Wide-Angle Lens

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a lens, and more particularly to a wide-angle lens.

2. Description of the Related Art

In recent years, the requirements for camera with wide field of view are greatly increased due to the rise of the sports market. Lens assemblies that are used for such kind of cameras have been developed toward wide field of view and miniaturization in order to capture a wider range of images and carry conveniently. Therefore, the requirements for lens assemblies with wide field of view and miniaturization are greatly increased. However, the known wide-angle lens can't satisfy such requirements. Therefore, a wide-angle lens with new structure to meet the requirements of wide field of view and miniaturization is needed.

BRIEF SUMMARY OF THE INVENTION

The invention provides a wide-angle lens to solve the above problems. The wide-angle lens of the invention is provided with characteristics of a shortened total lens length, a wider field of view and still has a good optical performance.

The wide-angle lens in accordance with an exemplary embodiment of the invention, from an object side to an image side along an optical axis, includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, a sixth lens, a seventh lens, an eighth lens and a ninth lens. The first, second and third lens are with negative refractive power. The fourth, fifth, sixth and seventh lens are with refractive power. The eighth lens is a biconvex lens with positive refractive power. The ninth lens is a biconvex lens with positive refractive power. The first lens, the second lens and the third lens satisfy −26<f₁/f<f₂/f<f₃/f<−3 and −1.64<f₁₂₃/f<−1.6, wherein f₁is an effective focal length of the first lens, f₂is an effective focal length of the second lens, f₃is an effective focal length of the third lens, f is an effective focal length of the wide-angle lens, and f₁₂₃is an effective focal length of the combination of the first lens, the second lens and the third lens.

In another exemplary embodiment, the eighth lens and the ninth lens satisfy 30<D/D<271, wherein D is an interval between an object side surface of the first lens and an image plane along the optical axis, and D₈₉is an interval between an image side surface of the eighth lens and an object side surface of the ninth lens along the optical axis.

In yet another exemplary embodiment, the fourth lens satisfies −226<R₄₁/f<19, wherein R₄₁is a radius of curvature of an object side surface of the fourth lens and f is an effective focal length of the wide-angle lens.

In another exemplary embodiment, the sixth lens satisfies −63<R₆₁/f<7, wherein R₆₁is a radius of curvature of an object side surface of the sixth lens and f is an effective focal length of the wide-angle lens.

In yet another exemplary embodiment, the ninth lens satisfies 4.2<f₉/f<5.6, wherein f₉is an effective focal length of the ninth lens and f is an effective focal length of the wide-angle lens.

In another exemplary embodiment, the fifth lens, the sixth lens, the seventh lens and the eighth lens satisfy −16<f₇₈/f₅₆<254, wherein f₇₈is an effective focal length of the combination of the seventh lens and the eighth lens, and f₅₆is an effective focal length of the combination of the fifth lens and the sixth lens.

In yet another exemplary embodiment, the wide-angle lens satisfies −0.7<f₆₇₈₉/f₁₂₃₄₅<0.8, wherein f₁₂₃₄₅is an effective focal length of the combination of the first lens, the second lens, the third lens, the fourth lens and the fifth lens, and f₆₇₈₉is an effective focal length of the combination of the sixth lens, the seventh lens, the eighth lens and the ninth lens.

In another exemplary embodiment, the fourth lens and the fifth lens form a first cemented lens, and the sixth lens and the seventh lens form a second cemented lens.

In yet another exemplary embodiment, the wide-angle lens further includes an aperture disposed between the fifth lens and the sixth lens.

In another exemplary embodiment, the wide-angle lens further includes an aperture disposed between the fourth lens and the seventh lens.

In yet another exemplary embodiment, the fourth lens is with negative refractive power, the fifth lens is with positive refractive power, the sixth lens is with positive refractive power and the seventh lens is with negative refractive power.

In another exemplary embodiment, at least one surface of the second lens is an aspheric surface.

In yet another exemplary embodiment, at least one surface of the third lens is an aspheric surface.

In another exemplary embodiment, at least one surface of the ninth lens is an aspheric surface.

In yet another exemplary embodiment, the second lens is made of glass material.

In another exemplary embodiment, the third lens is made of glass material.

In yet another exemplary embodiment, the ninth lens is made of glass material.

In another exemplary embodiment, the wide-angle lens further includes an optical filter disposed between the ninth lens and an image plane.

