JP7693373B2 - Optical system and imaging device having the same - Google Patents

Description

The present invention relates to an optical system that is suitable for digital video cameras, digital still cameras, broadcast cameras, cameras for silver halide film, surveillance cameras, etc.

In recent years, imaging devices have become smaller, and imaging elements used in imaging devices have become more highly pixelated. As imaging elements become smaller and more highly pixelated, optical systems used in imaging devices are required to have high optical performance, be small, and lightweight. Patent Document 1 discloses an optical system that satisfies these requirements, and is composed of six lenses arranged in order from the object side to the image side: a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and a sixth lens. The first lens is a lens with positive refractive power and a convex surface facing the object side near the optical axis. The second lens is a lens with negative refractive power and a concave surface facing the image side near the optical axis. The third lens is a lens with a convex surface facing the object side near the optical axis. The fourth lens is a lens with a convex surface facing the image side near the optical axis. The fifth lens is a lens with a convex surface facing the object side near the optical axis. The sixth lens is a lens with a concave surface facing the image side near the optical axis.

JP 2020-115174 A

In order to make the optical system smaller, it is effective to adopt a telephoto power arrangement and strengthen the positive refractive power on the object side and the negative refractive power on the image side. However, strengthening the negative refractive power on the image side causes significant distortion, making it difficult to simultaneously correct both distortion and curvature of field with a limited number of lenses.

The optical system described in Patent Document 1 corrects distortion and field curvature by using multiple aspheric lenses, but because the Petzval sum of the entire system is large, there are issues with correcting field curvature when applying it to an image pickup device with a large sensor size.

The objective of the present invention is to provide a small, lightweight optical system with high optical performance by appropriately setting the refractive index and power arrangement of each lens.

An optical system according to one aspect of the present invention is an optical system consisting of four or five lenses, which are arranged in succession from the most image side, including a first lens having positive refractive power and a second lens having negative refractive power, the optical system including the lens having positive refractive power arranged closest to the object side, wherein when an average refractive index at the d-line of materials of all the positive lenses included in the optical system is PNdave, an object-side paraxial radius of curvature of the first lens is R11, an image-side paraxial radius of curvature of the first lens is R12, an object-side paraxial radius of curvature of the second lens is R21, an image-side paraxial radius of curvature of the second lens is R22 , a focal length of the first lens is f1, a focal length of the optical system is f, a distance on the optical axis from an aperture stop to an image plane when the back focus is an air-equivalent length is SPIP, and a distance on the optical axis from the object-side lens surface of the lens arranged closest to the object side to the image plane when the back focus is an air-equivalent length is TTL ,
1.70<PNdave<2.10
-100<(R11+R12)/(R12-R11)<0.60
2.90<(R21+R22)/(R22-R21)<100
0.80<f1/f<8.00
0.80<SPIP/TTL<0.95
The present invention is characterized in that the following conditional expression is satisfied:

Other objects and features of the present invention are described in the following embodiments.

The present invention provides a compact, lightweight optical system with high optical performance.

FIG. 2 is a cross-sectional view of the optical system of the first embodiment. 6A to 6C are aberration diagrams of Example 1 when focusing on an object at infinity. FIG. 11 is a cross-sectional view of an optical system according to a second embodiment. 13A to 13C are aberration diagrams of Example 2 when focused on an object at infinity. FIG. 11 is a cross-sectional view of an optical system according to a third embodiment. 13A to 13C are aberration diagrams of Example 3 when focused on an object at infinity. FIG. 11 is a cross-sectional view of an optical system according to a fourth embodiment. 13A to 13C are aberration diagrams of Example 4 when focused on an object at infinity. FIG. 13 is a cross-sectional view of an optical system according to a fifth embodiment. 13A to 13C are aberration diagrams of Example 5 when focusing on an object at infinity. FIG. 13 is a cross-sectional view of an optical system according to a sixth embodiment. 13A to 13C are aberration diagrams of Example 6 when focusing on an object at infinity. FIG. 13 is a cross-sectional view of an optical system according to a seventh embodiment. 13A to 13C are aberration diagrams of Example 7 when focusing on an object at infinity. FIG. 13 is a cross-sectional view of an optical system according to an eighth embodiment. 13A to 13C are aberration diagrams of Example 8 when focusing on an object at infinity. FIG. 13 is a cross-sectional view of an optical system according to a ninth embodiment. 13A to 13C are aberration diagrams of Example 9 when focused on an object at infinity. FIG. 1 is a schematic diagram of an imaging device.

Below, an embodiment of the optical system of the present invention and an imaging device having the same will be described with reference to the attached drawings. In each drawing, the same components are given the same reference numbers, and duplicated descriptions will be omitted.

Figures 1, 3, 5, 7, 9, 11, 13, 15, and 17 are cross-sectional views of the optical system L0 of Examples 1 to 9, respectively. The optical system L0 of each Example is an optical system used in imaging devices such as digital video cameras, digital still cameras, broadcast cameras, silver halide film cameras, and surveillance cameras.

In each lens cross-sectional view, the left side is the object side and the right side is the image side. The optical system L0 in each embodiment is composed of multiple lenses. In each lens cross-sectional view, "Li" (i is a natural number) represents the "i-th lens" when the lenses constituting the optical system L0 are counted in order from the image side to the object side. L1 represents the lens included in the optical system L0 that is located closest to the image side. L2 represents the lens included in the optical system L0 that is located second from the image side.

