Optical system and imaging apparatus

Abstract

To provide an optical system capable of performing imaging for obtaining a high quality omnidirectional image.SOLUTION: The optical system includes a first negative lens Gn1. When a half-open angle at an effective diameter position of an object-side surface of the first negative lens is defined as θ1, the optical system satisfies a condition of 90°<θ1≤180°.SELECTED DRAWING: Figure 1

Description

[Technical Field]

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

[0002] When a 360° angle of view cannot be obtained with a single optical system when performing omnidirectional imaging, a stitching process is performed to join together multiple captured images obtained using multiple optical systems and imaging elements provided for each optical system, as disclosed in Patent Document 1. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-025255 Summary of the Invention [Problem to be solved by the invention]

[0004] However, in stitching, misalignment occurs at the seams of captured images due to misalignment of the nodal points (entrance pupils) of multiple optical systems, making it difficult to obtain high-quality omnidirectional images.

[0005] The present invention provides an optical system that enables imaging to obtain a high-quality omnidirectional image. [Means for solving the problem]

[0006] An optical system according to one aspect of the present invention includes a first negative lens, wherein when a half aperture angle at an effective diameter position of a lens surface on the object side of the first negative lens is θ1, 90°<θ1≦180° The optical system is characterized by satisfying the following conditions: An imaging device including the optical system described above also constitutes another aspect of the present invention. [Effects of the Invention]

[0007] According to the present invention, it is possible to provide an optical system that enables imaging to obtain a high-quality omnidirectional image. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 2 is a cross-sectional view showing the configuration and optical paths of the optical system of the first embodiment. [Figure 2] FIG. 4 is a longitudinal aberration diagram of the optical system of Example 1. [Figure 3] FIG. 10 is a cross-sectional view showing the configuration and optical paths of an optical system according to a second embodiment. [Figure 4] 10A and 10B are longitudinal aberration diagrams of the optical system of Example 2. [Figure 5] FIG. 1 is a diagram showing an imaging device including an optical system according to a first or second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0010] Next, the imaging optical system of each embodiment will be described.

[0011] 1 and 3 show cross sections of the optical systems of Examples 1 and 2, respectively. These figures also show the optical paths of the axial light beam and the light beam at the maximum half angle of view. In each figure, the left side is the object side (front side), and the right side is the image side (rear side).

[0012] The optical system of each embodiment is used as an imaging optical system for imaging devices such as digital cameras, video cameras, broadcast cameras, cinema cameras, surveillance cameras, and cameras for silver halide film.

[0013] The optical system in each embodiment forms an optical image of a subject (not shown) located on the object side. The image plane IP is located on the image plane IP, where the imaging surface (light receiving surface) of an imaging element such as a CCD sensor or a CMOS sensor, or the film surface (photosensitive surface) of a silver halide film is located.

[0014] The optical system of each embodiment can also be used as a projection optical system that magnifies light from a display element such as a liquid crystal panel or a digital micromirror device located at a position corresponding to the image plane IP and projects the magnified light onto a projection surface such as a spherical screen. In this case, the object side in each diagram is the magnification conjugate side, and the image side is the reduction conjugate side.

[0015] The optical system of each embodiment is composed of a first lens group L1 with positive refractive power, an aperture stop SP, and a second lens group L2 with positive refractive power, arranged in this order from the object side to the image side. The first lens group L1 includes a first negative lens group Gn1, which is a negative meniscus lens arranged closest to the object side. Note that a light-transmitting member other than a lens, such as a cover glass with no or almost no refractive power, may be arranged closer to the object side than the first negative lens group Gn1. Each lens group is composed of one or more lenses.

[0016] Furthermore, the object-side lens surface of the first negative lens Gn1 has a half aperture angle exceeding 90° at its effective diameter position (which will be described later). That is, when the half aperture angle at the effective diameter position of the object-side lens surface of the first negative lens Gn1 is θ1, the condition of the following formula (1) is satisfied.

[0017] 90°<θ1≦180° (1) The effective diameter position is the position of the intersection of the lens surface and the marginal ray. A marginal ray is a ray that passes through a lens surface and has an intersection point at the farthest position along the optical axis from the vertex of the lens surface.

[0018] A first negative lens with a half aperture angle θ1 of 90° or less cannot capture light rays with a half angle of view of 180° or more that wrap around from the image side of the optical system. In order to capture light rays with a half angle of view of 180° or more, a first negative lens with a half angle of view larger than 90° is required, and a larger half angle is preferable in order to capture light rays with a wider angle of view.