A detailed description is given in the following embodiments with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein:

FIG. 1 is a lens layout diagram of a wide-angle lens in accordance with a first embodiment of the invention;

FIG. 2A depicts a longitudinal aberration diagram of the wide-angle lens assembly in accordance with the first embodiment of the invention;

FIG. 2B is a field curvature diagram of the wide-angle lens in accordance with the first embodiment of the invention;

FIG. 2C is a distortion diagram of the wide-angle lens in accordance with the first embodiment of the invention;

FIG. 2D is a lateral color diagram of the wide-angle lens in accordance with the first embodiment of the invention;

FIGS. 2E-2G are transverse ray fan diagrams of the wide-angle lens in accordance with the first embodiment of the invention;

FIG. 3 is a lens layout diagram of a wide-angle lens in accordance with a second embodiment of the invention;

FIG. 4A depicts a longitudinal aberration diagram of the wide-angle lens assembly in accordance with the second embodiment of the invention;

FIG. 4B is a field curvature diagram of the wide-angle lens in accordance with the second embodiment of the invention;

FIG. 4C is a distortion diagram of the wide-angle lens in accordance with the second embodiment of the invention;

FIG. 4D is a lateral color diagram of the wide-angle lens in accordance with the second embodiment of the invention;

FIGS. 4E-4G are transverse ray fan diagrams of the wide-angle lens in accordance with the second embodiment of the invention;

FIG. 5 is a lens layout diagram of a wide-angle lens in accordance with a third embodiment of the invention;

FIG. 6A depicts a longitudinal aberration diagram of the wide-angle lens assembly in accordance with the third embodiment of the invention;

FIG. 6B is a field curvature diagram of the wide-angle lens in accordance with the third embodiment of the invention;

FIG. 6C is a distortion diagram of the wide-angle lens in accordance with the third embodiment of the invention;

FIG. 6D is a lateral color diagram of the wide-angle lens in accordance with the third embodiment of the invention; and

FIGS. 6E-6G are transverse ray fan diagrams of the wide-angle lens in accordance with the third embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The following description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the appended claims.

Referring to FIG. 1, FIG. 1 is a lens layout diagram of a wide-angle lens in accordance with a first embodiment of the invention. The wide-angle lens 1, from an object side to an image side along an optical axis OA1, includes a first lens L11, a second lens L12, a third lens L13, a fourth lens L14, a fifth lens L15, an aperture ST1, a sixth lens L16, a seventh lens L17, an eighth lens L18, a ninth lens L19, an optical filter OF1 and a cover glass CG1. In operation, an image of light rays from the object side is formed at an image plane IMA1. The first lens L11 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S11 is a convex surface, the image side surface S12 is a concave surface and both of the object side surface S11 and image side surface S12 are spherical surfaces. The second lens L12 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S13 is a convex surface, the image side surface S14 is a concave surface and both of the object side surface S13 and image side surface S14 are spherical surfaces. The third lens L13 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S15 is a convex surface, the image side surface S16 is a concave surface and both of the object side surface S15 and image side surface S16 are aspheric surfaces. The fourth lens L14 is a convex-concave lens and made of glass material, wherein the object side surface S17 is a convex surface, the image side surface S18 is a concave surface and both of the object side surface S17 and image side surface S18 are spherical surfaces. The fifth lens L15 is a biconvex lens and made of glass material, wherein both of the object side surface S18 and image side surface S19 are spherical surfaces. The sixth lens L16 is a biconvex lens and made of glass material, wherein both of the object side surface S111 and image side surface S112 are spherical surfaces. The seventh lens L17 is a biconcave lens and made of glass material, wherein both of the object side surface S112 and image side surface S113 are spherical surfaces. The eighth lens L18 is a biconvex lens and made of glass material, wherein both of the object side surface S114 and image side surface S115 are spherical surfaces. The ninth lens L19 is a biconvex lens and made of glass material, wherein both of the object side surface S116 and image side surface S117 are aspheric surfaces. The fourth lens L14 and the fifth lens L15 are cemented together to form a cemented lens. The sixth lens L16 and the seventh lens L17 are cemented together to form a cemented lens. Both of the object side surface S118 and image side surface S119 of the optical filter OF1 are plane surfaces. Both of the object side surface S120 and image side surface S121 of the cover glass CG1 are plane surfaces.

In order to maintain excellent optical performance of the wide-angle lens in accordance with the first embodiment of the invention, the wide-angle lens 1 must satisfies the following eight conditions:

−26<f1₁/f1<f1₂/f1<f1₃/f1<−3 (1)

−1.64<f1₁₂₃/f1<−1.6 (2)

30<D1/D1₈₉<271 (3)

−226<R1₄₁f1<19 (4)

−63<R1₆₁/f1<7 (5)

4.2<f1₉/f1<5.6 (6)

−16<f1₇₈/f1₅₆<254 (7)

−0.7<f1₆₇₈₉/f1₁₂₃₄₅<0.8 (8)

wherein f1₁is an effective focal length of the first lens L11, f1₂is an effective focal length of the second lens L12, f1₃is an effective focal length of the third lens L13, f1 is an effective focal length of the wide-angle lens 1, f1₁₂₃is an effective focal length of the combination of the first lens L11, the second lens L12 and the third lens L13, D1 is an interval between the object side surface S11 of the first lens L11 and the image plane IMA1 along the optical axis OA1, D1₈₉is an interval between the image side surface S115 of the eighth lens L18 and the object side surface S116 of the ninth lens L19 along the optical axis OA1, R1₄₁is a radius of curvature of the object side surface S17 of the fourth lens L14, R1₆₁is a radius of curvature of the object side surface S111 of the sixth lens L16, f1₉is an effective focal length of the ninth lens L19, f1₇₈is an effective focal length of the combination of the seventh lens L17 and the eighth lens L18, f1₅₆is an effective focal length of the combination of the fifth lens L15 and the sixth lens L16, f1₁₂₃₄₅is an effective focal length of the combination of the first lens L11, the second lens L12, the third lens L13, the fourth lens L14 and the fifth lens L15, and f1₆₇₈₉is an effective focal length of the combination of the sixth lens L16, the seventh lens L17, the eighth lens L18 and the ninth lens L19.

