Freeform imaging lens and freeform imaging system using the same
A freeform imaging lens defined in a (x, y, z) coordinate is provided. The freeform imaging lens comprises a first surface and a second surface opposite to the first surface. The first surface comprises a first freeform surface and a second freeform surface symmetrical about x-z plane. The first freeform surface and the second freeform surface are 5 th order xy-polynomial curve surfaces. The second surface is a 10 th order aspheric surface. The present disclosure also relates to a freeform imaging system using the above freeform imaging lens.
1. A freeform imaging lens, defined in a (x,y,z) coordinate, comprising:
a first surface and a second surface opposite to the first surface, wherein the first surface comprises a first freeform surface and a second freeform surface that are symmetrical about an x-z plane, the first freeform surface and the second freeform surface are both 5 th order xy-polynomial curve surfaces, and the second surface is a 10 th order aspheric surface, wherein an analytic form of the first freeform surface satisfies:
z
(
x
,
y
)
=
c
1
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
)
c
1
2
(
x
2
+
y
2
)
+
A
2
y
+
A
3
x
2
+
A
5
y
2
+
A
7
x
2
y
+
A
9
y
3
+
A
10
x
4
+
A
12
x
2
y
2
+
A
14
y
4
+
A
16
x
4
y
+
A
18
x
2
y
3
+
A
20
y
5
,
wherein, c 1 is curvature of the first freeform surface; k is a conic constant; A 2 , A 3 , A 5 , A 7 , A 9 , A 10 , A 12 , A 14 , A 16 , A 18 and A 20 are coefficients.
2. The freeform imaging lens of claim 1 , wherein values of the curvature c 1 , the conic constant k, and the coefficients A 2 , A 3 , A 5 , A 7 , A 9 , A 10 , A 12 , A 14 , A 16 , A 18 A 20 are listed as following:
c 1
−0.00840342361559533
k
−13.1593092531843
A 2
−5.52278890932116E−14
A 3
2.96489354878911E−03
A 5
2.91326939497068E−03
A 7
4.76838525024617E−08
A 9
7.82831155179962E−08
A 10
6.19731744269923E−07
A 12
−1.27490547215523E−08
A 14
−1.79954964051450E−07
A 16
−2.11928233145496E−08
A 18
−8.66202887985918E−10
A 20
9.97940014815302E−10.
3. The freeform imaging lens of claim 1 , wherein an analytic form of the second freeform surface satisfies:
z
(
x
,
y
)
=
c
2
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
′
)
c
2
2
(
x
2
+
y
2
)
+
A
2
′
y
+
A
3
′
x
2
+
A
5
′
y
2
+
A
7
′
x
2
y
+
A
9
′
y
3
+
A
10
′
x
4
+
A
12
′
x
2
y
2
+
A
14
′
y
4
+
A
16
′
x
4
y
+
A
18
′
x
2
y
3
+
A
20
′
y
5
,
wherein, c 2 is curvature; k′ is conic constant; A′ 2 , A′ 3 , A′ 5 , A′ 7 , A′ 9 , A′ 10 , A′ 12 , A′ 14 , A′ 16 , A′ 18 and A′ 20 are coefficients.
4. The freeform imaging lens of claim 3 , wherein values of the curvature c 2 , conic constant k′, and the coefficients A′ 2 , A′ 3 , A′ 5 , A′ 7 , A′ 9 , A′ 10 , A′ 12 , A′ 14 , A′ 16 , A′ 18 and A′ 20 are listed as following:
c 2
−0.00840342361559533
K′
−13.1593092531843
A′ 2
5.52278890932116E−14
A′ 3
2.96489354878911E−03
A′ 5
2.91326939497068E−03
A′ 7
−4.76838525024617E−08
A′ 9
−7.82131155179962E−08
A′ 10
6.19731744269923E−07
A′ 12
−1.27490547215523E−08
A′ 14
−1.79954964051450E−07
A′ 16
2.11928233145496E−08
A′ 18
8.66202887985918E−10
A′ 20
−9.97940014815302E−10.
5. The freeform imaging lens of claim 1 , wherein an analytic form of the second surface satisfies:
z
(
x
,
y
)
=
c
1
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
1
)
c
1
2
(
x
2
+
y
2
)
+
D
(
x
2
+
y
2
)
2
+
E
(
x
2
+
y
2
)
3
+
F
(
x
2
+
y
2
)
4
+
G
(
x
2
+
y
2
)
5
,
wherein, c 3 is curvature; k 1 is conic constant; D, E, F, and G are coefficients.
6. The freeform imaging lens of claim 5 , wherein values of the curvature c 3 , conic constant k 1 , and the coefficients D, E, F, G are listed as following:
c 3
0.00796808853571445
K 1
0.637349059540081
D
1.42634797718698E−07
E
−8.51981255927027E−12
F
9.81455629012912E−16
G
−1.30179502542930E−19.
