e-07 A 8= 9.02357e-11 A10 = -6.59274e-13 A 3=-2.17200e-04 A 5= 1.78119e-06 A 7= 1.46834e-08 The 4th surface K = -5.26042e-01 A4 = 2.12966e-05 A6 = -1.21820e-07 A8 = 2.59322e-09 A10 = -3.86620e-12 A3 = -2.58486e-04 A5 = 3.78322e-07 A7 = -3.36819e-08 The 22nd surface K = 1.26329e+02 A4 = -​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​1 1 -36.84 35.11 0.64 -30.49 2 9 -91.00 0.95 -0.46 -1.06 3 11 29.36 47.03 22.79 -35.11 [Numerical Example 9] Unit: mm Surface data Surface number r d nd νd Effective diameter 1 61.672 3.00 1.80400 46.5 48.73 2 21.951 5.87 [No value for 35.96 in the original, so it's hard to translate accurately without more context] 3* 19.773 2.00 1.53110 55.9 32.20 4* 11.901 10.75 [No value for 27.39 in the original, so it's hard to translate accurately without more context] 5 -53.528 2.49 1.49700 81.7 26.91 6 27.475 0.39 [No value for 24.56 in the original, so it's hard to translate accurately without more context] 7 29.238 9.96 2.00100 29.1 24.55 8 -1532.768 (Variable) 21.25 9 -31.485 0.95 1.57229 42.3 17.23 10 -67.450 (Variable) 17.77 11 286.741 1.81 1.79104 46.9 19.27 12 -89.606 2.86 [No value for 19.48 in the original, so it's hard to translate accurately without more context] 13 (Aperture) ∞ 4.67 20.04 14 19.264 5.87 1.49700 81.7 21.35 15 -220.405 0.64 20.58 16 33.154 2.39 1.91082 35.3 19.32 17 111.065 2.59 [No value for 18.55 in the original, so it's hard to translate accurately without more context] 18 -90.861 1.00 1.72047 34.7 16.73 19 11.295 10.91 1.59282 68.6 14.88 Some values in the original text seem incomplete or lack clear context for accurate translation. I've done my best to translate what's available while highlighting those areas.20 -16.629 1.00 1.92286 20.9 17.32 21 -113.531 1.77 19.01 22* -201.522 2.25 1.53110 55.9 19.58 23* 123.132 3.31 23.33 24 282.336 6.36 1.94594 18.0 30.41 25 -33.703 31.72 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.36342e-05 A 6=-4.03371e-07 A 8= 6.60751e-11 A10 = -6.20778e-13 A 3=-2.12379e-04 A 5= 1.74485e-06 A 7= 1.46651e-08 Side 4 K =-5.27201e-01 A 4= 1.65573e-05 A 6=-1.27547e-07 A 8= 2.55518e-09 A10 = -3.80300e-12 A 3=-2.40726e-04 A 5= 5.93738e-07 A 7=-3.32344e-08 Page 22 K = 7.14403e+01 A 4=-1.83493e-04 A 6=-1.61211e-06 A 8=-5.55301e-09 A 3= 1.18637e-04 A 5= 9.07414e-06 A 7= 1.53931e-07 Page 23 K = 0.00000e+00 A 4=-1.16886e-04 A 6=-1.09627e-06 A 8=-3.75357e-09 A 3= 1.56895e-04 A 5= 7.96569e-06 A 7= 1.18250e-07 Various data Focal length 15.10 F number 1.85 Half angle of view (°) 55.09 Image height 21.64 Overall length of lens 112.66 BF 16.66 Object distance / Magnification Infinity 0.15x d 8 10.16 3.31 d10 3.00 9.85 Entrance pupil position 20.91 Exit pupil position -92.04 Front principal point position 33.91 Rear principal point position 1.56 Lens group data Group Starting surface Focal length Lens configuration length Front principal point position Rear principal point position 1 1 -36.24 34.45 0.43 -29.97 2 9 -104.18 0.95 -0.53 -1.14 3 11 30.01 47.44 23.66 -34.95 [Numerical example 10] Unit mm Surface data Surface number r d nd νd Effective diameter 1 47.492 3.00 1.80400 46.5 44.26 2 22.595 1.27 34.77 3* 20.062 2.00 1.53110 55.9 33.76 4* 12.872 11.95 28.89 5 -58.581 2.50 1.49700 81.7 27.53 6 28.186 0.20 24.53 7 26.633 4.92 2.00100 29.1 24.46 8 856.976 (Variable) 23.26 9 -23.106 0.95 1.64966 45.9 16.64 10 -332.239 (variable) 17.57 11 308.164 7.64 1.90262 35.5 19.61 12 -65.195 2.80 21.48 13 (aperture) ∞ 2.08 22.36 14 20.008 6.87 1.49700 81.7 23.80 15 -143.353 0.20 23.00 16 32.560 2.84 1.91082 35.3 21.53 17 108.185 2.29 20.57 18 -89.774 1.00 1.72047 34.7 19.12 19 11.013 10.56 1.59282 68.6 16.56 20 -17.768 1.00 1.92286 20.9 17.24 21 -77.157 1.12 18.74 22* -213.253 2.32 1.53110 55.9 19.08 23* 140.895 5.54 22.05 24 -2063.405 8.16 1.94594 18.0 29.74 25 -36.449 32.36 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.06229e-05 A 6=-2.88298e-07 A 8= 1.56685e-10 A10 = -5.41246e-13 A 3=-2.19267e-04 A 5= 1.35733e-06 A 7= 8.95441e-09 Side 4 K =-5.63871e-01 A 4= 1.71401e-05 A 6=-5.46858e-08 A 8= 2.43602e-09 A10 = -3.00202e-12 A 3=-2.43953e-04 A 5= 1.01654e-06 A 7=-3.28305e-08 Page 22 K =-9.62006e+01 A 4=-1.66789e-04 A 6=-1.82043e-06 A 8=-5.76952e-09 A 3= 5.68993e-05 A 5= 1.00843e-05 A 7= 1.65815e-07 Page 23 K = 0.00000e+00 A 4=-1.08167e-04 A 6=-1.18554e-06 A 8=-3.92314e-09 A 3= 7.57089e-05 