Optical lens for a photodiode-equipped device
The invention relates to an optical lens ( 10 ) for a photodiode-equipped device, which is arrangeable at and/or in the photodiode-equipped device in such a way that light beams ( 14 ) emitted by at least two photodiodes of the photodiode-equipped device transmit into the optical lens ( 10 ) through a light entrance side (S 1 ) of the optical lens ( 10 ) and emerge from the optical lens ( 10 ) at a light exit side (S 2 ) of the optical lens ( 10 ), and for which a central longitudinal axis ( 16 ) extending centrally through the light entrance side (S 1 ) and centrally through the light exit side (S 2 ) is definable, wherein the light entrance side (S 1 ) of the optical lens ( 10 ) and the light exit side (S 2 ) of the optical lens ( 10 ) are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams ( 14 ) emitted by the photodiodes ( 32 ) arranged on a circular path around the central longitudinal axis ( 16 ) are focused off-axis by means of the optical lens ( 10 ).
1. An optical lens for a photodiode-equipped device,
which is arrangeable at and/or in the photodiode-equipped device in such a way that light beams emitted by at least two photodiodes of the photodiode-equipped device transmit into the optical lens through a light entrance side of the optical lens and emerge from the optical lens at a light exit side of the optical lens; and
for which a central longitudinal axis extending centrally through the light entrance side and centrally through the light exit side is defined, wherein
the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the photodiodes arranged on a circular path around the central longitudinal axis are focused off-axis by means of the optical lens;
the central longitudinal axis defines an axis of symmetry of the optical lens; and
the light entrance side of the optical lens and/or the light exit side of the optical lens are/is embodied in accordance with a three-fold rotationally symmetrical polynomial term such that the following equation holds true for all points P(r, φ) of the light entrance side and/or of the light exit side in a cylindrical coordinate system—
z
=
cr
2
1
+
1
-
(
1
+
k
)
*
c
2
*
r
2
+
(
α
*
r
7
+
β
*
r
5
+
γ
*
r
3
)
*
cos
(
3
φ
)
,
in which c is a curvature, k is a conic constant and α, β and γ are polynomial coefficients in each case of the light entrance side and/or of the light exit side.
2. The optical lens according to claim 1 , wherein the optical lens has a triangular edge in a cross-sectional plane oriented perpendicular to its axis of symmetry.
3. A photodiode equipped device comprising:
an optical lens according to claim 1 ; and
the at least two photodiodes;
wherein the optical lens is arranged at and/or in the photodiode-equipped device in such a way that the light beams emitted by the at least two photodiodes transmit into the optical lens through the light entrance side of the optical lens and emerge from the optical lens at the light exit side of the optical lens.
4. The photodiode-equipped device according to claim 3 , wherein the optical lens is arranged with respect to a light-transmissive cover glass of a housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying between the light exit side of the optical lens and the light-transmissive cover glass.
5. The photodiode-equipped device according to claim 3 , wherein the optical lens is arranged with respect to the light-transmissive cover glass of the housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying in the external surroundings of the photodiode-equipped device, said beam intersection point lying at a distance of at least 2 millimetres from the light-transmissive cover glass.
6. An optical lens for a photodiode-equipped device,
which is arrangeable at and/or in the photodiode-equipped device in such a way that light beams emitted by at least two photodiodes of the photodiode-equipped device transmit into the optical lens through a light entrance side of the optical lens and emerge from the optical lens at a light exit side of the optical lens; and
for which a central longitudinal axis extending centrally through the light entrance side and centrally through the light exit side is defined, wherein
the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the photodiodes arranged on a circular path around the central longitudinal axis are focused off-axis by means of the optical lens;
the central longitudinal axis defines an axis of symmetry of the optical lens, and
the light entrance side of the optical lens and/or the light exit side of the optical lens are/is embodied in accordance with a Zernike polynomial such that the following equation holds true for all points P(r, φ) of the light entrance side and/or of the light exit side in a cylindrical coordinate system—
z=Σ n=0 M Σ m ( Z n m +Z n −m ),
in which m lies in a range between −n and n, m is odd if n is odd, and m is even if n is even, in which m is divisible by N, and in which the following equations hold true—
Z
n
m
=
R
n
m
*
con
(
m
*
φ
)
,
Z
n
-
m
=
R
n
m
*
sin
(
m
*
φ
)
and
R
n
m
(
r
)
=
∑
k
=
0
2
(
-
1
)
k
*
(
n
-
k
)
!
k
!