SP is an aperture stop. IP is an image plane, and when the optical system L0 of each embodiment is used as the photographing optical system of a digital still camera or digital video camera, the imaging surface of a solid-state image sensor (photoelectric conversion element) such as a CCD sensor or CMOS sensor is disposed thereon. When the optical system L0 of each embodiment is used as the photographing optical system of a silver halide film camera, a photosensitive surface equivalent to the film surface is disposed on the image plane IP.

Focusing from an object point at infinity to an object point at a close distance is also performed by moving the entire optical system L0 along the optical axis.

In the optical system L0 of each embodiment, one or more lenses may be decentered to include a component perpendicular to the optical axis during image blur correction, so that the optical system has the function of an anti-vibration optical system. In addition, a parallel plate that has substantially no refractive power, such as a low-pass filter or an infrared cut filter, may be placed between the lens located closest to the image side and the imaging surface.

Figures 2, 4, 6, 8, 10, 12, 14, 16, and 18 are aberration diagrams of the optical system L0 of Examples 1 to 9 when focused at infinity.

In the spherical aberration diagram, Fno is the F-number, and shows the amount of spherical aberration for the d-line (wavelength 587.56 nm) and g-line (wavelength 435.84 nm). In the astigmatism diagram, dS shows the amount of astigmatism on the sagittal image plane, and dM shows the amount of astigmatism on the meridional image plane. In the distortion diagram, the amount of distortion for the d-line is shown. In the magnification chromatic aberration diagram, the amount of magnification chromatic aberration for the g-line is shown. ω is the half angle of view (°).

Next, we will describe the characteristic configuration of the optical system L0 in each embodiment.

The optical system L0 in each embodiment has a first lens L1 with positive refractive power, a second lens L2 with negative refractive power, and multiple lenses arranged in succession from the image side.

Furthermore, the optical system L0 of each embodiment satisfies the following conditional expression (1) when the average refractive index at the d-line (wavelength 587.56 nm) of the materials of all the positive lenses included in the optical system L0 is PNdave.

1.70<PNdave<2.10...(1)
Conditional expression (1) specifies the average refractive index of the positive lenses included in optical system L0. If the refractive index is higher than the upper limit of conditional expression (1), the color dispersion increases, making it difficult to correct axial chromatic aberration, which is not preferable. If the refractive index is lower than the lower limit of conditional expression (1), the Petzval sum of optical system L0 increases, making it difficult to correct field curvature, which is not preferable.

Furthermore, the optical system L0 in each embodiment satisfies the following conditional expression (2) when the object-side paraxial radius of curvature of the first lens L1 is R11 and the image-side paraxial radius of curvature of the first lens L1 is R12.

-100<(R11+R12)/(R12-R11)<0.60...(2)
Conditional formula (2) defines the shape of the first lens L1. If the upper limit of conditional formula (2) is exceeded and the object-side paraxial radius of curvature of the first lens L1 becomes small, the distance between the first lens L1 and the second lens L2 at the periphery becomes large, and the diameter of the first lens L1 becomes large, which is not preferable. If the lower limit of conditional formula (2) is exceeded and the difference between the object-side paraxial radius of curvature and the image-side paraxial radius of curvature becomes small, the pincushion distortion is not corrected sufficiently, which is not preferable.

Furthermore, the optical system L0 in each embodiment satisfies the following conditional expression (3) when the object-side paraxial radius of curvature of the second lens L2 is R21 and the image-side paraxial radius of curvature of the second lens L2 is R22.

2.90<(R21+R22)/(R22-R21)<100...(3)
Conditional formula (3) defines the shape of the second lens L2. If the upper limit of conditional formula (3) is exceeded and the difference between the object-side paraxial radius of curvature and the image-side paraxial radius of curvature becomes small, it is not preferable because the correction of the field curvature becomes insufficient. If the lower limit of conditional formula (3) is exceeded and the image-side paraxial radius of curvature becomes small, it is not preferable because the distance between the second lens L2 and the first lens L1 at the periphery becomes large and the diameter of the first lens L1 becomes large.

It is preferable that the numerical ranges of conditional expressions (1) to (3) are the numerical ranges of the following conditional expressions (1a) to (3a).

1.705<PNdave<2.000...(1a)
-50.0<(R11+R12)/(R12-R11)<0.60...(2a)
2.90<(R21+R22)/(R22-R21)<50.0...(3a)
It is further preferable that the numerical ranges of the conditional expressions (1) to (3) be set to the numerical ranges of the following conditional expressions (1b) to (3b).

1.709<PNdave<2.000...(1b)
-10.0<(R11+R12)/(R12-R11)<0.6...(2b)
2.90<(R21+R22)/(R22-R21)<45.0...(3b)
Next, conditions and configurations that are preferably satisfied by the optical system L0 of each embodiment will be described. It is preferable that the optical system L0 of each embodiment satisfies one or more of the following conditional expressions (4) to (9) and the following configurations.

In each embodiment, the optical system L0 preferably has a lens Lp with positive refractive power arranged closest to the object side in order to shorten the overall optical length by using a telephoto power arrangement.

