Hologram and method of manufacturing an optical element using a hologram
View Patent ↗A method of manufacturing an optical element ( 5 ) comprises testing an optical surface ( 3 ) of the optical element, using an interferometer 1 a directing measuring light ( 23 a ) onto the optical surface wherein the measuring light traverses two successive holograms ( 44, 48 ) disposed in the beam path of the measuring light upstream of the optical surface.
1. An optical element comprising at least one optical surface fulfilling the following relationships:
σ
RMS
<
1.0
nm
and
max
(
β
(
ϕ
,
x
,
y
)
)
min
(
β
(
ϕ
,
x
,
y
)
)
>
1.2
with
β
(
ϕ
,
x
,
y
)
=
1
/
c
(
ϕ
,
x
,
y
)
*
cos
3
(
α
(
x
,
y
)
)
(
z
(
x
,
y
)
-
d
+
1
/
c
(
ϕ
,
x
,
y
)
*
cos
(
α
(
x
,
y
)
)
)
wherein:
σ RMS is a root-mean-square value of a surface roughness of the optical surface, determined for a spatial length scale in a range from 0.3 mm to 10.0 mm;
max(β(φ,x,y)) is a maximum value of β for all locations (x,y) on the optical surface and all orientations (φ);
min(β(φ,x,y)) is a minimum value of β for all locations (x,y) on the optical surface and all orientations φ;
α(x,y) is an angle between a surface normal of the optical surface at location (x,y) and an average over the surface normals at all locations of the optical surface;
c(φ,x,y) is a curvature of the optical surface at location (x,y) and determined at orientation φ,
z(x,y) is a surface elevation of the optical surface at location (x,y), wherein for at least one location (x0,y0) z(x0,y0)=0 is fulfilled; and
d is a constant with:
d =max( z ( x,y ))+50 mm,
wherein
max(z(x,y)) is a maximum value of z for all locations (x,y) on the optical surface.
2. The optical element according to claim 1 , wherein
max
(
β
(
ϕ
,
x
,
y
)
)
min
(
β
(
ϕ
,
x
,
y
)
)
>
1.5
.
3. The optical element according to claim 1 , wherein σ RMS <0.2 nm.
4. The optical element according to claim 1 , wherein σ RMS is determined for a spatial length scale in a range from 0.3 mm to 3.0 mm.
5. The optical element according to claim 1 , wherein σ RMS is determined for a spatial length scale in a range from 1.0 mm to 10.0 mm.
6. An optical element comprising at least one rotationally symmetric optical surface fulfilling the following relationships:
σ
RMS
a
<
1.0
nm
and
max
(
β
(
ϕ
,
x
,
y
)
)
min
(
β
(
ϕ
,
x
,
y
)
)
>
1.2
with
β
(
ϕ
,
x
,
y
)
=
1
/
c
(
ϕ
,
x
,
y
)
*
cos
3
(
α
(
x
,
y
)
)
(
z
(
x
,
y
)
-
d
+
1
/
c
(
ϕ
,
x
,
y
)
*
cos
(
α
(
x
,
y
)
)
)
wherein:
σ RMSa is a root-mean-square value of an absolute non-rotationally-symmetric surface error of the optical surface;
max(β(φ,x,y)) is a maximum value of β for all locations (x,y) on the optical surface and all orientations φ;
min(βφ,x,y)) is a minimum value of β for all locations (x,y) on the optical surface and all orientations φ;
α(x,y) is an angle between a surface normal of the optical surface at location (x,y) and an average over the surface normals at all locations of the optical surface;
R(x,y) is a radius of curvature of the optical surface at location (x,y),
c(φ,x,y) is a curvature of the optical surface at location (x,y) and determined at orientation φ, and
d is a constant with:
d =max( z ( x,y ))+50 mm, wherein
max(z(x,y)) is a maximum value of z for all locations (x,y) on the optical surface.
7. The optical element according to claim 6 , wherein
max
(
β
(
ϕ
,
x
,
y
)
)
min
(
β
(
ϕ
,
x
,
y
)
)
>
1.5
.
8. The optical element according to claim 6 , wherein σ RMSa <0.2 nm.