A 5= 7.57119e-06 A 7= 1.19903e-07 Various data Focal length 19.12 F-number 1.85 Half-angle (°): 48.53 Image height 21.64 Lens length: 111.78 BF 19.73 Object distance / magnification infinite 0.18x d 8 7.87 4.72 d10 3.00 6.15 Entrance pupil position 21.61 Exit pupil position -81.11 Front principal point position 37.10 Back principal point position 0.61 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -62.43 25.83 -5.03 -30.29 2 9 -38.27 0.95 -0.04 -0.62 3 11 29.03 54.40 23.82 -41.54 [Numerical Example 11] Unit: mm Surface data Face number rd nd νd Effective diameter 1 44.995 3.00 1.80400 46.5 45.27 2 23.479 2.33 36.20 3* 20.142 2.00 1.53110 55.9 33.97 4* 13.445 12.50 29.38 5 -55.555 2.50 1.49700 81.7 27.55 6 29.366 0.33 24.49 7 26.149 4.79 2.00100 29.1 24.34 8 720.040 (Variable) 23.18 9 -23.157 0.95 1.71974 40.9 17.07 10 576.649 (Variable) 18.07 11 332.960 7.34 1.95583 31.8 20.23 12 -61.680 2.80 22.16 13 (aperture) ∞ 1.94 23.15 14 20.499 7.32 1.49700 81.7 24.74 15 -112.567 0.20 23.92 16 32.928 2.81 1.91082 35.3 22.22 17 112.590 2.05 21.30 18 -82.502 1.00 1.72047 34.7 20.19 19 11.259 10.84 1.59282 68.6 17.38 20 -18.050 1.02 1.92286 20.9 17.74 21 -85.969 1.17 19.28 22* -286.544 2.37 1.53110 55.9 19.62 23* 139.178 5.63 22.56 24 -1443.348 7.30 1.94594 18.0 30.08 25 -36.947 32.19 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 9.54008e-06 A 6=-3.05259e-07 A 8= 8.91085e-11 A10 = -5.09648e-13 A 3=-1.67828e-04 A 5= 1.65643e-06 A 7= 1.01331e-08 Side 4 K =-5.99532e-01 A 4= 1.69383e-05 A 6=-6.86604e-08 A 8= 2.30816e-09 A10 = -2.98039e-12 A 3=-1.73229e-04 A 5= 1.60704e-06 A 7=-3.06031e-08 Page 22 K =-5.00447e+00 A 4=-1.59931e-04 A 6=-1.83007e-06 A 8=-5.70648e-09 A 3= 4.61818e-05 A 5= 1.02649e-05 A 7= 1.66893e-07 Page 23 K = 0.00000e+00 A 4=-1.07010e-04 A 6=-1.21177e-06 A 8=-3.89460e-09 A 3= 5.15450e-05 A 5= 7.61463e-06 A 7= 1.19823e-07 Various data Focal length 20.48 F-number 1.85 Half-angle (°): 46.56 Image height 21.64 Lens length: 114.78 BF 22.15 Object distance / magnification infinite 0.20x d 8 7.45 4.70 d10 3.00 5.75 Entrance pupil position 23.48 Exit pupil position -76.02 Front principal point position 39.69 Back principal point position 1.67 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -89.79 27.44 -10.89 -40.48 2 9 -30.91 0.95 0.02 -0.53 3 11 28.37 53.79 22.38 -41.52 [Numerical Example 12] Unit: mm Surface data Face number rd nd νd Effective diameter 1 31.684 1.80 1.80400 46.5 43.38 2 22.709 3.35 37.20 3* 21.068 2.85 1.53110 55.9 36.32 4* 14.860 6.87 30.32 5 118.519 1.30 1.49700 81.7 29.64 6 18.636 0.42 24.66 7 19.343 10.00 1.73700 28.0 24.55 8 -176.097 0.48 18.97 9 -84.073 1.54 2.00127 29.1 18.15 10 20.549 (variable) 15.46 11 -19.351 2.49 2.00104 29.1 15.46 12 -28.823 (variable) 17.66 13 117.449 3.04 1.92286 20.9 22.49 14 -53.903 2.80 22.96 15 (aperture) ∞ 2.47 24.17 16 22.148 8.71 1.49700 81.7 26.21 17 -91.591 0.87 25.19 18 34.952 2.77 1.91082 35.3 23.00 19 116.563 1.51 22.13 20 -125.869 1.00 1.72047 34.7 21.53 21 12.119 10.30 1.59282 68.6 18.57 22 -16.045 1.00 1.92286 20.9 17.23 23 -60.384 4.07 18.03 24* -698.577 1.80 1.53110 55.9 20.26 25* 308.374 8.20 22.00 26 307.006 4.37 1.94594 18.0 30.15 27 -54.651 30.82 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4=-3.51883e-05 A 6=-3.67603e-07 A 8=-1.87348e-10 A10 = -2.58894e-13 A 3=-2.59992e-04 A 5= 3.39735e-06 A 7= 1.77451e-08 Side 4 K =-3.00432e-01 A 4=-7.70077e-06 A 6= 2.44429e-08 A 8= 2.36989e-09 A10 = -2.82828e-12 A 3=-5.11273e-04 A 5=-1.23531e-07 A 7=-3.06036e-08 Page 24 K =-5.50254e+04 A 4=-1.11270e-04 A 6=-2.75785e-07 A 8=-2.76248e-09 A 3= 3.40562e-05 A 5=-3.88171e-08 A 7= 5.51799e-08 Page 25 K = 0.00000e+00 A 4=-1.01994e-04 A 6=-7.15544e-07 A 8=-2.56233e-09 A 3= 1.99517e-04 A 5= 4.83185e-06 A 7= 7.72270e-08 Various data Focal length 18.31 F-number 1.85 Half-angle (°): 49.76 Image height 21.64 Lens length: 115.97 BF 21.04 Object distance / magnification infinite 0.18x d10 7.93 4.61 d12 2.99 6.31 Entrance pupil position 25.45 Exit pupil position -91.01 Front principal point position 40.76 Back principal point position 2.73 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -15.39 28.60 17.28 -2.19 2 11 -67.74 2.49 -2.93 -4.37 3 13 27.85 52.91 21.11 -50.99 [Numerical Example 13] Unit: mm Surface data Face number rd nd νd Effective diameter 1 32.906 3.00 1.88595 38.1 36.64 2 17.053 