In each embodiment, it is preferable that the optical system L0 satisfies the following conditional expression (4), where fp is the focal length of the lens Lp arranged closest to the object, and f is the focal length of the optical system L0.

0.55<fp/f<2.00...(4)
Conditional expression (4) defines the ratio between the focal length of lens Lp and the focal length of optical system L0. If the upper limit of conditional expression (4) is exceeded and the refractive power of lens Lp becomes weak, it becomes difficult to maintain the telephoto type power arrangement, and the total optical length becomes large, which is not preferable. If the lower limit of conditional expression (4) is exceeded and the refractive power of lens Lp becomes strong, pincushion distortion becomes large, and it becomes difficult to achieve both field curvature and distortion, which is not preferable.

When the focal length of the first lens L1 is f1, it is preferable that the optical system L0 in each embodiment satisfies the following conditional expression (5).

0.80<f1/f<8.00...(5)
Conditional expression (5) defines the ratio between the focal length of the first lens L1 and the focal length of the optical system L0. If the upper limit of conditional expression (5) is exceeded and the refractive power of the first lens L1 is weakened, the pincushion distortion is insufficiently corrected, and it becomes difficult to achieve both the curvature of field and the distortion, which is not preferable. If the lower limit of conditional expression (5) is exceeded and the refractive power of the first lens L1 is strong, it becomes difficult to maintain the telephoto type power arrangement, and the total optical length becomes large, which is not preferable.

In the optical system L0 of each embodiment, when the distance on the optical axis from the image-side lens surface of the first lens L1 to the image plane (air-equivalent length) is sk, it is preferable that the optical system L0 satisfies the following conditional expression (6):

0.20<sk/f<0.50...(6)
Conditional expression (6) defines the ratio between the back focus and the focal length of the optical system L0. If the back focus is long and exceeds the upper limit of conditional expression (6), the total optical length increases, which is not preferable. If the back focus is short and falls below the lower limit of conditional expression (6), the shadow of a foreign object attached to the lens is likely to be reflected in a photograph, which is not preferable.

The optical system L0 in each embodiment preferably satisfies the following conditional expression (7). SPIP is the distance on the optical axis from the aperture stop SP to the image plane IP (paraxial), with the back focus being the air-equivalent length, and TTL is the distance on the optical axis from the object-side lens surface of the lens located closest to the object to the image plane IP (paraxial), with the back focus being the air-equivalent length.

0.60<SPIP/TTL<0.95...(7)
Conditional formula (7) specifies the ratio between the position of the aperture stop SP and the total optical length. If the position of the aperture stop SP is on the object side and exceeds the upper limit of conditional formula (7), biased vignetting is likely to occur, and the shape of the blur becomes irregular, which is not preferable. If the position of the aperture stop SP is on the image side and falls below the lower limit of conditional formula (7), the angle of the off-axis light rays incident on the image plane IP becomes large, and shading by the image sensor is likely to occur, which is not preferable.

In the optical system L0 of each embodiment, it is preferable to place the aperture stop SP adjacent to the image side of the lens located closest to the object in order to reduce the angle of off-axis rays incident on the image plane IP and reduce shading caused by the image sensor.

When the imaging half angle of view (°) of the optical system L0 in each embodiment is ω, it is preferable that the optical system L0 satisfies the following conditional expression (8). The half angle of view may be defined as the half angle of view of light that forms an image at the end of the image circle of the optical system L0, or may be defined as the half angle of view of light that forms an image at the maximum image height of the image sensor of the imaging device to which the optical system L0 is attached.

1.40<TTL/ftanω<3.20 (8)
Conditional expression (8) defines the total optical length of the optical system L0. If the upper limit of conditional expression (8) is exceeded, the total optical length becomes large, which is not preferable. If the lower limit of conditional expression (8) is exceeded, the total optical length becomes short, which is not preferable, because the power arrangement of the telephoto type becomes strong, making it difficult to achieve both curvature of field and distortion.

In the optical system L0 of each embodiment, when the refractive index at the d-line of the second lens L2 is Nd2 and the Abbe number is νd2, it is preferable that the optical system L0 satisfies the following conditional expression (9):

Nd2<4.19450/νd2+1.52010 (9)
Conditional expression (9) defines the refractive index of lens L2. If the refractive index of negative lens L2 exceeds the upper limit of conditional expression (9), the Petzval sum of optical system L0 increases, making it difficult to correct curvature of field, which is not preferable.

It is preferable that the numerical ranges of conditional expressions (4) to (9) are the numerical ranges of the following conditional expressions (4a) to (9a).

0.55<fp/f<1.50...(4a)
0.80<f1/f<4.00...(5a)
0.23<sk/f<0.40...(6a)
0.70<SPIP/TTL<0.90...(7a)
1.9<TTL/(f×tanω)<3.1 (8a)
Nd2<4.19450/νd2+1.48010...(9a)
It is further preferable that the numerical ranges of the conditional expressions (4) to (9) be the numerical ranges of the following conditional expressions (4b) to (9b).