By the above design of the lenses and the aperture ST1, the wide-angle lens 1 is provided with a shortened total lens length, an increased field of view and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the wide-angle lens 1 in accordance with the first embodiment of the invention is provided with the optical specifications shown in Table 1, which include the effective focal length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens and Abbe number of each lens. Table 1 shows that the effective focal length is equal to 0.8054 mm and F-number is equal to 2.8 for the wide-angle lens 1 of the first embodiment of the invention.

TABLE 1

Effective Focal Length = 0.8054 mm F-number = 2.8

Surface
Radius of
Thickness

Number
Curvature (mm)
(mm)
Nd
Vd
Remark

S11
19.3
3.32
1.788001
47.368522
The First Lens L11

S12
8.2
3.01

S13
14.26
1.05
1.788001
47.368522
The Second Lens L12

S14
4.65
2.3

S15
10.616
1
1.75046
45.428159
The Third Lens L13

S16
1.603
1.68

S17
8.2
0.8
1.740999
52.636502
The Fourth Lens L14

S18
2.38
4.87
1.84666
23.77794
The Fifth Lens L15

S19
−19.3
0.35

S110
∞
0.16

Aperture ST1

S111
5.1
1.28
1.696797
55.532241
The Sixth Lens L16

S112
−2.38
0.52
1.84666
23.77794
The Seventh Lens L17

S113
8.2
0.2

S114
6.44
2
1.58913
61.135024
The Eighth Lens L18

S115
−6.44
0.1

Interval D1₈₉

S116
3.778
2.28
1.56073
57.101819
The Ninth Lens L19

S117
−4.823
0.2

S118
∞
0.3
1.5168
64.167336
Optical Filter OF1

S119
∞
0.948

S120
∞
0.5
1.5168
64.167336
Cover Glass CG1

S121
∞
0.175

The aspheric surface sag z of each lens in table 1 can be calculated by the following formula:

z=ch
²/{1+[1−(k+1)c2h²]^1/2}+Ah⁴+Bh⁶+Ch⁸+Dh¹⁰+Eh¹²+Fh¹⁴

where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E and F are aspheric coefficients.

In the first embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F of each surface are shown in Table 2.

TABLE 2

Surface

Number
k
A
B
c
D
E
F

S15
2.065979
−2.44E−04
−1.20E−04
3.55E−06
1.28E−07
−7.25604E−09
0

S16
−0.9641265
0.001570318
−0.000233663
−3.21E−05
6.09E−06
−3.78E−07
0

S116
−1.212168
−8.22E−04
−7.44E−06
6.09E−08
1.47E−06
−3.40716E−07
−1.51881E−07

S117
−9.345112
4.34E−03
7.88E−05
−2.17E−05
−3.14625E−06
−5.59517E−07
−3.2104E−08

For the wide-angle lens 1 of the first embodiment, the effective focal length f1₁of the first lens L11 is equal to −20.8395 mm, the effective focal length f1₂of the second lens L12 is equal to 9.1988 mm, the effective focal length f1₃of the third lens L13 is equal to −2.6414 mm, the effective focal length f1 of the wide-angle lens 1 is equal to 0.8054 mm, the effective focal length f1₁₂₃of the combination of the first lens L11, the second lens L12 and the third lens L13 is equal to −1.3101 mm, the interval D1 between the object side surface S11 of the first lens L11 and the image plane IMA1 along the optical axis OA1 is equal to 27.043 mm, the interval D1₈₉between the image side surface S115 of the eighth lens L18 and the object side surface S116 of the ninth lens L19 along the optical axis OA1 is equal to 0.1 mm, the radius of curvature R1₄₁of the object side surface S17 of the fourth lens L14 is equal to 8.2 mm, the radius of curvature R1₆₁of the object side surface S111 of the sixth lens L16 is equal to 5.1 mm, the effective focal length f1₉of the ninth lens L19 is equal to 4.1756 mm, the effective focal length f1₇₈of the combination of the seventh lens L17 and the eighth lens L18 is equal to 98.4482 mm, the effective focal length f1₅₆of the combination of the fifth lens L15 and the sixth lens L16 is equal to 6.2650 mm, the effective focal length f1₁₂₃₄₅of the combination of the first lens L11, the second lens L12, the third lens L13, the fourth lens L14 and the fifth lens L15 is equal to 4.9129 mm, and the effective focal length f1₆₇₈₉of the combination of the sixth lens L16, the seventh lens L17, the eighth lens L18 and the ninth lens L19 is equal to 3.2963 mm. According to the above data, the following values can be obtained:

f1₁/f1=−25.8749,

f1₂/f1=−−11.4215,

f1₃/f1=−3.2797,

D1/D1₈₉=270.43,

R1₄₁/f1=10.1814,

R1₆₁/f1=6.3323,

f1₉/f1=5.1846,

f1₇₈/f1₅₆=−15.7140,

f1₆₇₈₉/f1₁₂₃₄₅=−0.6710,

which respectively satisfy the above conditions (1)-(8).