3.32 27.94 3* 24.770 2.65 1.53110 55.9 27.15 4* 17.717 5.91 23.49 5 -82.887 1.30 1.49700 81.7 22.86 6 24.069 0.20 20.31 7 24.092 5.15 1.92180 24.0 20.23 8 30.297 (Variable) 17.46 9 -24.588 2.59 1.85165 40.8 17.70 10 -33.899 (variable) 19.58 11 73.817 2.88 1.84607 24.6 23.52 12 -101.430 2.80 23.79 13 (aperture) ∞ 4.80 24.49 14 21.327 7.64 1.49700 81.7 26.38 15 -169.796 1.56 25.40 16 33.567 2.76 1.72676 28.6 22.75 17 105.689 1.34 21.83 18 -213.570 1.00 1.72047 34.7 21.26 19 11.518 11.98 1.59282 68.6 18.21 20 -14.546 1.00 1.92286 20.9 16.98 21 -215.737 1.07 18.77 22* -279.101 1.80 1.53110 55.9 19.15 23* -329.583 4.08 20.88 24 -710.181 4.49 1.94594 18.0 26.13 25 -34.246 27.13 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 7.48183e-06 A 6=-4.21874e-07 A 8=-3.46329e-10 A10 = -3.43284e-13 A 3=-6.64607e-05 A 5= 3.05823e-06 A 7= 2.54093e-08 Side 4 K =-7.80427e-01 A 4= 4.24803e-05 A 6=-7.86338e-08 A 8= 2.42425e-09 A10 = -4.49468e-12 A 3=-1.77123e-04 A 5= 4.94981e-07 A 7=-1.61106e-08 Page 22 K =-1.65667e+02 A 4=-1.47486e-04 A 6=-1.68216e-06 A 8=-6.06118e-09 A 3= 1.87935e-04 A 5= 1.00354e-05 A 7= 1.72071e-07 Page 23 K = 0.00000e+00 A 4=-1.08788e-04 A 6=-1.27228e-06 A 8=-4.28618e-09 A 3= 2.26996e-04 A 5= 8.92501e-06 A 7= 1.27848e-07 Various data Focal length 17.46 F-number 1.85 Half-angle (°): 51.09 Image height 21.64 Lens length: 113.62 BF 26.25 Object distance / magnification infinite 0.18x d 8 11.06 4.47 d10 3.00 9.59 Entrance pupil position 19.70 Exit pupil position -73.42 Front principal point position 34.11 Back principal point position 8.78 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -17.76 21.53 9.40 -5.54 2 9 -120.51 2.59 -4.23 -5.83 3 11 29.43 49.20 20.45 -39.36 [Numerical Example 14] Unit: mm Surface data Face number rd nd νd Effective diameter 1 63.995 2.05 1.80400 46.5 49.25 2 22.950 8.18 37.60 3* 19.505 2.00 1.53110 55.9 32.04 4* 11.845 11.90 27.44 5 -59.796 2.50 1.49700 81.7 25.78 6 27.084 0.32 23.50 7 28.246 7.50 2.00100 29.1 23.48 8 -195.976 (variable) 21.28 9 -28.714 0.95 1.69821 29.7 16.63 10 -113.862 (variable) 17.22 11 484.877 3.67 1.82106 38.1 19.12 12 -69.917 2.80 19.74 13 (aperture) ∞ 4.58 20.31 14 19.324 5.96 1.49700 81.7 21.59 15 -220.037 0.54 20.79 16 32.344 2.44 1.91082 35.3 19.52 17 106.239 2.65 18.72 18 -94.598 1.00 1.72047 34.7 16.81 19 11.083 10.59 1.59282 68.6 14.85 20 -16.880 1.00 1.92286 20.9 17.14 21 -77.873 1.75 18.68 22* -159.413 2.13 1.53110 55.9 19.31 23* 103.675 4.99 22.83 24 376.377 6.39 1.94594 18.0 31.72 25 -35.425 32.97 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.47465e-05 A 6=-4.09601e-07 A 8= 9.47305e-11 A10 = -6.39666e-13 A 3=-2.30753e-04 A 5= 1.74126e-06 A 7= 1.45848e-08 Side 4 K =-5.22244e-01 A 4= 1.80497e-05 A 6=-1.22610e-07 A 8= 2.59466e-09 A10 = -3.87126e-12 A 3=-2.64519e-04 A 5= 2.58594e-07 A 7=-3.37604e-08 Page 22 K = 1.30148e+02 A 4=-1.77686e-04 A 6=-1.58990e-06 A 8=-5.72904e-09 A 3= 1.02393e-04 A 5= 8.53693e-06 A 7= 1.53883e-07 Page 23 K = 0.00000e+00 A 4=-1.15845e-04 A 6=-1.11441e-06 A 8=-3.80765e-09 A 3= 1.47371e-04 A 5= 7.95161e-06 A 7= 1.18414e-07 Various data Focal length 15.41 F-number 1.85 Half-angle (°): 54.53 Image height 21.64 Lens length: 112.16 BF 14.94 Object distance / magnification infinite 0.15x d 8 7.40 3.25 d10 3.93 8.08 Entrance pupil position 21.24 Exit pupil position -102.13 Front principal point position 34.63 Back principal point position -0.47 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -65.24 34.45 -12.95 -56.46 2 9 -55.25 0.95 -0.19 -0.75 3 11 30.29 50.49 25.40 -39.20 [Numerical Example 15] Unit: mm Surface data Face number rd nd νd Effective diameter 1 72.693 1.86 1.80400 46.5 51.24 2 24.217 10.56 39.29 3* 19.609 2.01 1.53110 55.9 31.99 4* 12.105 14.88 27.63 5 -62.649 2.50 1.49700 81.7 23.10 6 26.905 0.29 21.01 7 27.970 9.96 2.00100 29.1 20.98 8 -128.574 (variable) 17.44 9 -28.796 0.95 1.78963 27.5 17.46 10 -462.438 (variable) 18.11 11 353.074 2.08 1.89263 32.7 19.75 12 -63.391 2.80 20.02 13 (aperture) ∞ 5.76 20.59 14 19.348 6.19 1.49700 81.7 22.06 15 -178.411 0.20 21.23 16 32.541 2.49 1.91082 35.3 20.00 17 107.506 2.45 19.17 18 -91.892 1.00 1.72047 34.7 17.42 19 10.904 10.98 1.59282 68.6 15.24 20 -17.168 1.00 1.92286 20.9 17.45 21 -67.652 1.88 18.88 22* -186.893 2.36 1.53110 55.9 19.57 23* 84.125 5.87 23.22 24 1732.934 6.28 1.94594 18.0 32.25 25 -35.022 33.49 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.48996e-05 A 6=-3.98821e-07 A 8= 1.05859e-10 A10 = -6.60157e-13 A 3=-2.56711e-04 A 5= 1.61043e-06 A 7= 1.40911e-08 Side 4 K =-5.13331e-01 A 4= 1.58904e-05 A 6=-1.20252e-07 A 8= 2.60366e-09 A10 = -3.79474e-12 A 3=-2.88252e-04 A 5= 2.69752e-07 A 7=-3.42404e-08 Page 22 K = 7.70036e+01 A 4=-1.82183e-04 A 6=-1.61373e-06 A 8=-5.60261e-09 A 3= 9.27069e-05 A 5= 8.69396e-06 A 7= 1.53909e-07 Page 23 K = 0.00000e+00 A 4=-1.16419e-04 A 6=-1.11816e-06 A 8=-3.85116e-09 A 3= 1.32571e-04 A 5= 7.89814e-06 A 7= 1.18734e-07 Various data Focal length 15.26 F-number 1.85 Half-angle (°): 54.80 Image height 21.64 Lens length: 116.92 BF 14.15 Object distance / magnification infinite 0.15x d 8 5.42 2.56 d10 3.00 5.87 Entrance pupil position 22.00 Exit pupil position -122.68 Front principal point position 35.56 Back principal point position -1.11 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -168.18 42.06 -66.89 -176.78 2 9 -38.93 0.95 -0.04 -0.57 3 11 30.80 51.33 26.15 -44.61 [Numerical Example 16] Unit: mm Surface data Face number rd nd νd Effective diameter 1 74.630 1.92 1.80400 46.5 52.56 2 24.543 11.72 40.14 3* 19.634 2.00 1.53110 55.9 32.23 4* 12.164 15.65 27.95 5 -67.970 2.50 1.49700 81.7 22.91 6 27.011 0.27 20.87 7 27.870 9.50 2.00100 29.1 20.84 8 -123.341 (variable) 17.58 9 -28.726 0.95 1.80156 26.9 17.60 10 -730.560 (variable) 18.25 11 344.990 2.12 1.89063 32.0 19.87 12 -63.194 2.80 20.14 13 (aperture) ∞ 5.81 20.69 14 19.349 6.22 1.49700 81.7 22.11 15 -172.603 0.20 21.27 16 32.699 2.48 1.91082 35.3 20.01 17 107.893 2.41 19.18 18 -92.384 1.00 1.72047 34.7 17.45 19 10.875 10.94 1.59282 68.6 15.25 20 -17.209 1.00 1.92286 20.9 17.37 21 -70.324 1.91 18.80 22* -184.036 2.33 1.53110 55.9 19.51 23* 83.025 5.85 23.13 24 1929.722 6.27 1.94594 18.0 32.14 25 -34.895 33.38 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.46284e-05 A 6=-3.98528e-07 A 8= 1.05251e-10 A10 = -6.69790e-13 A 3=-2.62183e-04 A 5= 1.59814e-06 A 7= 1.41107e-08 Side 4 K =-5.11509e-01 A 4= 1.47710e-05 A 6=-1.20712e-07 A 8= 2.59890e-09 A10 = -3.79119e-12 A 3=-2.94375e-04 A 5= 2.79259e-07 A 7=-3.42577e-08 Page 22 K = 6.60852e+01 A 4=-1.83574e-04 A 6=-1.61713e-06 A 8=-5.53054e-09 A 3= 9.56867e-05 A 5= 8.84689e-06 A 7= 1.52888e-07 Page 23 K = 0.00000e+00 A 4=-1.16357e-04 A 6=-1.11713e-06 A 8=-3.86319e-09 A 3= 1.31844e-04 A 5= 7.90789e-06 A 7= 1.18787e-07 Various data Focal length 15.21 F-number 1.85 Half-angle (°): 54.89 Image height 21.64 Lens length: 118.38 BF 14.12 Object distance / magnification infinite 0.15x d 8 5.43 2.57 d10 3.00 5.86 Entrance pupil position 22.59 Exit pupil position -120.42 Front principal point position 36.08 Back principal point position -1.09 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -337.09 43.55 -155.70 -366.70 2 9 -37.33 0.95 -0.02 -0.55 3 11 30.84 51.33 26.00 -44.55 [Numerical Example 17] Unit: mm Surface data Face number rd nd νd Effective diameter 1 49.562 1.82 1.80400 46.5 47.19 2 22.849 5.46 37.43 3* 21.687 2.00 1.58313 59.4 34.52 4* 12.749 12.09 29.35 5 -57.580 2.50 1.43875 94.7 28.06 6 27.466 0.47 25.40 7 28.450 10.00 2.00100 29.1 25.37 8 778.383 (Variable) 21.67 9 -26.853 0.95 1.62590 55.2 17.17 10 -102.433 (variable) 17.88 11 278.646 3.89 1.82252 43.3 19.58 12 -96.831 2.80 20.29 13 (aperture) ∞ (variable) 21.08 14 20.536 6.34 1.49700 81.7 22.86 15 -136.243 0.33 22.17 16 32.456 2.61 1.91082 35.3 20.86 17 108.593 2.24 20.06 18 -101.010 1.00 1.72047 34.7 18.67 19 11.475 11.32 1.59282 68.6 16.42 20 -18.177 1.00 1.92286 20.9 18.38 21 -113.148 1.15 19.92 22* 801.314 2.32 1.53110 55.9 20.24 23* 91.304 (variable) 23.32 24 2295.372 6.12 1.94594 18.0 31.41 25 -34.271 32.58 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.08748e-05 A 6=-3.42276e-08 A 8= 1.50287e-10 A10 = -2.84548e-13 A 3=-2.41567e-04 A 5=-1.40410e-06 A 7= 5.28246e-10 Side 4 K =-6.12681e-01 A 4= 2.72151e-05 A 6= 5.16164e-08 A 8= 9.72809e-10 A10 = -1.18951e-12 A 3=-2.76213e-04 A 5=-1.94043e-06 A 7=-1.56769e-08 Page 22 K = 4.28682e+03 A 4=-1.44165e-04 A 6=-1.32874e-06 A 8=-4.07539e-09 A 3= 7.05410e-05 A 5= 6.89407e-06 A 7= 1.18829e-07 Page 23 K = 0.00000e+00 A 4=-8.95319e-05 A 6=-8.82445e-07 A 8=-2.62287e-09 A 3= 1.17923e-04 A 5= 5.51519e-06 A 7= 8.76857e-08 Various data Focal length 16.53 F-number 1.85 Half-angle (°): 52.63 Image height 