0.79<fp/f<1.35...(4b)
0.85<f1/f<1.90...(5b)
0.25<sk/f<0.39 (6b)
0.80<SPIP/TTL<0.90...(7b)
1.9<TTL/(f×tanω)<2.5 (8b)
Nd2<4.19450/νd2+1.45710...(9b)
In order to achieve both high optical performance and compactness, the optical system L0 in each embodiment has three or more lenses having positive refractive power and two or more lenses having negative refractive power, and it is preferable that the total number of lenses included in the optical system L0 is eight or less.

In each embodiment, the optical system L0 preferably has an aspheric lens made of a resin material on the image side of the aperture stop to correct field curvature.

Note that cover glass, IR cut filters, etc. are not considered to be lenses, and cover glass, IR cut filters, etc. may be placed on the object side of lens Lp in optical system L0 in each embodiment, or between first lens L1 and the image plane. Furthermore, the refractive power of a lens refers to the refractive power near the optical axis (paraxial). Here, near the optical axis refers to the paraxial region, and in the case of an aspheric lens, the concave and convex surfaces near the optical axis are defined by the sign of the paraxial radius of curvature. Similarly, the positive and negative refractive powers are calculated from the paraxial radius of curvature.

Next, the optical system L0 of each embodiment will be described in detail.

The optical system L0 of Example 1 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, an aperture stop SP, and a sixth lens L6, arranged in that order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power near the optical axis. The fourth lens L4 has positive refractive power. The fifth lens L5 has negative refractive power. The sixth lens L6 has positive refractive power. The sixth lens L6 is lens Lp. The second lens L2 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side. The third lens L3 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and the concave surface facing the image side near the optical axis, and the image-side surface facing the image side near the optical axis.

The optical system L0 of Example 2 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, an aperture stop SP, and a sixth lens L6, arranged in that order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power near the optical axis. The fourth lens L4 has positive refractive power. The fifth lens L5 has negative refractive power. The sixth lens L6 has positive refractive power. The sixth lens L6 is lens Lp. The second lens L2 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side. The third lens L3 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and the concave surface facing the image side near the optical axis, and the image-side surface facing the image side near the optical axis.

The optical system L0 of Example 3 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, an aperture stop SP, and a sixth lens L6, arranged in that order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power near the optical axis. The fourth lens L4 has positive refractive power. The fifth lens L5 has negative refractive power. The sixth lens L6 has positive refractive power. The sixth lens L6 is lens Lp. The second lens L2 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side. The third lens L3 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and the concave surface facing the image side near the optical axis, and the image-side surface facing the image side near the optical axis.

The optical system L0 of Example 4 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, an aperture stop SP, and a sixth lens L6, arranged in that order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power near the optical axis. The fourth lens L4 has positive refractive power. The fifth lens L5 has negative refractive power. The sixth lens has positive refractive power. The sixth lens L6 is lens Lp. The second lens L2 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side. The third lens L3 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and the concave surface facing the image side near the optical axis, and the image-side surface facing the image side near the optical axis.

The optical system L0 of Example 5 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, a sixth lens L6, an aperture stop SP, and a seventh lens L7, arranged in order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power. The fourth lens L4 has negative refractive power near the optical axis. The fifth lens L5 has positive refractive power. The sixth lens L6 has negative refractive power. The seventh lens has positive refractive power. The seventh lens L7 is lens Lp. The second lens L2 has aspheric surfaces on both sides, and the object-side surface faces the object side concavely near the optical axis, and the image-side surface faces the image side convexly near the optical axis. The fourth lens L4 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side.

The optical system L0 of Example 6 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, a sixth lens L6, an aperture stop SP, and a seventh lens L7, arranged in order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power. The fourth lens L4 has positive refractive power near the optical axis. The fifth lens L5 has positive refractive power. The sixth lens L6 has negative refractive power. The seventh lens L7 has positive refractive power. The seventh lens L7 is lens Lp. The second lens L2 has aspheric surfaces on both sides, and the object-side surface faces the object side concavely near the optical axis, and the image-side surface faces the image side convexly near the optical axis. The fourth lens L4 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side.

The optical system L0 of Example 7 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, a sixth lens L6, an aperture stop SP, and a seventh lens L7, arranged in order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power. The fourth lens L4 has negative refractive power near the optical axis. The fifth lens L5 has positive refractive power. The sixth lens L6 has negative refractive power. The seventh lens L7 has positive refractive power. The seventh lens L7 is lens Lp. The second lens L2 has aspheric surfaces on both sides, and the object-side surface faces the object side concavely near the optical axis, and the image-side surface faces the image side convexly near the optical axis. The fourth lens L4 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and the concave surface facing the image side near the optical axis, and the image-side surface facing the image side near the optical axis.

The optical system L0 of Example 8 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, a sixth lens L6, an aperture stop SP, and a seventh lens L7, arranged in order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power. The fourth lens L4 has positive refractive power near the optical axis. The fifth lens L5 has positive refractive power. The sixth lens L6 has negative refractive power. The seventh lens L7 has positive refractive power. The seventh lens L7 is lens Lp. The second lens L2 has aspheric surfaces on both sides, and the object-side surface faces the object side concavely near the optical axis, and the image-side surface faces the image side convexly near the optical axis. The fourth lens L4 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side.

