Catadioptric optical system
A catadioptric optical system in sequence of ray tracing comprises a first mirrors group of Ritchey-Chrétien type hyperbolic mirrors with positive diopter including a concave primary mirror having a central through hole and a convex secondary mirror, a second corrector lens group with negative diopter positioned at the image-side of the first mirrors group including a first meniscus lens element having positive refractive power and a convex object-side surface, a second lens element having negative refractive power and biconcave surfaces, a third meniscus lens element having negative refractive power and a concave object-side surface, and a fourth lens element having positive refractive power and biconvex surfaces. The infinite conjugate beams of incident light within field of view pass through the catadioptric optical system to become a corrected beam having a small CRA angle.
1. A catadioptric optical system, comprising in sequence of ray tracing:
a first mirrors group of Ritchey-Chrétien type hyperbolic mirrors with positive diopter including a concave primary mirror having a central through hole and a convex secondary mirror; and
a second corrector lens group with negative diopter positioned at an image side of the first mirrors group and from the image side of the first mirrors group in order including a first meniscus lens element having positive refractive power and a convex object-side surface, a second lens element with negative refractive power having a concave object-side surface and a concave image-side surface, a third meniscus lens element having negative refractive power and a concave object-side surface, and a fourth lens element with positive refractive power having a convex object-side surface and a convex image-side surface;
wherein a diopter of the whole catadioptric optical system is DW, a diopter of the second corrector lens group is DL, and the following condition is satisfied:
DL
DW
=
(
P
4
EFL
4
+
P
3
EFL
3
+
P
2
EFL
2
+
P
1
EFL
+
P
0
)
*
(
1
±
10
%
)
;
wherein
P 0 =−4.95*10 −1 ;
P 1 =−1.81*10 −3 ;
P 2 =5.59*10 −7 ;
P 3 =−7.76*10 −11 ;
P 4 =4.4*10 −15 ; and
EFL is an effective focal length of the catadioptric optical system.
2. The catadioptric optical system of claim 1 , wherein the first lens element is constituted of a singular lens element and has an image-side surface being concave.
3. The catadioptric optical system of claim 1 , wherein the third lens element is constituted of a singular lens element and has an image-side surface being convex.
4. The catadioptric optical system of claim 1 , wherein a diopter of the first lens element is DL1, a diopter of the second lens element is DL2, a diopter of the third lens element is DL3, a diopter of the fourth lens element is DL4, and the following conditions are satisfied:
DL
1
DL
=
(
K
4
EFL
4
+
K
3
EFL
3
+
K
2
EFL
2
+
K
1
EFL
+
K
0
)
*
(
1
±
10
%
)
;
wherein
K
0
=
-
3.32
;
K
1
=
1.23
*
10
-
3
;
K
2
=
-
3.86
*
10
-
7
;
K
3
=
5.68
*
10
-
11
;
K
4
=
-
3.56
*
10
-
15
;
DL
2
DL
=
(
L
4
EFL
4
+
L
3
EFL
3
+
L
2
EFL
2
+
L
1
EFL
+
L
0
)
*
(
1
±
10
%
)
;
wherein
L
0
=
9.82
;
L
1
=
-
4.91
*
10
-
4
;
L
2
=
-
2.48
*
10
-
7
;
L
3
=
7.24
*
10
-
11
;
L
4
=
-
3.11
*
10
-
15
;
DL
3
DL
=
(
M
4
EFL
4
+
M
3
EFL
3
+
M
2
EFL
2
+
M
1
EFL
+
M
0
)
*
(
1
±
10
%
)
;
wherein
M
0
=
2.74
;
M
1
=
1.32
*
10
-
3
;
M
2
=
-
8.02
*
10
-
7
;
M
3
=
1.53
*
10
-
10
;
M
4
=
-
9.43
*
10
-
15
;
DL
4
DL
=
(
N
4
EFL
4
+
N
3
EFL
3
+
N
2
EFL
2
+
N
1
EFL
+
N
0
)
*
(
1
±
10
%
)
;
wherein
N 0 =−5.99;
N 1 =−1.52*10 −3 ;
N 2 =1*10 −6 ;
N 3 =−1.95*10 −10 ;
N 4 =1.11*10 −14 ; and
EFL is an effective focal length of the catadioptric optical system.