21.64 Lens length: 118.10 BF 19.70 Object distance / magnification infinite 0.17x d 8 9.15 4.72 d10 3.00 7.43 d13 4.11 3.67 d23 5.72 6.17 Entrance pupil position 21.83 Exit pupil position -102.69 Front principal point position 36.12 Back principal point position 3.17 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -50.57 34.34 -4.33 -37.53 2 9 -58.43 0.95 -0.21 -0.80 3 11 87.78 6.69 1.59 -3.35 4 14 38.17 28.32 -11.73 -24.04 5 24 35.74 6.12 3.10 -0.05 [Numerical Example 18] Unit: mm Surface data Face number rd nd νd Effective diameter 1 63.477 3.00 1.70929 55.9 53.30 2 22.042 (variable) 38.18 3* 22.881 2.00 1.58313 59.4 36.64 4* 13.963 (variable) 31.88 5 -44.232 2.50 1.43875 94.7 29.30 6 28.484 0.83 26.22 7 31.162 10.00 2.00100 29.1 26.17 8 -552.191 (variable) 22.66 9 -29.356 2.95 1.64612 33.0 21.13 10 -186.815 (variable) 22.98 11 91.478 4.14 1.81335 47.8 25.52 12 -88.332 2.80 25.94 13 (aperture) ∞ 6.32 26.30 14* 21.664 7.73 1.49700 81.7 27.36 15* -213.273 0.20 26.20 16 30.234 2.66 1.91082 35.3 23.93 17 60.984 2.13 22.89 18 -120.198 1.00 1.72047 34.7 22.21 19 12.568 14.16 1.59282 68.6 18.95 20 -17.395 1.00 1.92286 20.9 20.91 21 -118.697 1.89 23.02 22* 84.122 2.38 1.53110 55.9 23.60 23* 57.483 2.62 27.77 24 618.342 7.64 1.94594 18.0 33.12 25 -30.590 34.56 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.48205e-05 A 6= 2.36798e-07 A 8= 5.14747e-10 A10 = -3.94700e-13 A 3=-1.75521e-04 A 5=-3.61806e-06 A 7=-1.40081e-08 Side 4 K =-7.97401e-01 A 4= 5.30744e-05 A 6= 4.65123e-07 A 8= 1.72823e-09 A10 = -1.64022e-12 A 3=-2.88569e-04 A 5=-5.96635e-06 A 7=-3.81462e-08 Side 14 K = 0.00000e+00 A 4= 1.16379e-07 A 6= 7.51008e-10 A 8= 3.70427e-11 Page 15 K = 0.00000e+00 A 4= 2.89557e-06 A 6= 5.43076e-09 A 8=-1.54892e-11 Page 22 K = 3.45493e+01 A 4=-1.30089e-04 A 6=-8.50172e-07 A 8=-2.98229e-09 A 3=-7.14251e-05 A 5= 1.67963e-07 A 7= 9.88303e-08 Page 23 K = 0.00000e+00 A 4=-9.72026e-05 A 6=-8.55559e-07 A 8=-3.23623e-09 A 3= 9.14608e-05 A 5= 2.72393e-06 A 7= 1.07493e-07 Various data Focal length 14.59 F-number 1.40 Half-angle (°): 56.00 Image height 21.64 Lens length: 121.56 BF 14.50 Object distance / magnification infinite 0.16x d 2 4.84 3.79 d 4 14.11 15.16 d 8 7.16 3.66 d10 3.00 6.50 Entrance pupil position 21.97 Exit pupil position -255.28 Front principal point position 35.77 Back principal point position -0.09 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -49.08 3.00 2.77 0.96 2 3 -66.96 2.00 3.53 2.15 3 5 104.36 13.33 7.27 -0.04 4 9 -54.30 2.95 -0.34 -2.14 5 11 34.04 56.67 34.65 -47.65 [Numerical Example 19] Unit: mm Surface data Face number rd nd νd Effective diameter 1 54.261 2.68 1.82048 43.1 47.71 2 22.213 4.57 36.39 3* 22.246 2.00 1.53514 48.1 34.91 4* 12.827 14.95 29.93 5 -68.928 2.50 1.51279 61.9 26.00 6 27.259 0.27 23.86 7 27.893 9.96 2.00100 29.1 23.86 8 -272.856 (variable) 20.54 9 -30.726 1.67 1.61925 47.8 17.40 10 -308.121 (variable) 18.22 11 292.789 2.94 1.90103 31.8 19.68 12 -97.585 3.35 20.12 13 (aperture) ∞ 4.32 20.84 14 19.691 6.50 1.49700 81.7 22.28 15 -110.967 0.38 21.46 16 31.664 2.35 1.91082 35.3 19.95 17 80.008 1.58 19.11 18 -109.727 1.40 1.72047 34.7 18.47 19 11.164 11.21 1.59282 68.6 16.02 20 -18.137 1.00 1.92286 20.9 18.02 21 -174.540 1.31 19.57 22* 294.582 1.83 1.53110 55.9 19.91 23* 98.133 5.65 22.51 24 -1057.283 5.88 1.94594 18.0 30.62 25 -33.034 31.82 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.08400e-05 A 6= 2.18344e-07 A 8= 4.39293e-10 A10 = -3.24547e-13 A 3=-2.86100e-04 A 5=-3.12404e-06 A 7=-1.34043e-08 Side 4 K =-6.57296e-01 A 4= 3.59457e-05 A 6= 4.93771e-07 A 8= 1.42747e-09 A10 = -1.17658e-12 A 3=-3.55444e-04 A 5=-5.47237e-06 A 7=-3.89629e-08 Page 22 K = 6.76629e+02 A 4=-1.51958e-04 A 6=-9.99970e-07 A 8=-3.67698e-09 A 3= 4.21031e-05 A 5= 4.03115e-06 A 7= 9.89842e-08 Page 23 K = 0.00000e+00 A 4=-9.93429e-05 A 6=-9.85332e-07 A 8=-3.11827e-09 A 3= 1.01109e-04 A 5= 5.11501e-06 A 7= 1.05269e-07 Various data Focal length 16.10 F-number 1.85 Half-angle (°): 53.34 Image height 21.64 Lens length: 117.46 BF 18.64 Object distance / magnification infinite 0.16x d 8 7.51 3.07 d10 3.00 7.43 Entrance pupil position 21.47 Exit pupil position -94.09 Front principal point position 35.27 Back principal point position 2.54 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -68.85 36.93 -14.58 -60.35 2 9 -55.24 1.67 -0.11 -1.15 