The optical system L0 of Example 9 is composed of a first lens L1, a second lens L2, a third lens L3, a fourth lens L4, a fifth lens L5, a sixth lens L6, an aperture stop SP, and a seventh lens L7, arranged in order from the image side to the object side. The first lens L1 has positive refractive power. The second lens L2 has negative refractive power near the optical axis. The third lens L3 has negative refractive power. The fourth lens L4 has positive refractive power near the optical axis. The fifth lens L5 has positive refractive power. The sixth lens L6 has negative refractive power. The seventh lens L7 has positive refractive power. The seventh lens L7 is lens Lp. The second lens L2 has aspheric surfaces on both sides, and the object-side surface faces the object side concavely near the optical axis, and the image-side surface faces the image side convexly near the optical axis. The fourth lens L4 has aspheric surfaces on both sides, with the object-side surface facing the object side near the optical axis and a concave surface facing the object side, and the image-side surface facing the image side near the optical axis and a convex surface facing the image side.

Below are numerical examples 1 to 9 corresponding to examples 1 to 9, respectively.

In the surface data of each numerical example, r represents the radius of curvature of each optical surface, and d (mm) represents the axial distance (distance on the optical axis) between the mth surface and the (m+1)th surface. Here, m is the surface number counted from the light incidence side. In addition, nd represents the refractive index of each optical member with respect to the d-line, and νd represents the Abbe number of the optical member. Note that the Abbe number νd of a certain material is given by Nd, NF, and NC, where Nd, NF, and NC are the refractive indices at the d-line (587.56 nm), F-line (486.13 nm), and C-line (656.27 nm) of the Fraunhofer lines, respectively.
νd=(Nd-1)/(NF-NC)
It is expressed as:

In each numerical example, d, focal length (mm), F-number, and half angle of view (°) are all values when the optical system L0 of each example is focused on an object at infinity. "Back focus" is the distance on the optical axis from the final lens surface (the lens surface closest to the image) to the paraxial image surface expressed as an air-equivalent length. "Total lens length" is the distance on the optical axis from the frontmost lens surface (the lens surface closest to the object) of optical system L0 to the final surface plus the back focus.

In addition, when an optical surface is aspheric, a symbol * is added to the right of the surface number. When X is the displacement from the apex of the surface in the optical axis direction, h is the height from the optical axis in a direction perpendicular to the optical axis, R is the paraxial radius of curvature, k is the conic constant, and A4, A6, A8, A10, A12, and A14 are aspheric coefficients of each order,
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 +A12×h ¹² +A14×h ¹⁴
In addition, "e±XX" in each aspheric coefficient means "×10± ^XX ."

[Numerical Example 1]
Unit: mm

Surface data surface number rd nd νd
1 12.364 3.19 1.61800 63.4
2 24.210 2.94
3(Aperture) ∞ 2.27
4 -50.169 0.69 1.60342 38.0
5 10.139 4.02 1.85150 40.8
6 -33.783 0.40
7* -34.470 1.33 1.63560 23.9
8* 70.659 5.80
9* -6.950 3.08 1.67070 19.3
10* -11.164 0.20
11 478.184 6.09 1.90366 31.3
12 -37.541 11.50
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-1.02966e-004 A 6= 1.45749e-005 A 8=-1.39350e-006
A10= 6.80905e-008 A12=-1.49610e-009 A14= 1.14433e-011

Side 8
K = 0.00000e+000 A 4= 6.02186e-006 A 6= 6.43923e-006 A 8=-3.91077e-007
A10= 1.43765e-008 A12=-2.09793e-010 A14= 8.50376e-013

9th page
K =-4.41191e+000 A 4=-1.47362e-003 A 6= 4.29446e-005 A 8=-1.68194e-006
A10= 4.49993e-008 A12=-7.25078e-010 A14= 4.77511e-012

Side 10
K = 0.00000e+000 A 4= 8.83309e-005 A 6= 9.25372e-008 A 8=-7.24772e-010
A10= 1.08868e-010 A12=-1.57886e-012 A14= 9.00701e-015

Focal length 33.13
F-number: 2.91
Half angle of view (°) 33.15
Image height 21.64
Lens length 41.51
BF 11.50

[Numerical Example 2]
Unit: mm

Surface data surface number rd nd νd
1 13.651 2.98 1.61800 63.4
2 26.798 2.88
3(Aperture) ∞ 2.70
4 -29.679 0.70 1.60342 38.0
5 11.727 4.28 1.85150 40.8
6 -23.783 0.40
7* -31.235 3.85 1.63560 23.9
8* 326.362 6.92
9* -8.020 3.77 1.67070 19.3
10* -12.457 0.20
11 73.939 4.84 1.90366 31.3
12 -254.677 10.00
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-1.34864e-004 A 6= 4.33017e-006 A 8=-2.94984e-007
A10= 1.08664e-008 A12=-1.73525e-010 A14= 8.43785e-013

Side 8
K = 0.00000e+000 A 4=-5.66667e-005 A 6= 1.20119e-006 A 8=-1.06066e-009
A10=-5.01855e-010 A12= 1.73403e-011 A14=-1.38734e-013

9th page
K =-4.34585e+000 A 4=-1.00898e-003 A 6= 2.14842e-005 A 8=-5.92000e-007
A10= 1.13215e-008 A12=-1.30734e-010 A14= 6.25651e-013

