Optical system, image pickup apparatus, in-vehicle system, and moving apparatus
An optical system includes, in order from an enlargement conjugate side to a reduction conjugate side, a front unit including a plurality of lenses, an aperture stop, and a rear unit including a plurality of lenses. A projection characteristic of the optical system representing a relationship between a half angle of view and an image height on an image plane satisfies a predetermined condition.
1. An optical system comprising, in order from an enlargement conjugate side to a reduction conjugate side, a front unit including a plurality of lenses, an aperture stop, and a rear unit including a plurality of lenses,
wherein the rear unit has a positive refractive power,
wherein a projection characteristic y(θ) of the optical system representing a relationship between a half angle of view θ and an image height y on an image plane satisfies the following inequality:
1
<
f
×
sin
θ
max
y
(
θ
max
)
≦
1
.
9
where θmax is a maximum half angle of view of the optical system, and f is a focal length of the optical system,
wherein a differential value dy(θ)/dθ at the half angle of view θ of the projection characteristic y(θ) has a local maximum value, and
wherein the differential value dy(θ)/dθ satisfies the following inequality:
0
.
0
3
≦
d
y
(
θ
)
d
θ
f
≦
0.15
at the maximum half angle of view θmax.
2. The optical system according to claim 1 , wherein the following inequality is satisfied:
0
.
1
5
≦
θ
a
θ
max
≦
0
.
3
5
where θa is a half angle of view at which the differential value dy(θ)/dθ has the local maximum value.
3. The optical system according to claim 1 , wherein the following inequality is satisfied:
y
(
θ
)
θ
>
f
at a half angle of view θ except for an angle of view of zero which is smaller than a half angle of view θa at which the differential value dy(θ)/dθ has the local maximum value.
4. The optical system according to claim 1 , wherein the following inequality is satisfied:
0.4
≦
θ
b
θ
max
≦
0
.
6
where θb is a half angle of view at which the differential value dy(θ)/dθ satisfies:
d
y
(
θ
)
d
θ
=
y
(
θ
max
)
θ
max
.
5. The optical system according to claim 1 , wherein the front unit includes a first aspherical lens.
6. The optical system according to claim 5 , wherein the first aspherical lens has a negative paraxial refractive power.
7. The optical system according to claim 5 , wherein the following conditional inequality is satisfied:
n
1
1
.
6
≧
1
.
0
where n 1 is a refractive index of the first aspherical lens for d-line.
8. The optical system according to claim 5 , wherein the front unit includes a second aspherical lens disposed on the reduction conjugate side of the first aspherical lens.
9. The optical system according to claim 8 , wherein the second aspherical lens has a meniscus shape with a convex surface facing the enlargement conjugate side.
10. The optical system according to claim 8 , wherein the following inequality is satisfied:
n
2
n
1
>
1
.
0
where n 1 is a refractive index of the first aspherical lens for d-line, and n 2 is a refractive index of the second aspherical lens for the d-line.
11. The optical system according to claim 8 , wherein each of the first aspherical lens and the second aspherical lens includes an aspherical surface having an inflection point.
12. The optical system according to claim 11 , wherein at least one of the first aspherical lens and the second aspherical lens includes an aspherical surface having a plurality of inflection points.
13. The optical system according to claim 1 , wherein the following inequality is satisfied:
|
f
f
a
|
≦
0
.
9
where fa is a focal length of the front unit.
14. The optical system according to claim 1 , wherein a lens closest to a reduction conjugate position has a positive paraxial refractive power and a positive refractive power at a periphery.
15. The optical system according to claim 1 , wherein the following inequality is satisfied:
θ
max
π
≧
7
1
8
.
16. An image pickup apparatus comprising:
the optical system according to claim 1 ; and
an image sensor configured to image an object via the optical system.
17. An in-vehicle system comprising:
the image pickup apparatus according to claim 16 ; and
a determiner configured to determine a likelihood of collision between a vehicle and the object based on distance information of the object acquired from the image pickup apparatus.
18. A moving apparatus comprising the image pickup apparatus according to claim 16 , and movable while holding the image pickup apparatus.
19. An optical system comprising, in order from an enlargement conjugate side to a reduction conjugate side, a front unit including a plurality of lenses, an aperture stop, and a rear unit including a plurality of lenses,
wherein the rear unit has a positive refractive power,
wherein a projection characteristic y(θ) of the optical system representing a relationship between a half angle of view θ and an image height y on an image plane satisfies the following inequality:
1
<
f
×
sin
θ
max
y
(
θ
max
)
≦
1.9
where θmax is a maximum half angle of view of the optical system, and f is a focal length of the optical system,
wherein a differential value dy(θ)/dθ at the half angle of view θ of the projection characteristic y(θ) has a local maximum value, and
wherein the following inequality is satisfied:
0.15
≦
θ
a
θ
max
≦
0.35
where θa is a half angle of view at which the differential value dy(θ)/dθ has the local maximum value.
20. An optical system comprising, in order from an enlargement conjugate side to a reduction conjugate side, a front unit including a plurality of lenses, an aperture stop, and a rear unit including a plurality of lenses,
wherein the rear unit has a positive refractive power,
wherein a projection characteristic y(θ) of the optical system representing a relationship between a half angle of view θ and an image height y on an image plane satisfies the following inequality:
1
<
f
×
sin
θ
max
y
(
θ
max
)
≦
1.9
where θmax is a maximum half angle of view of the optical system, and f is a focal length of the optical system,
wherein a differential value dy(θ)/dθ at the half angle of view θ of the projection characteristic y(θ) has a local maximum value, and
wherein the following inequality is satisfied:
0.4
≦
θ
b
θ
max
≦
0.6
where θb is a half angle of view at which the differential value dy(θ)/dθ satisfies:
dy
(
θ
)
d
θ
=
y
(
θ
max
)
θ
max
.
21. The optical system according to claim 1 , wherein a lens closest to the enlargement conjugate side has a negative refractive power.
22. The optical system according to claim 14 , wherein a lens adjacent to the lens closest to the reduction conjugate position has a negative refractive power.