3 11 30.72 49.71 25.06 -37.02 [Numerical Example 20] Unit: mm Surface data Face number rd nd νd Effective diameter 1 134.259 2.66 1.69169 57.0 75.16 2 33.812 1.03 55.39 3* 30.495 3.00 1.49475 82.8 54.74 4* 13.912 22.83 44.23 5 -58.478 1.52 1.43875 94.7 43.62 6 43.347 1.00 40.16 7 50.904 7.86 2.00100 29.1 40.16 8 -405.701 (variable) 38.75 9 -29.257 1.07 1.60342 38.0 27.87 10 -133.737 (variable) 27.47 11 -255.803 2.93 1.84845 40.2 26.54 12 -45.629 17.66 27.02 13 (aperture) ∞ 6.37 30.94 14* 24.762 9.53 1.49700 81.7 33.48 15* -174.088 0.20 32.40 16 43.703 2.87 2.00103 29.1 29.88 17 99.803 4.07 28.94 18 -261.548 1.00 1.72047 34.7 25.53 19 13.531 14.63 1.59282 68.6 21.54 20 -17.689 2.87 1.92286 20.9 22.11 21 -135.261 4.11 25.44 22* -58.211 1.80 1.53110 55.9 27.69 23* -52.296 1.70 30.11 24 192.856 8.10 1.94594 18.0 35.70 25 -35.367 36.85 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 1.00332e-05 A 6=-3.66730e-07 A 8=-2.09584e-10 A10 = 1.24792e-14 A 3=-5.70248e-05 A 5= 2.75890e-06 A 7= 1.45422e-08 Side 4 K =-7.05264e-01 A 4= 3.20232e-05 A 6=-6.31935e-08 A 8= 6.80113e-10 A10 = -3.45033e-13 A 3=-1.93535e-04 A 5= 8.94102e-08 A 7=-1.28612e-08 Side 14 K = 0.00000e+00 A 4=-6.81200e-07 A 6=-6.40685e-09 A 8= 7.27135e-12 Page 15 K = 0.00000e+00 A 4= 2.84618e-06 A 6=-6.94354e-09 A 8= 1.37661e-11 Page 22 K = 8.43642e+00 A 4=-4.15102e-05 A 6= 1.38203e-06 A 8= 2.00911e-09 A 3= 1.66027e-04 A 5=-6.30721e-06 A 7=-8.63597e-08 Page 23 K = 0.00000e+00 A 4=-3.86620e-05 A 6= 6.51115e-07 A 8= 5.70924e-10 A 3= 2.74896e-04 A 5=-7.69110e-07 A 7=-3.58567e-08 Various data Focal length 12.22 F-number 1.23 Half-angle (°): 60.54 Image height 21.64 Lens length: 149.65 BF 14.61 Object distance / magnification infinite 0.18x d 8 13.22 8.37 d10 3.00 7.85 Entrance pupil position 24.65 Exit pupil position 427.50 Front principal point position 37.24 Back principal point position 2.39 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -41.53 39.90 -2.15 -42.59 2 9 -62.30 1.07 -0.19 -0.86 3 11 55.88 77.84 88.26 -83.36 [Numerical Example 21] Unit: mm Surface data Face number rd nd νd Effective diameter 1 33.851 1.80 1.80400 46.5 36.93 2 20.532 2.02 30.59 3* 22.064 2.00 1.53110 55.9 29.51 4* 9.976 9.12 22.31 5 -60.282 1.30 1.49700 81.7 21.63 6 29.288 2.27 19.40 7 30.735 2.94 2.00100 29.1 18.38 8 -687.163 (variable) 17.55 9 -24.358 0.95 1.52382 76.7 11.37 10 200.000 1.17 1.52368 52.1 10.44 11 -183.913 (variable) 9.86 12 (aperture) ∞ 1.00 10.36 13 20.093 4.21 1.49700 81.7 10.88 14 -53.152 0.57 10.90 15 24.081 1.94 1.91082 35.3 10.76 16 1944.710 0.90 10.94 17 -88.604 4.07 1.72047 34.7 11.23 18 10.897 10.64 1.59282 68.6 13.08 19 -11.216 1.00 1.92286 20.9 15.54 20 -39.937 0.45 17.66 21* 136.406 1.80 1.53110 55.9 17.99 22* 43.529 3.86 21.05 23 133.165 5.23 1.94594 18.0 28.42 24 -43.871 29.50 Image plane ∞ Aspherical data 3rd page K = 0.00000e+00 A 4= 2.71549e-05 A 6=-7.22512e-08 A 8=-4.23607e-10 A10 = 3.63131e-13 A 3=-2.73761e-05 A 5=-2.04306e-06 A 7= 9.77488e-09 Side 4 K =-5.01063e-01 A 4=-2.04317e-05 A 6=-1.11307e-06 A 8=-8.64687e-10 A10 = -8.02651e-12 A 3= 1.37514e-04 A 5= 8.17815e-06 A 7= 5.38890e-08 Page 21 K = 1.34436e+02 A 4=-2.44939e-04 A 6=-1.28832e-06 A 8=-5.30929e-09 A 3= 5.47068e-05 A 5= 8.31877e-06 A 7= 1.13621e-07 Page 22 K = 0.00000e+00 A 4=-1.00039e-04 A 6= 4.73283e-07 A 8=-1.42888e-09 A 3=-3.12416e-05 A 5=-4.57653e-06 A 7= 2.77243e-08 Various data Focal length 15.06 F-number 3.00 Half-angle (°): 55.15 Image height 21.64 Lens length 83.50 BF 15.21 Object distance / magnification infinite 0.12x d 8 7.03 4.11 d11 2.00 4.92 Entrance pupil position 16.24 Exit pupil position -47.65 Front principal point position 27.70 Back principal point position 0.15 Lens group data Group starting plane Focal length Lens length Front principal point position Rear principal point position 1 1 -41.76 21.45 -3.49 -27.22 2 9 -53.84 2.12 -0.21 -1.61 3 12 21.45 35.68 11.05 -24.86 Figures 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, and 42 show the longitudinal aberrations (spherical aberration, astigmatism, distortion, and chromatic aberration) of the optical systems of numerical examples 1 to 21 at infinity focus. 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 at the sagittal image plane, and the dashed line M shows the astigmatism at 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 (°).