By the above arrangements of the lenses and the aperture ST1, the wide-angle lens 1 of the first embodiment can meet the requirements of optical performance as seen in FIGS. 2A-2G, wherein FIG. 2A shows the longitudinal aberration diagram of the wide-angle lens 1 in accordance with the first embodiment of the invention, FIG. 2B shows the field curvature diagram of the wide-angle lens 1 in accordance with the first embodiment of the invention, FIG. 2C shows the distortion diagram of the wide-angle lens 1 in accordance with the first embodiment of the invention, FIG. 2D shows the lateral color diagram of the wide-angle lens 1 in accordance with the first embodiment of the invention and FIGS. 2E-2G show the transverse ray fan diagrams of the wide-angle lens 1 in accordance with the first embodiment of the invention.

It can be seen from FIG. 2A that the longitudinal aberration in the wide-angle lens 1 of the first embodiment ranges from 0.001 mm to 0.008 mm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm. It can be seen from FIG. 2B that the field curvature of tangential direction and sagittal direction in the wide-angle lens 1 of the first embodiment ranges from 0.05 mm to 0.02 mm for the wavelength of 0.546 μm. It can be seen from FIG. 2C that the distortion in the wide-angle lens 1 of the first embodiment ranges from 200% to 0% for the wavelength of 0.546 μm. It can be seen from FIG. 2D that the lateral color with reference wavelength of 0.587 μm in the wide-angle lens 1 of the first embodiment ranges from 7 μm to 7 μm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm, with field ranged from 0 degrees to 107 degrees. It can be seen from FIGS. 2E-2G that the transverse ray aberration in the wide-angle lens 1 of the first embodiment ranges from 5.0 μm to 13.0 μm wherein the wavelength is 0.438 μm, 0.546 μm and 0.656 μm for field of 0.00 degrees, 75.00 degrees and 107.00 degrees, respectively. It is obvious that the longitudinal aberration, the field curvature, the distortion, the lateral color and the transverse ray aberration of the wide-angle lens 1 of the first embodiment can be corrected effectively. Therefore, the wide-angle lens 1 of the first embodiment is capable of good optical performance.

Referring to FIG. 3, FIG. 3 is a lens layout diagram of a wide-angle lens in accordance with a second embodiment of the invention. The wide-angle lens 2, from an object side to an image side along an optical axis OA2, includes a first lens L21, a second lens L22, a third lens L23, a fourth lens L24, a fifth lens L25, an aperture ST2, a sixth lens L26, a seventh lens L27, an eighth lens L28, a ninth lens L29, an optical filter OF2 and a cover glass CG2. In operation, an image of light rays from the object side is formed at an image plane IMA2. The first lens L21 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S21 is a convex surface, the image side surface S22 is a concave surface and both of the object side surface S21 and image side surface S22 are spherical surfaces. The second lens L22 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S23 is a convex surface, the image side surface S24 is a concave surface and both of the object side surface S23 and image side surface S24 are aspheric surfaces. The third lens L23 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S25 is a convex surface, the image side surface S26 is a concave surface and both of the object side surface S25 and image side surface S26 are spherical surfaces. The fourth lens L24 is a biconcave lens and made of glass material, wherein both of the object side surface S27 and image side surface S28 are spherical surfaces. The fifth lens L25 is a biconvex lens and made of glass material, wherein both of the object side surface S28 and image side surface S29 are spherical surfaces. The sixth lens L26 is a biconvex lens and made of glass material, wherein both of the object side surface S211 and image side surface S212 are spherical surfaces. The seventh lens L27 is a biconcave lens and made of glass material, wherein both of the object side surface S212 and image side surface S213 are spherical surfaces. The eighth lens L28 is a biconvex lens and made of glass material, wherein both of the object side surface S214 and image side surface S215 are spherical surfaces. The ninth lens L29 is a biconvex lens and made of glass material, wherein both of the object side surface S216 and image side surface S217 are aspheric surfaces. The fourth lens L24 and the fifth lens L25 are cemented together to form a cemented lens. The sixth lens L26 and the seventh lens L27 are cemented together to form a cemented lens. Both of the object side surface S218 and image side surface S219 of the optical filter OF2 are plane surfaces. Both of the object side surface S220 and image side surface S221 of the cover glass CG2 are plane surfaces.