[0019] It is more preferable to set the numerical range of the formula (1) as follows:

[0020] 92.6°≦θ1≦153.4° (1a) Furthermore, it is more preferable to set the numerical range of formula (1) as follows:

[0021] 95.3°≦θ1≦126.7° (1b) Such a lens with a half angle exceeding 90° can be manufactured, for example, by manufacturing it in a shape divided along a plane parallel to the optical axis and then bonding the divided parts together with adhesive or the like.

[0022] By satisfying the above configuration and conditions, it is possible to obtain a high-quality omnidirectional image without the inconsistency of the joints that occurs in the past.

[0023] Next, conditions and configurations that the optical system of each example should preferably satisfy will be described. The optical system of each example should preferably satisfy at least one of the conditions and configurations of the following expressions (3) to (8).

[0024] The optical system in each embodiment preferably includes multiple lenses on the image side of the first negative lens Gn1. By including multiple lenses on the image side of the first negative lens Gn1, the first negative lens Gn1, which is closest to the object, can capture light rays with a half angle of view of 180° or more, and the multiple lenses on the image side of that lens can form a good image of those light rays.

[0025] In addition, it is preferable that the optical system of each embodiment satisfies the condition of the following formula (2), where θ2 is the half aperture angle at the effective diameter position of the image-side lens surface of the first negative lens Gn1.

[0026] 90°<θ2≦180° (2) A first negative lens having a half aperture angle θ2 of 90° or less on the image-side lens surface is not preferable because it is difficult to take in light rays with a half angle of view of 180° or more.

[0027] It is more preferable to set the numerical range of the formula (2) as follows:

[0028] 95.5°≦θ2≦156.1° (2a) Furthermore, it is more preferable to set the numerical range of the formula (2) as follows.

[0029] 100.9°≦θ2≦132.1° (2b) In addition, it is preferable that the optical system of each embodiment satisfies the condition of the following formula (3), where FG1 is the focal length of the first negative lens Gn1 and f is the focal length of the entire optical system.

[0030] -75.0≦FG1 / |f|≦-30.0 (3) If the refractive power of the first negative lens Gn1 becomes so strong that FG1 / |f| falls below the lower limit of formula (3), off-axis aberrations such as field curvature, astigmatism, and lateral chromatic aberration will occur to a large extent, making it difficult to obtain a high-quality omnidirectional image, which is undesirable.If the refractive power of the first negative lens Gn1 becomes so weak that FG1 / |f| exceeds the upper limit of formula (3), it will be impossible to capture light rays with a half angle of view exceeding 180°, which is also undesirable.

[0031] It is more preferable to set the numerical range of the formula (3) as follows:

[0032] -68.2≦FG1 / |f|≦-38.6 (3a) Furthermore, it is more preferable to set the numerical range of the formula (3) as follows.

[0033] -64.9≦FG1 / |f|≦-47.2 (3b) Furthermore, it is preferable that the optical system of each embodiment satisfies the condition of the following formula (4), where nd is the refractive index of the first negative lens Gn1 at the d-line (wavelength 587.6 nm).

[0034] 1.6≦nd≦2.3 (4) If the refractive index of the first negative lens Gn1 is small so that nd is below the lower limit of formula (4), it is not possible to capture light rays with a half angle of view exceeding 180°, which is not preferable. If the refractive index of the first negative lens Gn1 is large so that nd exceeds the upper limit of formula (4), it is usually made of a high-dispersion material, which causes large chromatic aberration of magnification and makes it difficult to obtain a high-quality omnidirectional image, which is not preferable.

[0035] It is more preferable to set the numerical range of the formula (4) as follows:

[0036] 1.7≦nd≦2.2 (4a) Furthermore, it is more preferable to set the numerical range of the formula (4) as follows.

[0037] 1.9≦nd≦2.1 (4b) In the optical systems of the respective embodiments, the radius of curvature of the object-side lens surface of the first negative lens Gn1 is R1, the radius of curvature of the image-side lens surface is R2, and the shape factor S is S=(R1+R2) / (R1-R2) When the above definition is made, it is preferable to satisfy the condition of the following formula (5).