[0072] The values ​​of equations (1) to (12) for each numerical example are summarized in Table 1. The optical system for each numerical example satisfies all the conditions of equations (1) to (12).

[0073] [Table 1]

[0074] [Imaging device] Figure 43 shows a digital still camera used as an imaging device, employing the optical systems of each of the above embodiments as imaging optical systems.

[0075] 10 is the camera body, and 11 is the imaging optical system configured by any of the optical systems in Examples 1 to 21.

[0076] 12 is an image sensor (photoelectric conversion element) such as a CCD sensor or CMOS sensor that is built into the camera body 10 and captures the image of the subject (i.e., the subject through the imaging optical system 11) formed by the imaging optical system 11.

[0077] By using the optical systems of Examples 1 to 21 as the imaging optical system 11, a compact camera capable of high-speed focusing and high optical performance can be obtained.

[0078] The camera body 10 may be interchangeable-lens or fixed-lens, and may be a single-lens reflex type with a quick-return mirror, or a mirrorless type without a quick-return mirror.

[0079] The above embodiments include the following configuration.

[0080] (Composition 1) An optical system comprising a front group with negative refractive power containing at least one lens group, an intermediate lens group with negative refractive power, and a rear group with positive refractive power containing at least one lens group, arranged sequentially from the object side to the image side, wherein the spacing between adjacent lens groups changes during focusing, When focusing from infinity to near, the intermediate lens group moves toward the object. The aforementioned front group has at least two negative lenses and at least one positive lens, When the focal length of the optical system is f, the maximum half-angle of view of the optical system is ω, the length TTL is the distance along the optical axis from the lens surface closest to the object to the lens surface closest to the image to the optical system plus the air-equivalent distance along the optical axis from the lens surface closest to the image to the image plane, and the focal length of the intermediate lens group is fm, 1.0 ≤ TTL / (f × tanω) ≤ 9.0 0.5 ≤ -fm / f ≤ 9.0 An optical system characterized by satisfying the following conditions. (Configuration 2) The aforementioned front group has a first negative lens positioned closest to the object, When the radius of curvature of the object-side lens surface of the first negative lens is R11, and the radius of curvature of the image-side lens surface of the first negative lens group is R12, -1.0≦(R12-R11) / (R11+R12)<0.0 The optical system according to configuration 1, characterized by satisfying the following conditions. (Composition 3) The aforementioned front group has a second negative lens positioned closest to the image rather than the object, When the radius of curvature of the object-side lens surface of the second negative lens is R21, and the radius of curvature of the image-side lens surface of the second negative lens group is R22, -1.0≦(R21+R22) / (R22-R21)≦1.0 The optical system according to configuration 1 or 2, characterized by satisfying the following conditions. (Composition 4) When Rp1 is the radius of curvature of the object-side lens surface of the positive lens in the aforementioned front group, and Rp2 is the radius of curvature of the image-side lens surface of the positive lens, -1.0≦(Rp1+Rp2) / (Rp2-Rp1)≦30.0 An optical system according to any one of configurations 1 to 3, characterized by satisfying the following conditions. (Composition 5) When the lateral magnification of the aforementioned intermediate lens group is in focus on an object at infinity, let βm be the value of the intermediate lens group. 0.0 < βm ≤ 1.0 An optical system according to any one of configurations 1 to 4, characterized by satisfying the following conditions. (Composition 6) When νdn is the average value of the Abbe numbers with respect to the d line of all negative lenses included in the aforementioned group, 40 ≤ νdn ≤ 90 An optical system according to any one of configurations 1 to 5, characterized by satisfying the following conditions. (Composition 7) When Rm1 is the radius of curvature of the lens surface closest to the object in the intermediate lens group, and Rm2 is the radius of curvature of the lens surface closest to the image in the intermediate lens group, 0.5≦(Rm1+Rm2) / (Rm2-Rm1)≦30.0 An optical system according to any one of configurations 1 to 6, characterized by satisfying the following conditions. (Composition 8) When the distance on the optical axis between the image-side lens surface of the front lens group and the object-side lens surface of the intermediate lens group is in focus on an object at infinity, let Df be the distance on the optical axis between the image-side lens surface of the intermediate lens group and the object-side lens surface of the rear lens group is in focus on an object at infinity, 0.01 ≤ Dm / Df ≤ 1.00 An optical system according to any one of configurations 1 to 7, characterized by satisfying the following conditions. (Composition 9) When the focal length of the aforementioned front group is ff, -2.00 ≤ f / ff ≤ -0.01 An optical system according to any one of configurations 1 to 8, characterized by satisfying the following conditions. (Composition 10) When the focal length of the rear group is denoted as fr, 0.1 ≤ fr / f ≤ 6.0 An optical system according to any one of configurations 1 to 9, characterized by satisfying the following conditions. (Composition 11) When the minimum F-number of the optical system when it is in focus on an object at infinity is denoted as Fnо, 0.9 ≤ Fn ≤ 5.6 An optical system according to any one of configurations 1 to 10, characterized by satisfying the following conditions. (Composition 12) The optical system according to any one of configurations 1 to 11, characterized in that the front group has a first lens group with negative refractive power closest to the object, and the first lens group remains stationary during focusing. (Composition 13) The optical system according to any one of configurations 1 to 12, characterized in that the rear group has a lens with positive refractive power closest to the image. (Composition 14) The optical system according to any one of configurations 1 to 13, characterized in that the intermediate lens group is composed of one negative lens or one cemented lens consisting of a negative lens and a positive lens. (Composition 15) The optical system according to any one of configurations 1 to 14, characterized in that the front group is composed of one lens group consisting of a first negative lens, a negative lens, a second negative lens, and a positive lens arranged in order from the object side to the image side. (Composition 16) The optical system according to any one of configurations 1 to 14, characterized in that the front group is composed of one lens group consisting of a first negative lens, a negative lens, a negative lens, a positive lens, and a second negative lens, arranged in order from the object side to the image side. (Composition 17) The aforementioned front group is composed of a first lens group consisting of a first negative lens, a second lens group consisting of a negative lens, and a third lens group consisting of a second negative lens and a positive lens, arranged in order from the object side to the image side. The optical system according to any one of configurations 1 to 14, characterized in that the second lens group moves during focusing. (Composition 18) The system comprises a first lens group as the front group, a second lens group as the intermediate lens group, and a third, fourth, and fifth lens group constituting the rear group. The optical system according to any one of configurations 1 to 17, characterized in that the fourth lens group moves during focusing. (Composition 19) An optical system comprising a front group with negative refractive power containing at least one lens group, an intermediate lens group with negative refractive power, and a rear group with positive refractive power containing at least one lens group, arranged sequentially from the object side to the image side, wherein the spacing between adjacent lens groups changes during focusing, An optical system characterized in that the intermediate lens group moves toward the object when focusing from infinity to near. (Composition 20) The optical system described in any one of configurations 1 to 19, An imaging device characterized by having an image sensor that captures an image of a subject through the optical system.