Side 10
K = 0.00000e+000 A 4= 1.96956e-005 A 6= 7.34785e-007 A 8=-1.11185e-008
A10= 1.57907e-010 A12=-1.19765e-012 A14= 3.83183e-015

Focal length 34.60
F-number: 2.91
Half angle of view (°) 32.02
Image height 21.64
Lens length 43.50
BF 10.00

[Numerical Example 3]
Unit: mm

Surface data surface number rd nd νd
1 13.201 3.04 1.61800 63.4
2 26.031 2.89
3(Aperture) ∞ 2.44
4 -33.911 0.74 1.60342 38.0
5 9.811 4.21 1.85150 40.8
6 -33.263 0.40
7* -90.919 3.00 1.63560 23.9
8* 60.811 5.38
9* -8.390 4.00 1.67070 19.3
10* -17.176 0.20
11 -211.111 6.30 1.90366 31.3
12 -29.226 10.89
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-1.60984e-004 A 6= 7.75621e-006 A 8=-6.51995e-007
A10= 2.77714e-008 A12=-5.32718e-010 A14= 3.58464e-012

Side 8
K = 0.00000e+000 A 4=-6.81171e-005 A 6= 1.56038e-006 A 8=-2.02001e-008
A10=-6.01290e-010 A12= 4.31469e-011 A14=-4.65533e-013

9th page
K =-7.11991e+000 A 4=-1.50408e-003 A 6= 4.55541e-005 A 8=-1.63651e-006
A10= 3.84552e-008 A12=-5.40978e-010 A14= 3.19370e-012

Side 10
K = 0.00000e+000 A 4= 5.39631e-006 A 6=-1.49270e-007 A 8= 4.42673e-009
A10=-5.89346e-011 A12= 4.11714e-013 A14=-1.05328e-015

Focal length 34.39
F-number: 2.91
Half angle of view (°) 32.17
Image height 21.64
Lens length 43.50
BF 10.89

[Numerical Example 4]
Unit: mm

Surface data surface number rd nd νd
1 12.361 3.46 1.43875 94.7
2 28.265 2.82
3(Aperture) ∞ 2.59
4 -25.271 0.71 1.60342 38.0
5 9.882 4.60 1.89190 37.1
6 -21.765 0.40
7* -41.047 2.81 1.63560 23.9
8* 37.020 7.59
9* -7.504 2.10 1.67070 19.3
10* -11.582 0.20
11 335.485 7.11 1.80000 29.8
12 -38.684 10.10
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-3.16322e-004 A 6= 2.09879e-006 A 8= 5.06534e-008
A10=-6.29589e-009 A12= 2.24698e-010 A14=-2.68222e-012

Side 8
K = 0.00000e+000 A 4=-2.09731e-004 A 6= 1.97459e-006 A 8= 4.26758e-008
A10=-2.19133e-009 A12= 4.51796e-011 A14=-2.96237e-013

9th page
K =-5.19215e+000 A 4=-1.35545e-003 A 6= 3.94317e-005 A 8=-1.22569e-006
A10= 2.46402e-008 A12=-2.90244e-010 A14= 1.42214e-012

Side 10
K = 0.00000e+000 A 4= 9.26493e-005 A 6= 6.49815e-007 A 8=-1.78983e-008
A10= 3.22776e-010 A12=-2.73407e-012 A14= 1.10539e-014

Focal length 35.00
F-number: 2.91
Half angle of view (°) 31.72
Image height 21.64
Lens length 44.50
BF 10.10

[Numerical Example 5]
Unit: mm

Surface data surface number rd nd νd
1 12.361 3.01 1.69680 55.5
2 29.386 2.75
3(Aperture) ∞ 2.80
4 -36.916 1.10 1.69895 30.1
5 13.095 3.81 1.83481 42.7
6 -25.327 0.43
7* -44.694 1.18 1.53110 55.9
8* -515.202 3.67
9 -7.827 2.36 1.92286 20.9
10 -13.255 1.14
11* -11.047 1.50 1.53110 55.9
12* -14.897 0.40
13 361.960 6.85 2.00100 29.1
14 -36.352 11.50
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-3.89614e-004 A 6= 4.14518e-006 A 8=-1.47444e-008
A10=-2.48975e-009 A12= 9.04155e-011 A14=-6.59935e-013

Side 8
K = 0.00000e+000 A 4=-4.54696e-004 A 6= 3.57521e-006 A 8=-5.74335e-008
A10=-7.97906e-010 A12= 2.90616e-011 A14=-8.70907e-014

Page 11
K = 0.00000e+000 A 4= 9.93948e-005 A 6= 1.56916e-006 A 8=-6.45991e-008
A10= 8.11199e-010 A12=-6.87945e-012 A14= 3.43386e-014

Side 12
K = 0.00000e+000 A 4= 1.24290e-004 A 6= 1.34138e-006 A 8=-3.73663e-008
A10= 3.75035e-010 A12=-1.67485e-012 A14= 2.94387e-015

Focal length 35.49
F-number: 2.80
Half angle of view (°) 31.36
Image height 21.64
Lens length 42.50
BF 11.50