[0038] 2.0≦S≦5.5 (5) If S is below the lower limit of formula (5), the refractive power of the first negative lens Gn1 becomes strong, which causes significant off-axis aberrations such as field curvature, astigmatism, and lateral chromatic aberration, making it difficult to obtain a high-quality omnidirectional image, which is undesirable.If S is above the upper limit of formula (5), the refractive power of the first negative lens Gn1 becomes weak, making it difficult to capture light rays with a half angle of view of 180° or more, which is undesirable.

[0039] It is more preferable to set the numerical range of the formula (5) as follows:

[0040] 2.6≦S≦5.0 (5a) Furthermore, it is more preferable to set the numerical range of the formula (5) as follows.

[0041] 3.0≦S≦4.4 (5b) Furthermore, it is preferable that the optical system of each embodiment satisfies the condition of the following formula (6), where ω is the maximum half angle of view.

[0042] 180.0°≦ω (6) If ω falls below the lower limit of equation (6), image loss occurs in part of the omnidirectional image, which is not preferable.

[0043] It is more preferable to set the numerical range of the formula (6) as follows:

[0044] 181.7°≦ω (6a) Furthermore, it is more preferable to set the numerical range of the formula (6) as follows.

[0045] 183.3°≦ω (6b) Furthermore, it is preferable that the optical system of each embodiment satisfies the condition of the following equation (7), where D1 is the length (distance) on the optical axis from the object-side surface of the first negative lens Gn1 to the aperture stop SP, and D2 is the length on the optical axis from the aperture stop SP to the image plane IP.

[0046] 3.0≦D1 / D2≦12.0 (7) It is preferable that:

[0047] If D1 / D2 falls below the lower limit of equation (7), D1 becomes too short, and the refractive power of each lens, including the first negative lens Gn1 located closer to the object than the aperture stop SP, becomes too strong. As a result, the refractive power of the lens through which off-axis light rays pass at a high position becomes strong, resulting in significant off-axis aberrations such as field curvature, astigmatism, and lateral chromatic aberration, making it impossible to obtain a high-quality omnidirectional image, which is undesirable. If D1 / D2 exceeds the upper limit of equation (7), D1 becomes too long, and the diameter of the lens G1 closest to the object becomes too large, which is also undesirable.

[0048] It is more preferable to set the numerical range of the formula (7) as follows:

[0049] 3.6≦D1 / D2≦10.3 (7a) Furthermore, it is more preferable to set the numerical range of the formula (7) as follows.

[0050] 4.1≦D1 / D2≦8.5 (7b) Furthermore, it is preferable that the optical system of each embodiment satisfies the condition of the following formula (8), where f1 is the focal length of the first lens unit L1 and f is the focal length of the entire optical system.

[0051] 0.5≦f1 / f≦2.2 (8) The first lens group L1 is composed of an object-side negative group and an image-side positive group to capture light rays at a wide angle of view. In this case, if f1 / f is below the lower limit of formula (8), the refractive power of the object-side negative group in the first lens group L1 becomes weak, making it difficult to capture light rays at a wide angle of view, which is undesirable. If f1 / f is above the upper limit of formula (8), the refractive power of the object-side negative group in the first lens group L1 becomes strong, causing significant off-axis aberrations such as field curvature, astigmatism, and lateral chromatic aberration, making it difficult to obtain a high-quality omnidirectional image, which is undesirable.

[0052] It is more preferable to set the numerical range of the formula (8) as follows:

[0053] 0.7≦f1 / f≦1.9 (8a) Furthermore, it is more preferable to set the numerical range of the formula (8) as follows.

[0054] 0.8≦f1 / f≦1.5 (8b) Furthermore, it is preferable that the optical system (first lens group L1) in each embodiment includes a second negative lens Gn2 adjacent to the first negative lens Gn1 on the image side. When the half aperture angles at the effective diameter positions of the object-side and image-side lens surfaces of the second negative lens Gn2 are θ3 and θ4, respectively, it is preferable that the following conditions of formulas (a) and (b) are satisfied.

[0055] 40°<θ3≦100° (9) 65°<θ4≦110° (10) 48.2°<θ3≦90.7° (9a) 70.4°<θ4≦101.1° (10a) 56.3°<θ3≦81.3° (9b) 75.8°<θ4≦92.2° (10b) The optical system of Example 1 includes a first negative lens Gn1, a second negative lens Gn2, and two negative lenses as single negative lenses arranged consecutively in order from the object side in the first lens group L1. The optical system of Example 2 includes a first negative lens Gn1, a second negative lens Gn2, and three negative lenses as single negative lenses arranged consecutively in order from the object side in the first lens group L1.