In order to maintain excellent optical performance of the wide-angle lens in accordance with the second embodiment of the invention, the wide-angle lens 2 must satisfies the following eight conditions:

−26<f2₁/f2<f2₂/f2<f2₃/f2<−3 (9)

−1.64<f 2₁₂₃/f2<−1.6 (10)

30<D2/D2₈₉<271 (11)

−226<R2₄₁/f2<19 (12)

−63<R2₆₁/f2<7 (13)

4.2<f2₉/f2<5.6 (14)

−16<f2₂₈/f2₅₆<254 (15)

−0.7<f2₆₇₈₉/f2₁₂₃₄₅<0.8 (16)

wherein f2₁is an effective focal length of the first lens L21, f2₂is an effective focal length of the second lens L22, f2₃is an effective focal length of the third lens L23, f2 is an effective focal length of the wide-angle lens 2, f2₁₂₃is an effective focal length of the combination of the first lens L21, the second lens L22 and the third lens L23, D2 is an interval between the object side surface S21 of the first lens L21 and the image plane IMA2 along the optical axis OA2, D2₈₉is an interval between the image side surface S215 of the eighth lens L28 and the object side surface S216 of the ninth lens L29 along the optical axis OA2, R2₄₁is a radius of curvature of the object side surface S27 of the fourth lens L24, R2₆₁is a radius of curvature of the object side surface S211 of the sixth lens L26, f2₉is an effective focal length of the ninth lens L29, f2₇₈is an effective focal length of the combination of the seventh lens L27 and the eighth lens L28, f2₅₆is an effective focal length of the combination of the fifth lens L25 and the sixth lens L26, f2₁₂₃₄₅is an effective focal length of the combination of the first lens L21, the second lens L22, the third lens L23, the fourth lens L24 and the fifth lens L25, and f2₆₇₈₉is an effective focal length of the combination of the sixth lens L26, the seventh lens L27, the eighth lens L28 and the ninth lens L29.

By the above design of the lenses and the aperture ST2, the wide-angle lens 2 is provided with a shortened total lens length, an increased field of view and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the wide-angle lens 2 in accordance with the second embodiment of the invention is provided with the optical specifications shown in Table 3, which include the effective focal length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens and Abbe number of each lens. Table 3 shows that the effective focal length is equal to 0.8059 mm and F-number is equal to 2.8 for the wide-angle lens 2 of the second embodiment of the invention.

TABLE 3

Effective Focal Length = 0.8059 mm F-number = 2.8

Surface
Radius of
Thickness

Number
Curvature (mm)
(mm)
Nd
Vd
Remark

S21
24.28688
2.481849
1.788001
47.368522
The First Lens L21

S22
8.286387
3.059764

S23
15.64951
1.543395
1.69003
52.755504
The Second Lens L22

S24
4.705134
2.022385

S25
105.7127
2.283504
1.743299
49.221606
The Third Lens L23

S26
2.152162
1.19825

S27
−181.5149
0.5296468
1.740999
52.636502
The Fourth Lens L24

S28
2.279892
3.080823
1.84666
23.77794
The Fifth Lens L25

S29
−7.17175
0.1000026

S210
∞
0.6626973

Aperture ST2

S211
4.395139
1.306946
1.696797
55.532241
The Sixth Lens L26

S212
−2.108207
0.7123469
1.84666
23.77794
The Seventh Lens L27

S213
7.453903
0.09926276

S214
5.9582
1.928571
1.58913
61.135024
The Eighth Lens L28

S215
−6.794451
0.191463

Interval D2₈₉

S216
3.605159
1.593348
1.56073
57.101819
The Ninth Lens L29

S217
−4.956414
0.2

S218
∞
0.3
1.5168
64.167336
Optical Filter OF2

S219
∞
0.948

S220
∞
0.5
1.5168
64.167336
Cover Glass CG2

S221
∞
0.2215161

The aspheric surface sag z of each lens in table 3 can be calculated by the following formula:

z=ch
²/{1+[1−(k+1)c²h²]^1/2}Ah⁴+Bh⁶+Ch⁸+Dh¹⁰+Eh¹²+Fh¹⁴

where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E and F are aspheric coefficients.

In the second embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F of each surface are shown in Table 4.