7. A freeform imaging system, defined in a (x, y, z) coordinate, comprising:
a light source outputting a laser along a y-axis;
an entrance pupil located on a light path of the laser;
a reflector perpendicular to a y-z plane located on a side of the entrance pupil opposite to the light source and configured to reflect the laser to form a reflected light in the y-z plane, wherein the reflector has a center and is capable of revolve around the center;
a freeform imaging lens located on a light path of the reflected light comprising a front surface and a back surface opposite to the front surface, wherein the reflected light is refracted by the freeform imaging lens to form a refracted light, the front surface comprises a first freeform surface and a second freeform surface that are symmetrical about an x-z plane, the first freeform surface and the second freeform surface are both 5 th order xy-polynomial curve surfaces, and the back surface is a 10 th order aspheric surface; and
an image sensing element, parallel to a x-y plane, located on a light path of the refracted light, wherein an analytic form of the first freeform surface satisfies:
z
(
x
,
y
)
=
c
1
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
)
c
1
2
(
x
2
+
y
2
)
+
A
2
y
+
A
3
x
2
+
A
5
y
2
+
A
7
x
2
y
+
A
9
y
3
+
A
10
x
4
+
A
12
x
2
y
2
+
A
14
y
4
+
A
16
x
4
y
+
A
18
x
2
y
3
+
A
20
y
5
,
wherein, c 1 is curvature; k is conic constant; A 2 , A 3 , A 5 , A 7 , A 9 , A 10 , A 12 , A 14 , A 16 , A 18 and A 20 are coefficients.
8. The freeform imaging system of claim 7 , wherein values of the curvature c 1 , the conic constant k, and the coefficients A 2 , A 3 , A 5 , A 7 , A 9 , A 10 , A 12 , A 14 , A 16 , A 18 A 20 are listed as following:
c 1
−0.00840342361559533
k
−13.1593092531843
A 2
−5.52278890932116E−14
A 3
2.96489354878911E−03
A 5
2.91326939497068E−03
A 7
4.76838525024617E−08
A 9
7.82131155179962E−08
A 10
6.19731711269923E−07
A 12
−1.27490547215523E−08
A 14
−1.79954964051450E−07
A 16
−2.11928233145496E−08
A 18
−8.66202887985918E−10
A 20
9.97940014815302E−10.
9. The freeform imaging system of claim 7 , wherein an analytic form of the second freeform surface satisfies:
z
(
x
,
y
)
=
c
2
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
′
)
c
2
2
(
x
2
+
y
2
)
+
A
2
′
y
+
A
3
′
x
2
+
A
5
′
y
2
+
A
7
′
x
2
y
+
A
9
′
y
3
+
A
10
′
x
4
+
A
12
′
x
2
y
2
+
A
14
′
y
4
+
A
16
′
x
4
y
+
A
18
′
x
2
y
3
+
A
20
′
y
5
,
wherein, c 2 is curvature; k′ is conic constant; A′ 2 , A′ 3 , A′ 5 , A′ 7 , A′ 9 , A′ 10 , A′ 12 , A′ 14 , A′ 16 , A′ 18 and A′ 20 are coefficients.
10. The freeform imaging system of claim 9 , wherein values of the curvature c 2 , conic constant k′, and the coefficients A′ 2 , A′ 3 , A′ 5 , A′ 7 , A′ 9 , A′ 10 , A′ 12 , A′ 14 , A′ 16 , A′ 18 and A′ 20 are listed as following:
c 2
−0.00840342361559533
K′
−13.1593092531843
A′ 2
5.52278890932116E−14
A′ 3
2.96489354878911E−03
A′ 5
2.91326939497068E−03
A′ 7
−4.76838525024617E−08
A′ 9
−7.82131155179962E−08
A′ 10
6.19731744269923E−07
A′ 12
−1.27490547215523E−08
A′ 14
−1.79954961051450E−07
A′ 16
2.11928233145496E−08
A′ 18
8.66202887985918E−10
A′ 20
−9.97940014815302E−10.
11. The freeform imaging system of claim 7 , wherein an analytic form of the back surface satisfies:
z
(
x
,
y
)
=
c
1
(
x
2
+
y
2
)
1
+
1
-
(
1
+
k
1
)
c
1
2
(
x
2
+
y
2
)
+
D
(
x
2
+
y
2
)
2
+
E
(
x
2
+
y
2
)
3
+
F
(
x
2
+
y
2
)
4
+
G
(
x
2
+
y
2
)
5
,
wherein, c 3 is curvature; k 1 is conic constant; D, E, F, and G are coefficients.
12. The freeform imaging system of claim 11 , wherein values of the curvature c 3 , conic constant k 1 , and the coefficients D, E, F, G are listed as following:
c 3
0.00796808853571445
K 1
0.637349059540081
D
1.42634797718698E−07
E
−8.51981255927027E−12
F
9.81455629012912E−16
G
−1.30179502542930E−19.
13. The freeform imaging system of claim 7 , wherein an angle α formed between the reflector and the y-axis is in a range from about 15 degrees to about 75 degrees.
14. The freeform imaging system of claim 7 , wherein a width of the laser with a wavelength of about 780 nanometers is about 3 millimeters.
15. The freeform imaging system of claim 7 , wherein a material of the freeform imaging lens is PMMA with a refractive index of about 1.4917 and an Abbe number of about 76.
16. The freeform imaging system of claim 7 , wherein a filed angle of the freeform imaging system ranges from about −60 degrees to about +60 degrees.