[0056] Numerical Examples 1 and 2 corresponding to Examples 1 and 2, respectively, are shown below. In each numerical example, surface number i indicates the order of the surface when counted from the object side. r indicates the radius of curvature (mm) of the ith surface from the object side, and d indicates the lens thickness or air gap (mm) on the optical axis between the ith and (i+1)th surfaces. nd is the refractive index at the d-line of the optical material between the ith and (i+1)th surfaces. νd is the Abbe number based on the d-line of the optical material between the ith and (i+1)th surfaces.

[0057] The Abbe number νd based on the d-line is expressed as νd=(Nd-1) / (NF-NC), where Nd, NF, and NC are the refractive indices at the Fraunhofer d-line (587.6 nm), F-line (486.1 nm), and C-line (656.3 nm).

[0058] The distance d, focal length (mm), F-number, and half angle of view (°) are all values ​​when the optical system in each numerical example is focused on an object at infinity. BF represents back focus (mm). Back focus is the length on the optical axis from the lens surface closest to the image in the optical system to the paraxial image plane, expressed as the air-equivalent length. The total lens length is the distance on the optical axis from the lens surface closest to the object in the optical system to the lens surface closest to the image, plus the back focus.

[0059] 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 A4, A6, A8, and A10 are aspherical coefficients. The conic constant and the aspherical coefficients "e±Z" are expressed as x10±Z means.

[0060] x=(h 2 / R) / [1+{1-(1+K)(h / R) 2}] 1 / 2 +A4×h 4 +A6×h 6 +A8×h 8 +A10×h 10 The values ​​of formulas (1) to (8) in Numerical Examples 1 and 2 are summarized in Table 1. In each of the numerical examples, the d-line is used as the reference wavelength, and the values ​​shown in Table 1 are for this reference wavelength. The optical systems in each of the numerical examples satisfy all of the conditions in formulas (1) to (8).