[Numerical Example 6]
Unit: mm

Surface data surface number rd nd νd
1 12.175 2.99 1.69680 55.5
2 32.507 3.78
3(Aperture) ∞ 2.49
4 -103.585 1.10 1.69895 30.1
5 9.895 2.58 1.83481 42.7
6 -73.085 0.40
7* -60.538 1.10 1.53110 55.9
8* -202.964 1.77
9 -10.427 4.51 1.92286 20.9
10 -17.032 1.74
11* -13.129 1.50 1.53110 55.9
12* -26.262 0.40
13 58.652 7.61 2.00100 29.1
14 -202.025 9.00
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-4.27512e-005 A 6= 4.52994e-006 A 8= 1.98759e-007
A10=-1.52654e-008 A12= 6.70645e-010 A14=-9.38008e-012

Side 8
K = 0.00000e+000 A 4=-8.84659e-005 A 6= 4.96683e-006 A 8= 1.40348e-007
A10=-6.35911e-009 A12= 2.67567e-010 A14=-2.00325e-012

Page 11
K = 0.00000e+000 A 4=-4.97904e-004 A 6= 9.86601e-007 A 8= 3.57478e-008
A10=-1.42763e-009 A12= 1.32323e-011 A14= 5.54661e-014

Side 12
K = 0.00000e+000 A 4=-3.28690e-004 A 6= 3.26388e-006 A 8=-1.52971e-008
A10=-6.47841e-011 A12= 2.19990e-012 A14=-1.23384e-014

Focal length 34.88
F-number: 2.80
Half angle of view (°) 21.39
Image height 13.66
Lens length 40.98
BF 9.00

[Numerical Example 7]
Unit: mm

Surface data surface number rd nd νd
1 12.516 2.45 2.00100 29.1
2 29.514 2.57
3(Aperture) ∞ 2.21
4 56.644 1.10 1.96300 24.1
5 5.927 4.00 1.72916 54.7
6 -62.601 0.40
7* -43.848 1.10 1.53110 55.9
8* 64.119 3.18
9 -7.672 4.45 1.94594 18.0
10 -10.932 0.40
11* -26.173 1.50 1.53110 55.9
12* -52.347 0.40
13 61.126 4.12 2.00069 25.5
14 -61.126 13.10
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4= 6.20693e-005 A 6= 8.19347e-006 A 8=-6.06272e-007
A10= 4.15714e-008 A12=-1.38766e-009 A14= 1.89686e-011

Side 8
K = 0.00000e+000 A 4= 3.04001e-005 A 6= 5.79722e-006 A 8=-3.32536e-007
A10= 1.87865e-008 A12=-4.96337e-010 A14= 4.81005e-012

Page 11
K = 0.00000e+000 A 4=-3.01320e-004 A 6=-1.39174e-007 A 8= 3.50464e-008
A10=-1.06628e-009 A12= 1.12362e-011 A14=-3.69959e-014

Side 12
K = 0.00000e+000 A 4=-2.47472e-004 A 6= 7.98220e-007 A 8= 4.54547e-009
A10=-2.59575e-010 A12= 2.66091e-012 A14=-9.42725e-015

Focal length 34.76
F-number: 2.80
Half angle of view (°) 21.45
Image height 13.66
Lens length 40.98
BF 13.10

[Numerical Example 8]
Unit: mm

Surface data surface number rd nd νd
1 13.766 2.79 1.69680 55.5
2 34.764 2.64
3 (Aperture) ∞ 3.78
4 -32.448 1.10 1.69895 30.1
5 10.903 5.49 1.83481 42.7
6 -21.399 0.72
7* -27.309 1.10 1.53110 55.9
8* -148.417 3.87
9 -8.780 1.70 1.73800 32.3
10 -23.659 1.10
11* -76.516 2.01 1.53110 55.9
12* -80.440 0.40
13 359.385 7.79 2.00100 29.1
14 -38.414 10.00
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-5.60903e-004 A 6= 9.60410e-006 A 8=-1.15871e-007
A10= 2.61583e-010 A12= 2.85854e-011 A14=-2.47992e-013

Side 8
K = 0.00000e+000 A 4=-6.11260e-004 A 6= 9.86206e-006 A 8=-1.58943e-007
A10= 1.94628e-009 A12=-1.12356e-011 A14= 7.12536e-014

Page 11
K = 0.00000e+000 A 4=-1.04540e-004 A 6=-1.85115e-006 A 8= 2.32791e-008
A10=-2.00953e-010 A12= 5.29048e-013 A14= 1.26639e-015

Side 12
K = 0.00000e+000 A 4=-1.81722e-005 A 6=-1.26945e-006 A 8= 1.37153e-008
A10=-9.20735e-011 A12= 3.55152e-013 A14=-5.45787e-016

Focal length 37.37
F-number: 2.80
Half angle of view (°) 30.07
Image height 21.64
Lens length 44.50
BF 10.00

[Numerical Example 9]
Unit: mm

Surface data surface number rd nd νd
1 16.840 3.53 1.69680 55.5
2 44.066 2.91
3(Aperture) ∞ 5.61
4 -37.515 1.17 1.69895 30.1
5 15.004 8.83 1.83481 42.7
6 -22.795 1.05
7* -39.594 1.22 1.53110 55.9
8* 118.252 3.23
9 -10.937 1.10 1.92286 20.9
10 -16.525 0.84
11* -50.759 2.84 1.53110 55.9
12* -99.100 0.40
13 -39.836 5.96 1.95278 18.6
14 -26.557 14.80
Image plane ∞

