Method for producing a holographic optical element
The invention relates to a method for producing a holographic optical element by providing a recording stack comprising at least one recording element laminated on at least one supporting element, irradiating at least a part of the recording stack with at least one recording beam in an irradiating step, wherein during the irradiating step, the recording stack bends, providing a bending deviation threshold for the recording stack, and adjusting at least one first process parameter such that an expected maximum bending deviation of the recording stack does not exceed the bending deviation threshold, wherein the at least one first process parameter influences the bending behavior of the recording stack during the irradiating step.
1. A method for producing a holographic optical element from a photopolymeric recording medium, comprising:
providing a substantially flat recording stack comprising at least one recording element that includes a photopolymeric material laminated on at least one supporting element,
irradiating at least a part of the substantially flat recording stack with at least one recording beam in an irradiating step resulting in the recording stack bending,
determining a bending deviation threshold for the recording stack, the bending deviation threshold determined through calculation; and
adjusting at least one first process parameter such that a maximum bending deviation ξ max of the recording stack does not exceed the bending deviation threshold, wherein the at least one first process parameter influences the bending behavior of the recording stack during the irradiating step, and
wherein the first process parameter is a ratio R dim of lateral dimensions of the recording stack to a thickness of the recording stack, a coefficient of thermal expansion (CTE) of the recording stack, a fill factor of a recording element area versus a supporting element area, exposure time t exp at a fixed recording dosage E or both the supporting element area and the exposure time t exp ,
wherein the maximum bending deviation is determined prior to the irradiating step by calculating the maximum bending deviation ξ max based on equation
ξ
ma
x
=
A
·
⌊
3
2
σ
-
1
·
CTE
·
R
dim
2
·
β
(
τ
ex
p
)
⌋
if a fixture is supported, and based on equation
ξ max =A·└ 1·|CTE|· R 2 dim ·β(τ exp )┘
if the fixture is supported and clamped,
wherein A is a predefined scaling factor, σ is a Poisson ratio of recording stack, CTE is a coefficient of thermal expansion of the recording stack, R dim is a ratio of lateral dimensions of the recording stack to a thickness of the recording stack, and
β
(
τ
exp
)
=
Γ
isothermal
(
τ
exp
)
τ
exp
and
Γ
isothermal
(
τ
exp
)
=
∑
n
=
1
∞
(
π
2
·
(
2
·
n
-
1
/
2
)
·
(
-
1
)
n
+
2
4
·
(
2
·
n
-
1
/
2
)
4
·
(
1
-
exp
(
-
τ
exp
·
(
2
·
n
-
1
/
2
)
2
)
)
)
.
2. The method according to claim 1 , wherein the bending deviation threshold depends on at least one second process parameter, and
the bending deviation threshold for the recording stack is further determined based on the at least one second process parameter,
wherein the second process parameter is a slant angle, a grating vector of the recording element, a grating distance of the recording element or both the recording element and the grating distance.
3. The method according to claim 1 , wherein the maximum bending deviation threshold ξ max is equal to or smaller than
π
2
K
z
,
wherein K Z is a component of a grating vector in a thickness direction of the recording stack.
4. The method according to claim 1 , wherein the recording stack is irradiated by a reference beam and by an object beam in the irradiating step.
5. The method according claim 4 , wherein at least one of the reference beam or the object beam is generated by a laser, a laser diode or a directional light source.
6. The method according to claim 1 , wherein the recording element further comprises photoresist material, silver halide material, di-chromated gelatine material, photo-chromic material or photo-refractive material.
7. The method according to claim 1 , wherein the recording element comprises a photopolymer film comprising a cross-linked matrix and writing monomers comprising a cross-linked matrix and acrylate based monomers.
8. The method according to claim 1 , wherein the supporting element is a glass plate made from borosilicate glass, glass, ceramic glass, fused silica fused quartz or a float glass plate.
9. The method according to claim 1 , wherein the supporting element has an absolute value of a coefficient of thermal expansion (CTE) equal to or smaller than 7×10 −6 K −1 .