[0061] Figures 2 and 4 show the longitudinal aberrations (spherical aberration, astigmatism, distortion, and chromatic aberration) of the optical systems of Numerical Examples 1 and 2, respectively, when focused on an object 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 dashed line indicates the spherical aberration for the g-line (wavelength 435.8 nm). In the astigmatism diagrams, the solid line ΔS indicates the astigmatism on the sagittal image plane, and the dashed line ΔM indicates the astigmatism on the meridional image plane. The distortion diagrams show distortion at the d-line. Note that distortion is calculated based on equidistant projection. The chromatic aberration diagrams show lateral chromatic aberration at the g-line. ω is the half angle of view (°). [Numerical example 1] Unit: mm Surface Data Surface number rd nd νd 1 51.037 2.50 2.00502 28.9 2 30.339 18.85 3 30.875 2.00 1.90984 36.4 4 17.114 10.08 5 31.645 1.50 1.96763 25.9 6 8.583 11.13 7 -14.184 0.80 1.87280 40.5 8 12.756 1.72 9 26.631 6.23 1.87141 23.6 10 -15.148 3.46 11 -13.598 0.80 1.92845 34.6 12 -17.977 1.04 13 31.410 6.38 1.71016 30.9 14 -15.500 0.48 15 -9.748 0.50 1.49802 79.3 16 -79.400 1.00 17 17.151 1.19 1.91277 36.1 18 -25.037 0.53 19 (Aperture) ∞ 0.41 20 -13.139 0.50 1.82135 22.9 21 10.101 0.30 22 9.772 2.02 1.78043 48.7 23 145.789 0.30 24 150.450 1.03 1.76147 50.7 25 -12.785 0.40 26 8.793 1.35 1.50466 80.3 27 -9.126 0.32 28 -8.598 1.00 1.80815 22.8 29 -9.445 0.36 30 -7.249 0.80 1.81135 22.8 31 12.536 0.39 32 23.338 1.34 1.72923 54.7 33 -14.200 4.34 Image plane ∞ Various data Focal length 1.42 F-number 2.79 Half angle of view (°) 185.0 Image height 4.00 Lens length 85.02 BF 4.34 Lens group data Group starting plane focal length 1 1 1.64 2 19 27.57 [Numerical example 2] Unit: mm Surface Data Surface number rd nd νd 1 71.897 5.00 2.00100 29.1 2 39.099 22.20 3 37.580 2.50 2.00100 29.1 4 23.676 12.00 5* 31.554 2.00 1.88668 38.8 6 12.410 8.37 7 78.963 1.00 1.59522 67.7 8 12.638 5.16 9 -15.698 0.80 1.59522 67.7 10 11.710 2.30 11* 40.794 2.95 1.96568 24.9 12 -509.283 0.30 13 1062.045 4.21 1.93160 33.8 14* -17.841 7.92 15* -12.309 0.80 1.81466 22.8 16 -16.614 0.75 17 20.369 2.64 1.59513 67.5 18 341.584 1.20 19 273.339 2.16 1.72922 54.7 20 -16.554 0.41 21 -9.991 0.50 1.49700 81.5 22 -37.488 0.85 23 15.501 1.48 1.80725 46.0 24 -23.981 0.48 25 (Aperture) ∞ 0.39 26* -12.961 0.50 1.69301 29.3 27 10.172 0.47 28 11.950 1.09 1.73908 53.4 29 189.429 0.30 30 299.903 0.91 1.65588 61.0 31 -14.519 0.31 32 10.859 1.11 1.49700 81.5 33 -11.802 0.75 34 -10.865 0.80 1.80810 22.8 35 12.142 0.44 36 25.444 1.20 1.77250 49.6 37* -141.365 0.30 38 209.095 1.21 1.59522 67.7 39 -13.727 3.10 Image plane ∞ Aspheric data 5th page K = 0.00000e+00 A 4=-8.10166e-06 A 6= 1.38874e-08 A 8=-3.09318e-11 A10= 3.96310e-14 Page 11 K = 0.00000e+00 A 4=-2.38743e-05 A 6=-8.27601e-07 A 8=-7.32387e-09 A10=-2.64958e-11 Page 14 K = 0.00000e+00 A 4=-2.21199e-06 A 6=-3.65149e-07 A 8=-4.42720e-10 A10= 2.22297e-11 Page 15 K = 0.00000e+00 A 4= 8.11020e-05 A 6=-2.08816e-08 A 8= 1.94718e-07 A10=-4.55195e-09 Page 26 K = 0.00000e+00 A 4=-2.50906e-04 A 6=-1.88517e-04 A 8= 1.20885e-04 A10=-2.18158e-05 Page 37 K = 0.00000e+00 A 4=-5.47859e-05 A 6=-2.97190e-05 A 8= 4.25749e-07 A10=-1.66408e-07 Various data Focal length 1.55 F-number 2.79 Half angle of view (°) 185.0 Image height 4.00 Lens length 100.86 BF 3.10 Lens group data Group starting plane focal length 1 1 1.57 2 25 27.93

[0062] [Table 1]

[0063] [Imaging device] 5 shows an omnidirectional digital camera as an imaging device that uses the optical system of each of the above-described embodiments as its imaging optical system. 20 denotes a camera body, and 21 denotes an imaging optical system configured with the optical system of either Embodiment 1 or 2. 22 denotes a solid-state imaging element such as a CCD sensor or CMOS sensor that is built into the camera body 20 and photoelectrically converts the optical image (subject image) formed by the imaging optical system 21, i.e., captures the subject image through the imaging optical system 21. 23 denotes a recording unit that records image data generated by processing the imaging signal from the imaging element 22.

[0064] By using the optical system of each embodiment, it is possible to configure an omnidirectional digital camera capable of obtaining omnidirectional images as high-quality captured images. Note that the imaging optical system may be detachable (replaceable) from the camera body.

[0065] The above-described embodiment includes the following configurations.