TABLE 4

Surface

Number
k
A
B
c
D
E
F

S23
2.198471
0.000329868
−5.51E−07
−3.00E−08
−5.52E−10
6.05E−12
0

S24
−0.1333299
−0.000898423
−2.68E−05
−7.15E−07
−3.27E−08
−2.34E−09
0

S216
−0.9930042
−0.000113482
1.04E−05
1.79E−06
3.41E−06
−1.22E−07
−2.34E−07

S217
−11.08184
0.00664027
0.000285495
6.60E−07
−1.13E−06
−4.55E−07
−1.78E−09

For the wide-angle lens 2 of the second embodiment, the effective focal length f2₁of the first lens L21 is equal to −17.1318 mm, the effective focal length f2₂of the second lens L22 is equal to −10.3453 mm, the effective focal length f2₃of the third lens L23 is equal to 2.9835 mm, the effective focal length f2 of the wide-angle lens 2 is equal to 0.8059 mm, the effective focal length f2₁₂₃of the combination of the first lens L21, the second lens L22 and the third lens L23 is equal to 1.3211 mm, the interval D2 between the object side surface S21 of the first lens L21 and the image plane IMA2 along the optical axis OA2 is equal to 24.9638 mm, the interval D2₈₉between the image side surface S215 of the eighth lens L28 and the object side surface S216 of the ninth lens L29 along the optical axis OA2 is equal to 0.1915 mm, the radius of curvature R2₄₁of the object side surface S27 of the fourth lens L24 is equal to 181.5149 mm, the radius of curvature R2₆₁of the object side surface S211 of the sixth lens L26 is equal to 4.3951 mm, the effective focal length f2₉of the ninth lens L29 is equal to 3.9886 mm, the effective focal length f2₇₈of the combination of the seventh lens L27 and the eighth lens L28 is equal to 1667.5455 mm, the effective focal length f2₅₆of the combination of the fifth lens L25 and the sixth lens L26 is equal to 6.5694 mm, the effective focal length f2₁₂₃₄₅of the combination of the first lens L21, the second lens L22, the third lens L23, the fourth lens L24 and the fifth lens L25 is equal to 5.7721 mm, and the effective focal length f2₆₇₈₉of the combination of the sixth lens L26, the seventh lens L27, the eighth lens L28 and the ninth lens L29 is equal to 3.2366 mm. According to the above data, the following values can be obtained:

f2₁/f2=−21.2586,

f2₂/f2=−12.8374

f2₃/f2=−3.7021

f2₁₂₃/f2=−1.6394,

D2/D2₈₉=130.3843,

R2₄₁/f2=−225.2387,

R2₆₁/f2=5.4539,

f2₉/f2=4.9493,

f2₇₈/f2₅₆=−253.8345,

f2₆₇₈₉/f2₁₂₃₄₅=−0.5607,

which respectively satisfy the above conditions (9)-(16).

By the above arrangements of the lenses and the aperture ST2, the wide-angle lens 2 of the second embodiment can meet the requirements of optical performance as seen in FIGS. 4A-4G, wherein FIG. 4A shows the longitudinal aberration diagram of the wide-angle lens 2 in accordance with the second embodiment of the invention, FIG. 4B shows the field curvature diagram of the wide-angle lens 2 in accordance with the second embodiment of the invention, FIG. 4C shows the distortion diagram of the wide-angle lens 2 in accordance with the second embodiment of the invention, FIG. 4D shows the lateral color diagram of the wide-angle lens 2 in accordance with the second embodiment of the invention and FIGS. 4E-4G show the transverse ray fan diagrams of the wide-angle lens 2 in accordance with the second embodiment of the invention.

It can be seen from FIG. 4A that the longitudinal aberration in the wide-angle lens 2 of the second embodiment ranges from 0.008 mm to 0.015 mm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm. It can be seen from FIG. 4B that the field curvature of tangential direction and sagittal direction in the wide-angle lens 2 of the second embodiment ranges from 0.20 mm to 0.01 mm for the wavelength of 0.546 μm. It can be seen from FIG. 4C that the distortion in the wide-angle lens 2 of the second embodiment ranges from 200% to 0% for the wavelength of 0.546 μm. It can be seen from FIG. 4D that the lateral color with reference wavelength of 0.587 μm in the wide-angle lens 2 of the second embodiment ranges from 6 μm to 7 μm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm, with field ranged from 0 degrees to 107 degrees. It can be seen from FIGS. 4E-4G that the transverse ray aberration in the wide-angle lens 2 of the second embodiment ranges from 27.5 μm to 44.5 μm wherein the wavelength is 0.438 μm, 0.546 μm and 0.656 μm for field of 0.00 degrees, 75.00 degrees and 107.00 degrees, respectively. It is obvious that the longitudinal aberration, the field curvature, the distortion, the lateral color and the transverse ray aberration of the wide-angle lens 2 of the second embodiment can be corrected effectively. Therefore, the wide-angle lens 2 of the second embodiment is capable of good optical performance

Referring to FIG. 5, FIG. 5 is a lens layout diagram of a wide-angle lens in accordance with a third embodiment of the invention. The wide-angle lens 3, from an object side to an image side along an optical axis OA3, includes a first lens L31, a second lens L32, a third lens L33, a fourth lens L34, a fifth lens L35, an aperture ST3, a sixth lens L36, a seventh lens L37, an eighth lens L38, a ninth lens L39, an optical filter OF3 and a cover glass CG3. In operation, an image of light rays from the object side is formed at an image plane IMA3. The first lens L31 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S31 is a convex surface, the image side surface S32 is a concave surface and both of the object side surface S31 and image side surface S32 are spherical surfaces. The second lens L32 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S33 is a convex surface, the image side surface S34 is a concave surface and both of the object side surface S33 and image side surface S34 are spherical surfaces. The third lens L33 is a convex-concave lens, made of glass material and with negative refractive power, wherein the object side surface S35 is a convex surface, the image side surface S36 is a concave surface and both of the object side surface S35 and image side surface S36 are aspheric surfaces. The fourth lens L34 is a convex-concave lens and made of glass material, wherein the object side surface S37 is a convex surface, the image side surface S38 is a concave surface and both of the object side surface S37 and image side surface S38 are spherical surfaces. The fifth lens L35 is a biconvex lens and made of glass material, wherein both of the object side surface S38 and image side surface S39 are spherical surfaces. The sixth lens L36 is a concave-convex lens and made of glass material, wherein the object side surface S311 is a concave surface, the image side surface S312 is a convex surface and both of the object side surface S311 and image side surface S312 are spherical surfaces. The seventh lens L37 is a biconcave lens and made of glass material, wherein both of the object side surface S312 and image side surface S313 are spherical surfaces. The eighth lens L38 is a biconvex lens and made of glass material, wherein both of the object side surface S314 and image side surface S315 are spherical surfaces. The ninth lens L39 is a biconvex lens and made of glass material, wherein both of the object side surface S316 and image side surface S317 are aspheric surfaces. The fourth lens L34 and the fifth lens L35 are cemented together to form a cemented lens. The sixth lens L36 and the seventh lens L37 are cemented together to form a cemented lens. Both of the object side surface S318 and image side surface S319 of the optical filter OF3 are plane surfaces. Both of the object side surface S320 and image side surface S321 of the cover glass CG3 are plane surfaces.