5. The catadioptric optical system of claim 4 , wherein a composite diopter of the first lens element and the second lens element is DL12, a composite diopter of the second lens element and the third lens element is DL23, and a composite diopter of the third lens element and the fourth lens element is DL34, and the following conditions are satisfied:
DL
12
DL
=
(
R
4
EFL
4
+
R
3
EFL
3
+
R
2
EFL
2
+
R
1
EFL
+
R
0
)
*
(
1
±
10
%
)
;
wherein
R
0
=
6.05
;
R
1
=
-
2.7
*
10
-
4
;
R
2
=
-
1.43
*
10
-
7
;
R
3
=
4.21
*
10
-
11
;
R
4
=
-
1.66
*
10
-
15
;
DL
23
DL
=
(
S
4
EFL
4
+
S
3
EFL
3
+
S
2
EFL
2
+
S
1
EFL
+
S
0
)
*
(
1
±
10
%
)
;
wherein
S
0
=
11.7
;
S
1
=
2.38
*
10
-
3
;
S
2
=
-
1.74
*
10
-
6
;
S
3
=
3.46
*
10
-
10
;
S
4
=
-
1.98
*
10
-
14
;
DL
34
DL
=
(
T
4
EFL
4
+
T
3
EFL
3
+
T
2
EFL
2
+
T
1
EFL
+
T
0
)
*
(
1
±
10
%
)
;
wherein
T 0 =−4.23;
T 1 =1.66*10 −4 ;
T 2 =1.16*10 −7 ;
T 3 =−3.25*10 −11 ;
T 4 =1.2*10 −15 ; and
EFL is an effective focal length of the catadioptric optical system.
6. The catadioptric optical system of claim 1 , wherein the first lens element, the second lens element, the third lens element and the fourth lens element are made of the same optical material.
7. The catadioptric optical system of claim 6 , wherein the first lens element, the second lens element, the third lens element and the fourth lens element are made of glass material, a refractive index of the glass material is nd, an Abbe number of the glass material is νd, and the following conditions are satisfied:
1.44< nd< 1.47; and
64.41<ν d< 71.19.
8. The catadioptric optical system of claim 6 , further comprising a third reflective surfaces group and a fourth image sensing group, wherein the third reflective surfaces group is positioned at an image side of the second corrector lens group and includes a first reflective surface and a second reflective surface, a contained angle is between the first reflective surface and the second reflective surface, an apex of the contained angle is positioned at an optical axis of the catadioptric optical system and faces toward the second corrector lens group, the fourth image sensing group includes a first image sensing device and a second image sensing device respectively placed at an image side of the first reflective surface and an image side of the second reflective surface.
9. The catadioptric optical system of claim 8 , wherein a distance on the optical axis between the convex object-side surface of the first lens element facing toward the convex secondary mirror and the convex image-side surface of the fourth lens element facing toward the third reflective surfaces group is TLL1L4, and the following condition is satisfied:
TLL 1 L 4=( U 4 EFL 4 +U 3 EFL 3 +U 2 EFL 2 +U 1 EFL+U 0 )*(1±10%);
wherein
U 0 =−2.85*10 2 ;
U 1 =3.87*10 −1 ;
U 2 =−1.37*10 −4 ;
U 3 =2.23*10 −8 ;
U 4 =−1.28*10 −12 ; and
EFL is an effective focal length of the catadioptric optical system.
10. The catadioptric optical system of claim 1 , wherein a chief ray angle of a corrected beam of the incident light corrected through the catadioptric optical system is CRA, and the following condition is satisfied:
CRA< 3.5 degrees.