[0066] (Configuration 1) a first negative lens arranged closest to the object side, and a plurality of lenses arranged closer to the image side than the first negative lens; When the half aperture angle at the effective diameter position of the object-side lens surface of the first negative lens is θ1, 90°<θ1≦180° An optical system characterized by satisfying the following conditions: (Configuration 2) When the half aperture angle at the effective diameter position of the image-side lens surface of the first negative lens is θ2, 90°<θ2≦180° The optical system according to configuration 1, characterized in that the following condition is satisfied: (Configuration 3) When the focal length of the first negative lens is FG1 and the focal length of the optical system is f, -75.0≦FG1 / |f|≦-30.0 3. The optical system according to configuration 1 or 2, wherein the following condition is satisfied: (Configuration 4) When the refractive index of the first negative lens at the d-line is nd, 1.6≦nd≦2.3 4. The optical system according to any one of configurations 1 to 3, wherein the following condition is satisfied: (Configuration 5) a radius of curvature of the object-side lens surface of the first negative lens is R1, and a radius of curvature of the image-side lens surface of the first negative lens is R2, S=(R1+R2) / (R1-R2) When 2.0≦S≦5.5 5. The optical system according to any one of configurations 1 to 4, wherein the following condition is satisfied: (Configuration 6) When the maximum half angle of view of the optical system is ω, 180.0°≦ω 6. The optical system according to any one of configurations 1 to 5, wherein the following condition is satisfied: (Configuration 7) the optical system includes an aperture stop; When the length on the optical axis from the object-side lens surface of the first negative lens to the aperture stop is D1 and the length on the optical axis from the aperture stop to the image plane is D2, 3.0≦D1 / D2≦12.0 7. The optical system according to any one of configurations 1 to 6, wherein the following condition is satisfied: (Configuration 8) the optical system is composed of a first lens group having positive refractive power, an aperture stop, and a second lens group having positive refractive power, arranged in this order from the object side to the image side; When the focal length of the first lens group is f1 and the focal length of the optical system is f, 0.5≦f1 / f≦2.2 8. The optical system according to any one of configurations 1 to 7, wherein the following condition is satisfied: (Configuration 9) the optical system includes a second negative lens adjacent to the first negative lens on the image side, When half aperture angles at the effective diameter positions of the object-side lens surface of the second negative lens and the image-side lens surface of the second negative lens are θ3 and θ4, respectively, 90°<θ3≦180° 90°<θ4≦180° 9. The optical system according to any one of configurations 1 to 8, wherein the following condition is satisfied: (Configuration 10) The optical system described in configuration 9 is characterized in that the optical system includes the first negative lens, the second negative lens, and at least two negative lenses, which are single negative lenses arranged consecutively from the object side. (Configuration 11) The optical system according to any one of configurations 1 to 10; and an image sensor that captures an image of a subject through the optical system.

[0067] 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]

[0068] L1 First lens group L2 Second lens group Gn1 First negative lens Gn2 Second negative lens IP image plane SP aperture stop

Claims

1. 1. An optical system having a first negative lens, When the half aperture angle at the effective diameter position of the object-side lens surface of the first negative lens is θ1, 90°<θ1≦180° An optical system characterized by satisfying the following conditions:

2. When the half aperture angle at the effective diameter position of the image-side lens surface of the first negative lens is θ2, 90°<θ2≦180° 2. The optical system according to claim 1, wherein the following condition is satisfied:

3. When the focal length of the first negative lens is FG1 and the focal length of the optical system is f, -75.0≦FG1 / |f|≦-30.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

4. When the refractive index of the first negative lens at the d-line is nd, 1.6≦nd≦2.3 2. The optical system according to claim 1, wherein the following condition is satisfied:

5. a radius of curvature of the object-side lens surface of the first negative lens is R1, and a radius of curvature of the image-side lens surface of the first negative lens is R2, S=(R1+R2) / (R1-R2) When 2.0≦S≦5.5 2. The optical system according to claim 1, wherein the following condition is satisfied:

6. When the maximum half angle of view of the optical system is ω, 180.0°≦ω 2. The optical system according to claim 1, wherein the following condition is satisfied:

7. the optical system includes an aperture stop; When the length on the optical axis from the object-side lens surface of the first negative lens to the aperture stop is D1 and the length on the optical axis from the aperture stop to the image plane is D2, 3.0≦D1 / D2≦12.0 2. The optical system according to claim 1, wherein the following condition is satisfied:

8. the optical system is composed of a first lens group having a positive refractive power, an aperture stop, and a second lens group having a positive refractive power, arranged in this order from an object side to an image side; When the focal length of the first lens group is f1 and the focal length of the optical system is f, 0.5≦f1 / f≦2.2 2. The optical system according to claim 1, wherein the following condition is satisfied:

9. the optical system includes a second negative lens adjacent to the first negative lens on the image side, When half aperture angles at the effective diameter positions of the object-side lens surface of the second negative lens and the image-side lens surface of the second negative lens are θ3 and θ4, respectively, 90°<θ3≦180° 90°<θ4≦180° 2. The optical system according to claim 1, wherein the following condition is satisfied:

10. 10. The optical system according to claim 9, wherein the optical system includes the first negative lens, the second negative lens, and at least two negative lenses as single negative lenses arranged successively from the object side.

11. An optical system according to any one of claims 1 to 10; and an image sensor that captures an image of a subject through the optical system.

Images