In order to maintain excellent optical performance of the wide-angle lens in accordance with the third embodiment of the invention, the wide-angle lens 3 must satisfies the following eight conditions:

−26<f3₁/f3<f3₂/f3<f3₃/f3<−3 (17)

−1.64<f3₁₂₃/f3<−1.6 (18)

30<D3/D3₈₉<271 (19)

−226<R3₄₁/f3<19 (20)

−63<R3₆₁/f3<7 (21)

4.2<f3₉/f3<5.6 (22)

−16<f3/f3₅₆<254 (23)

−0.7<f3₆₇₈₉/f3₁₂₃₄₅<0.8 (24)

wherein f3₁is an effective focal length of the first lens L31, f3₂is an effective focal length of the second lens L32, f3₃is an effective focal length of the third lens L33, f3 is an effective focal length of the wide-angle lens 3, f3₁₂₃is an effective focal length of the combination of the first lens L31, the second lens L32 and the third lens L33, D3 is an interval between the object side surface S31 of the first lens L31 and the image plane IMA3 along the optical axis OA3, D3₈₉is an interval between the image side surface S315 of the eighth lens L38 and the object side surface S316 of the ninth lens L39 along the optical axis OA3, R3₄₁is a radius of curvature of the object side surface S37 of the fourth lens L34, R3₆₁is a radius of curvature of the object side surface S311 of the sixth lens L36, f3₉is an effective focal length of the ninth lens L39, f3₇₈is an effective focal length of the combination of the seventh lens L37 and the eighth lens L38, f3₅₆is an effective focal length of the combination of the fifth lens L35 and the sixth lens L36, f3₁₂₃₄₅is an effective focal length of the combination of the first lens L31, the second lens L32, the third lens L33, the fourth lens L34 and the fifth lens L35, and f3₆₇₈₉is an effective focal length of the combination of the sixth lens L36, the seventh lens L37, the eighth lens L38 and the ninth lens L39.

By the above design of the lenses and the aperture ST3, the wide-angle lens 3 is provided with a shortened total lens length, an increased field of view and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the wide-angle lens 3 in accordance with the third embodiment of the invention is provided with the optical specifications shown in Table 5, which include the effective focal length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens and Abbe number of each lens. Table 5 shows that the effective focal length is equal to 0.8054 mm and F-number is equal to 2.8 for the wide-angle lens 3 of the third embodiment of the invention.

TABLE 5

Effective Focal Length = 0.8054 mm F-number = 2.8

Surface
Radius of
Thickness

Number
Curvature (mm)
(mm)
Nd
Vd
Remark

S31
19.31827
3.590254
1.834
37.160487
The First Lens L31

S32
8.199993
2.999932

S33
14.18683
1.142584
1.743299
49.221606
The Second Lens L32

S34
4.747653
1.98049

S35
10.5936
2.001565
1.743299
49.221606
The Third Lens L33

S36
1.518124
1.400966

S37
14.61463
0.4999947
1.696797
55.532241
The Fourth Lens L34

S38
2.725911
4.996861
1.84666
23.77794
The Fifth Lens L35

S39
−4.690879
0.1326738

S310
∞
0.1373505

Aperture ST3

S311
−50.00004
1.17864
1.696797
55.532241
The Sixth Lens L36

S312
−1.807204
0.5167029
1.84666
23.77794
The Seventh Lens L37

S313
15.27071
0.09996228

S314
4.808219
2.034078
1.58913
61.135024
The Eighth Lens L38

S315
−8.122065
0.8981988

Interval D3₈₉

S316
4.04169
2.092175
1.58913
61.135024
The Ninth Lens L39

S317
−3.981513
0.2

S318
∞
0.3
1.5168
64.167336
Optical Filter OF3

S319
∞
0.948

S320
∞
0.5
1.5168
64.167336
Cover Glass CG3

S321
∞
0.151991

The aspheric surface sag z of each lens in table 5 can be calculated by the following formula:

z=ch
²/{1+[1−(k+1)c²h²]^1/2}+Ah⁴+Bh⁶+Ch⁸+Dh¹⁰+Eh¹²+Fh¹⁴

where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E and F are aspheric coefficients.