[0081] 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]

[0082] Lf front group Lm Intermediate Lens Group Lr postgroup

Claims

1. An optical system comprising a front group with negative refractive power including at least one lens group, an intermediate lens group with negative refractive power, and a rear group with positive refractive power including at least one lens group, arranged sequentially from the object side to the image side, wherein the spacing between adjacent lens groups changes during focusing, When focusing from infinity to near, the intermediate lens group moves toward the object. The aforementioned front group has at least two negative lenses and at least one positive lens, When the focal length of the optical system is f, the maximum half-angle of view of the optical system is ω, TTL is the length obtained by adding the distance along the optical axis from the lens surface closest to the object to the lens surface closest to the image to the lens surface closest to the image to the air-equivalent distance along the optical axis from the lens surface closest to the image to the image plane, and the focal length of the intermediate lens group is fm, 1.0 ≤ TTL / (f × tanω) ≤ 9.0 0.5≦-fm / f≦9.0 An optical system characterized by satisfying the following conditions.

2. The aforementioned front group has a first negative lens positioned closest to the object, When the radius of curvature of the object-side lens surface of the first negative lens is R11, and the radius of curvature of the image-side lens surface of the first negative lens group is R12, -1.0≦(R12-R11) / (R11+R12)<0.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

3. The aforementioned front group has a second negative lens positioned closest to the image side rather than the object side. When the radius of curvature of the object-side lens surface of the second negative lens is R21, and the radius of curvature of the image-side lens surface of the second negative lens group is R22, -1.0≦(R21+R22) / (R22-R21)≦1.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

4. When Rp1 is the radius of curvature of the object-side lens surface of the positive lens in the aforementioned front group, and Rp2 is the radius of curvature of the image-side lens surface of the positive lens, -1.0≦(Rp1+Rp2) / (Rp2-Rp1)≦30.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

5. When the lateral magnification of the aforementioned intermediate lens group is in focus on an object at infinity, let βm be the value of the intermediate lens group. 0.0 < βm ≤ 1.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

6. When νdn is the average value of the Abbe numbers with respect to the d-line of all negative lenses included in the aforementioned group, 40 ≤ νdn ≤ 90 The optical system according to claim 1, characterized in that it satisfies the following conditions.

7. When Rm1 is the radius of curvature of the lens surface closest to the object in the intermediate lens group, and Rm2 is the radius of curvature of the lens surface closest to the image in the intermediate lens group, 0.5≦(Rm1+Rm2) / (Rm2-Rm1)≦30.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

8. When the distance on the optical axis between the image-side lens surface of the front lens group and the object-side lens surface of the intermediate lens group is in focus on an object at infinity, let Df be the distance on the optical axis between the image-side lens surface of the intermediate lens group and the object-side lens surface of the rear lens group is in focus on an object at infinity, 0.01 ≤ Dm / Df ≤ 1.00 The optical system according to claim 1, characterized in that it satisfies the following conditions.

9. When the focal length of the aforementioned front group is ff, -2.00 ≤ f / ff ≤ -0.01 The optical system according to claim 1, characterized in that it satisfies the following conditions.

10. When the focal length of the aforementioned rear group is denoted as fr, 0.1 ≤ fr / f ≤ 6.0 The optical system according to claim 1, characterized in that it satisfies the following conditions.

11. When the minimum F-number of the optical system when it is in focus on an object at infinity is denoted as Fno, 0.9 ≤ Fn ≤ 5.6 The optical system according to claim 1, characterized in that it satisfies the following conditions.

12. The optical system according to claim 1, characterized in that the front group has a first lens group with negative refractive power closest to the object, and the first lens group remains stationary during focusing.

13. The optical system according to claim 1, characterized in that the rear group has a lens with positive refractive power closest to the image.

14. The optical system according to claim 1, characterized in that the intermediate lens group is composed of one negative lens or one cemented lens consisting of a negative lens and a positive lens.

15. The optical system according to claim 1, characterized in that the front group is composed of one lens group consisting of a first negative lens, a negative lens, a second negative lens, and a positive lens arranged in order from the object side to the image side.

16. The optical system according to claim 1, characterized in that the front group is composed of one lens group consisting of a first negative lens, a negative lens, a negative lens, a positive lens, and a second negative lens, arranged in order from the object side to the image side.

17. The aforementioned front group is composed of a first lens group consisting of a first negative lens, a second lens group consisting of a negative lens, and a third lens group consisting of a second negative lens and a positive lens, arranged in order from the object side to the image side. The optical system according to claim 1, characterized in that the second lens group moves during focusing.

18. The system comprises a first lens group as the front group, a second lens group as the intermediate lens group, and a third, fourth, and fifth lens group constituting the rear group. The optical system according to claim 1, characterized in that the fourth lens group moves during focusing.

19. An optical system comprising a front group with negative refractive power including at least one lens group, an intermediate lens group with negative refractive power, and a rear group with positive refractive power including at least one lens group, arranged sequentially from the object side to the image side, wherein the spacing between adjacent lens groups changes during focusing, An optical system characterized in that the intermediate lens group moves toward the object when focusing from infinity to near.

20. An optical system according to any one of claims 1 to 19, An imaging device characterized by having an image sensor that captures an image of a subject through the optical system.

Images