Aspheric data No. 7
K = 0.00000e+000 A 4=-6.04132e-004 A 6= 8.13921e-006 A 8=-8.37679e-008
A10= 2.77490e-010 A12= 7.03383e-012 A14=-5.45325e-014

Side 8
K = 0.00000e+000 A 4=-6.72264e-004 A 6= 7.83183e-006 A 8=-9.25804e-008
A10= 5.36563e-010 A12= 1.76231e-012 A14=-1.86736e-014

Page 11
K = 0.00000e+000 A 4=-1.88796e-004 A 6=-2.28010e-006 A 8= 3.22885e-008
A10=-3.71707e-010 A12= 2.29235e-012 A14=-4.11221e-015

Side 12
K = 0.00000e+000 A 4=-8.75801e-005 A 6=-8.46350e-007 A 8= 1.18038e-008
A10=-7.36711e-011 A12= 2.66163e-013 A14=-4.09408e-016

Focal length 46.55
F-number: 2.80
Half angle of view (°) 24.93
Image height 21.64
Lens length 53.50
BF 14.80

The various values in each numerical example are summarized in Table 1 below.

[Imaging device]
Next, an embodiment of a digital still camera (imaging device) 10 using the optical system L0 of each embodiment as an imaging optical system will be described with reference to Fig. 19. In Fig. 19, 13 denotes a camera body, and 11 denotes an imaging optical system constituted by any of the optical systems L0 described in the first to ninth embodiments. 12 denotes a solid-state imaging element (photoelectric conversion element) such as a CCD sensor or a CMOS sensor that is built into the camera body 13 and receives an optical image formed by the imaging optical system 11 and photoelectrically converts it. The camera body 13 may be a so-called single-lens reflex camera having a quick-turn mirror, or may be a so-called mirrorless camera having no quick-turn mirror.

In this way, by applying the optical system L0 of each embodiment to an imaging device such as a digital still camera, an imaging device with a small lens can be obtained.

The above describes preferred embodiments of the present invention, but the present invention is not limited to these embodiments, and various combinations, modifications, and variations are possible within the scope of the gist of the invention.

L1: First lens L2: Second lens

Claims (11)

An optical system including a first lens having a positive refractive power, a second lens having a negative refractive power, and four or five lenses arranged in succession from the image side,
the optical system includes a lens having a positive refractive power arranged closest to the object,
Let PNdave be the average refractive index at the d-line of the materials of all the positive lenses included in the optical system, R11 be the object-side paraxial radius of curvature of the first lens, R12 be the image-side paraxial radius of curvature of the first lens, R21 be the object-side paraxial radius of curvature of the second lens, R22 be the image-side paraxial radius of curvature of the second lens, f1 be the focal length of the first lens, f be the focal length of the optical system, SPIP be the distance on the optical axis from the aperture stop to the image plane when the back focus is the air-equivalent length, and TTL be the distance on the optical axis from the object-side lens surface of the lens arranged closest to the object to the image plane when the back focus is the air-equivalent length.
1.70<PNdave<2.10
-100<(R11+R12)/(R12-R11)<0.60
2.90<(R21+R22)/(R22-R21)<100
0.80<f1/f<8.00
0.80<SPIP/TTL<0.95
An optical system characterized in that the following condition is satisfied: Let fp be the focal length of the lens having positive refractive power arranged closest to the object side , and f be the focal length of the optical system.
0.55<fp/f<2.00
2. The optical system according to claim 1 , wherein the following condition is satisfied: When the focal length of the first lens is f1 and the focal length of the optical system is f,
0.80<f1/f<8.00
3. The optical system according to claim 1, wherein the following condition is satisfied: 4. The optical system according to claim 1 , further comprising an aperture stop arranged adjacent to the image side of the lens arranged closest to the object side. Let TTL be the distance on the optical axis from the object side lens surface of the lens arranged closest to the object side to the image plane, with the back focus being the air-equivalent length, f be the focal length of the optical system, and ω be the half angle of view (°), as follows:
1.40<TTL/(f×tanω)<3.20
5. The optical system according to claim 1 , wherein the following condition is satisfied: When the refractive index of the second lens at the d line is Nd2 and the Abbe number of the second lens at the d line is νd2,
Nd2<4.19450/νd2+1.52010
6. The optical system according to claim 1 , wherein the following condition is satisfied: the optical system has three or more lenses with positive refractive power and two or more lenses with negative refractive power;
7. The optical system according to claim 1 , wherein the total number of lenses included in the optical system is eight or less. 8. The optical system according to claim 1 , further comprising an aspheric lens made of a resin material and disposed on the image side of an aperture stop. 9. The optical system according to claim 1, wherein the optical system comprises, in order from the image side to the object side, the first lens, the second lens, a third lens, a fourth lens, a fifth lens, an aperture stop, and a sixth lens. 10. The optical system according to claim 1, wherein the optical system comprises, in order from the image side to the object side, the first lens, the second lens, a third lens, a fourth lens, a fifth lens, a sixth lens, an aperture stop, and a seventh lens. An imaging device comprising: the optical system according to claim 1 ; and an imaging element that receives an image formed by the optical system.