In the third embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F of each surface are shown in Table 6.

TABLE 6

Surface

Number
k
A
B
C
D
E
F

S35
1.899669
−0.000269805
−0.000121194
3.65E−06
1.39E−07
−6.78E−09
0

S36
−0.9248761
0.003237759
−0.000167584
0
4.03E−05
0
0

S316
−0.9840762
−0.000370541
9.57E−05
3.43E−05
−6.13E−06
0
0

S317
−8.476654
0.00523031
0.000313991
0
0
0
0

For the wide-angle lens 3 of the third embodiment, the effective focal length f3₁of the first lens L31 is equal to 20.0225 mm, the effective focal length f3₂of the second lens L32 is equal to 10.1217 mm, the effective focal length f3₃of the third lens L33 is equal to 2.6314 mm, the effective focal length f3 of the wide-angle lens 3 is equal to 0.8054 mm, the effective focal length f3₁₂₃of the combination of the first lens L31, the second lens L32 and the third lens L33 is equal to 1.2912 mm, the interval D3 between the object side surface S31 of the first lens L31 and the image plane IMA3 along the optical axis OA3 is equal to 27.8024 mm, the interval D3₈₉between the image side surface S315 of the eighth lens L38 and the object side surface S316 of the ninth lens L39 along the optical axis OA3 is equal to 0.8982 mm, the radius of curvature R3₄₁of the object side surface S37 of the fourth lens L34 is equal to 14.6146 mm, the radius of curvature R3₆₁of the object side surface S311 of the sixth lens L36 is equal to 50.0000 mm, the effective focal length f3₉of the ninth lens L39 is equal to 3.7687 mm, the effective focal length f3₇₈of the combination of the seventh lens L37 and the eighth lens L38 is equal to 6.4432 mm, the effective focal length f3₅₆of the combination of the fifth lens L35 and the sixth lens L36 is equal to 4.3457 mm, the effective focal length f3₁₂₃₄₅of the combination of the first lens L31, the second lens L32, the third lens L33, the fourth lens L34 and the fifth lens L35 is equal to 4.2520 mm, and the effective focal length f3₆₇₈₉of the combination of the sixth lens L36, the seventh lens L37, the eighth lens L38 and the ninth lens L39 is equal to 3.1448 mm. According to the above data, the following values can be obtained:

f3₁/f3=−24.8601,

f3₂/f3=−12.5672

f3₃/f3=−3.2671

f3₁₂₃/f3=−1.6031,

D3/D3₈₉=30.9535,

R3₄₁/f3=18.1456,

R3₆₁/f3=−62.0803,

f3₉/f3=4.6792,

f3₇₈/f3₅₆=1.4826,

f3₆₇₈₉/f3₁₂₃₄₅=0.7396,

which respectively satisfy the above conditions (17)-(24).

By the above arrangements of the lenses and the aperture ST3, the wide-angle lens 3 of the third embodiment can meet the requirements of optical performance as seen in FIGS. 6A-6G, wherein FIG. 6A shows the longitudinal aberration diagram of the wide-angle lens 3 in accordance with the third embodiment of the invention, FIG. 6B shows the field curvature diagram of the wide-angle lens 3 in accordance with the third embodiment of the invention, FIG. 6C shows the distortion diagram of the wide-angle lens 3 in accordance with the third embodiment of the invention, FIG. 6D shows the lateral color diagram of the wide-angle lens 3 in accordance with the third embodiment of the invention and FIGS. 6E-6G show the transverse ray fan diagrams of the wide-angle lens 3 in accordance with the third embodiment of the invention.

It can be seen from FIG. 6A that the longitudinal aberration in the wide-angle lens 3 of the third embodiment ranges from 0.001 mm to 0.006 mm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm. It can be seen from FIG. 6B that the field curvature of tangential direction and sagittal direction in the wide-angle lens 3 of the third embodiment ranges from 20 μm to 4 μm for the wavelength of 0.546 μm. It can be seen from FIG. 6C that the distortion in the wide-angle lens 3 of the third embodiment ranges from 200% to 0% for the wavelength of 0.546 μm. It can be seen from FIG. 6D that the lateral color with reference wavelength of 0.587 μm in the wide-angle lens 3 of the third embodiment ranges from 5 μm to 6 μm for the wavelength of 0.438 μm, 0.486 μm, 0.546 μm, 0.587 μm and 0.656 μm, with field ranged from 0 degrees to 107 degrees. It can be seen from FIGS. 6E-6G that the transverse ray aberration in the wide-angle lens 3 of the third embodiment ranges from 8.0 μm to 8.5 μm wherein the wavelength is 0.438 μm, 0.546 μm and 0.656 μm for field of 0.00 degrees, 75.00 degrees and 107.00 degrees, respectively. It is obvious that the longitudinal aberration, the field curvature, the distortion, the lateral color and the transverse ray aberration of the wide-angle lens 3 of the third embodiment can be corrected effectively. Therefore, the wide-angle lens 3 of the third embodiment is capable of good optical performance.

Wide-Angle Lens

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