*
(
n
+
k
2
-
k
)
!
*
(
n
-
k
2
-
k
)
!
*
r
r
0
.
7. A photodiode equipped device comprising:
an optical lens according to claim 6 ; and
the at least two photodiodes,
wherein the optical lens is arranged at and/or in the photodiode-equipped device in such a way that the light beams emitted by the at least two photodiodes transmit into the optical lens through the light entrance side of the optical lens and emerge from the optical lens at the light exit side of the optical lens.
8. A method for producing an optical lens for a photodiode-equipped device comprising the following steps:
embodying the optical lens with a light entrance side and with a light exit side in such a way that after arranging the finished optical lens in the photodiode-equipped device, light beams emitted by at least two photodiodes of the photodiode-equipped device transmit into the optical lens through the light entrance side and emerge from the optical lens at the light exit side and a central longitudinal axis extending centrally through the light entrance side and centrally through the light exit side is present, wherein
the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the photodiodes arranged on a circular path around the central longitudinal axis are focused off-axis by means of the optical lens,
the central longitudinal axis defines an axis of symmetry of the optical lens, and
the light entrance side of the optical lens and/or the light exit side of the optical lens are/is embodied in accordance with a three-fold rotationally symmetrical polynomial term such that the following equation holds true for all points P(r, φ) of the light entrance side and/or of the light exit side in a cylindrical coordinate system—
z
=
cr
2
1
+
1
-
(
1
+
k
)
*
c
2
*
r
2
+
(
α
*
r
7
+
β
*
r
5
+
γ
*
r
3
)
*
cos
(
3
φ
)
,
in which c is a curvature, k is a conic constant and α, β and γ are polynomial coefficients in each case of the light entrance side and/or of the light exit side.
9. The method according to claim 8 , wherein the optical lens is arranged with respect to a light-transmissive cover glass of a housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying between the light exit side of the optical lens and the light-transmissive cover glass.
10. The method according to claim 8 , wherein the optical lens is arranged with respect to the light-transmissive cover glass of the housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying in the external surroundings of the photodiode-equipped device, said beam intersection point lying at a distance of at least 2 millimetres from the light-transmissive cover glass.
11. A method for producing an optical lens for a photodiode-equipped device comprising the following steps:
embodying the optical lens with a light entrance side and with a light exit side in such a way that after arranging the finished optical lens in the photodiode-equipped device, light beams emitted by at least two photodiodes of the photodiode-equipped device transmit into the optical lens through the light entrance side and emerge from the optical lens at the light exit side and a central longitudinal axis extending centrally through the light entrance side and centrally through the light exit side is present, wherein
the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the photodiodes arranged on a circular path around the central longitudinal axis are focused off-axis by means of the optical lens,
the central longitudinal axis defines an axis of symmetry of the optical lens, and
the light entrance side of the optical lens and/or the light exit side of the optical lens are/is embodied in accordance with a Zernike polynomial such that the following equation holds true for all points P(r, φ) of the light entrance side and/or of the light exit side in a cylindrical coordinate system—
z=Σ n=0 M Σ m ( Z n m +Z n −m ),
in which m lies in a range between −n and n, m is odd if n is odd, and m is even if n is even, in which m is divisible by N, and in which the following equations hold true:
Z
n
m
=
R
n
m
*
con
(
m
*
φ
)
,
Z
n
-
m
=
R
n
m
*
sin
(
m
*
φ
)
and
R
n
m
(
r
)
=
∑
k
=
0
2
(
-
1
)
k
*
(
n
-
k
)
!
k
!
*
(
n
+
k
2
-
k
)
!
*
(
n
-
k
2
-
k
)
!
*
r
r
0
.
12. The method according to claim 11 , wherein the optical lens is arranged with respect to a light-transmissive cover glass of a housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying between the light exit side of the optical lens and the light-transmissive cover glass.
13. The method according to claim 11 , wherein the optical lens is arranged with respect to the light-transmissive cover glass of the housing of the photodiode-equipped device in such a way that the light beams emerging from the optical lens at the light exit side transmit through the light-transmissive cover glass into external surroundings of the photodiode-equipped device, and wherein the light entrance side of the optical lens and the light exit side of the optical lens are embodied in each case as a freeform surface for off-axis projection in such a way that the light beams emitted by the at least two photodiodes and deflected by means of the optical lens intersect at a beam intersection point lying in the external surroundings of the photodiode-equipped device, said beam intersection point lying at a distance of at least 2 millimetres from the light-transmissive cover glass.