US 2021/0341733 A1Published application

Method and program for predicting bending in optical products

AssigneeTokai Optical Co., Ltd.

InventorsMuneo SUGIURA, Koichi TAMURA, Takuro YOSHIDA

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Abstract

In the optical product bending prediction method according to the present invention, bending δ of a substrate having a film is predicted by a computer performing calculation (steps S11 to S13) of the following Expressions (A1), (B1), etc., in which a and Td are set as fitting parameters and have been optimized in each coating condition using a plurality of samples. Here, σint is intrinsic stress, Ef is a Young's modulus of a multilayer film, vf is a Poisson's ratio of the multilayer film, αf is a linear coefficient expansion of the multilayer film, αs is a linear coefficient expansion of the substrate, T is a room temperature, d is a film thickness, b is a substrate thickness, l is a radius of the substrate, Es is a Young's modulus of the substrate, and vs is a Poisson's ratio of the substrate. [ Mathematical ⁢ ⁢ 1 ] δ = 3 ⁢ l 2 b 2 ⁢ ( 1 - v s E s ) ⁢ d ⁢ ⁢ σ ( A1 ) σ = a ⁢ ⁢ σ int + ( α s - α f ) ⁢ ( E f 1 - v f ) ⁢ ( T - T d ) ( B1 )

Claims16

Dependent claims

An optical product bending prediction method of predicting bending δ of a substrate having a film by a computer performing calculation of the following Expressions (A1) to (I) in which a is set as a first fitting parameter and Td is set as a second fitting parameter, and these parameters have been optimized in each coating condition using a plurality of samples,

[
Mathematical
⁢
⁢
1
]
δ
=
3
⁢
l
2
b
2
⁢
(
1
-
v
s
E
s
)
⁢
d
⁢
⁢
σ
(
A1
)
σ
=
a
⁢
⁢
σ
i
⁢
n
⁢
C
+
(
α
s
-
α
f
)
⁢
(
E
f
1
-
v
f
)
⁢
(
T
-
T
a
)
(
B1
)
d
=
d
H
+
d
L
(
C
)
σ
int
=
d
~
H
⁢
σ
H
+
d
~
L
⁢
σ
L
(
D
)
d
~
H
=
d
H
/
d
(
E
)
d
~
L
=
d
L
/
d
(
F
)
E
f
=
d
~
H
⁢
E
H
+
d
~
L
⁢
E
L
(
G
)
v
f
=
d
~
H
⁢
v
H
+
d
~
L
⁢
v
L
(
H
)
α
r
=
d
~
H
⁢
a
H
+
d
~
L
⁢
α
L
(
I
)
where σint is intrinsic stress, Ef is a Young's modulus of a multilayer film, EH is a Young's modulus of a high refractive index layer, EL is a Young's modulus of a low refractive index layer, αf is a Poisson's ratio of the multilayer film, vH is a Poisson's ratio of the high refractive index layer, vL is a Poisson's ratio of the low refractive index layer, αf is a coefficient of linear expansion of the multilayer film, αH is a coefficient of linear expansion of the high refractive index layer, αL is a coefficient of linear expansion of the low refractive index layer, αs is a coefficient of linear expansion of the substrate, T is a room temperature, d is a film thickness, b is a thickness of the substrate, 1 is a radius of the substrate, Es is a Young's modulus of the substrate, vs is a Poisson's ratio of the substrate, dr′ is a total film thickness of the high refractive index layer, dL is a total film thickness of the low refractive index layer, σH is intrinsic stress of the high refractive index layer, and σL is intrinsic stress of the low refractive index layer.

175 more elements

An optical product bending prediction method of predicting bending δ of a substrate having a film by a computer performing calculation of the following Expressions (A1) to (I) in which aH is set as a first primary fitting parameter, aL is set as a first secondary fitting parameter, and Td is set as a second fitting parameter, and these parameters have been optimized in each coating condition using a plurality of samples,

[
Mathematical
⁢
⁢
2
]
δ
=
3
⁢
l
2
b
2
⁢
(
1
-
v
s
E
s
)
⁢
d
⁢
⁢
σ
(
A1
)
σ
=
a
H
⁢
σ
H
⁢
d
~
H
+
a
L
⁢
σ
L
⁢
d
~
L
+
(
α
s
-
a
f
)
⁢
(
E
f
1
-
v
f
)
⁢
(
T
-
T
d
)
(
B2
)
d
=
d
H
+
d
L
(
C
)
d
˜
H
=
d
H
/
d
(
E
)
d
~
L
=
d
L
/
d
(
F
)
E
f
=
d
~
H
⁢
E
H
+
d
~
L
⁢
E
L
(
G
)
v
f
=
d
~
H
⁢
v
H
+
d
~
L
⁢
v
L
(
H
)
α
f
=
d
~
H
⁢
α
H
+
d
~
L
⁢
α
L
(
I
)
where σint is intrinsic stress, Ef is a Young's modulus of a multilayer film, EH is a Young's modulus of a high refractive index layer, EL is a Young's modulus of a low refractive index layer, vf is a Poisson's ratio of the multilayer film, vH is a Poisson's ratio of the high refractive index layer, vf is a Poisson's ratio of the low refractive index layer, αf is a coefficient of linear expansion of the multilayer film, αH is a coefficient of linear expansion of the high refractive index layer, αL is a coefficient of linear expansion of the low refractive index layer, αs is a coefficient of linear expansion of the substrate, T is a room temperature, d is a film thickness, b is a thickness of the substrate, l is a radius of the substrate, Es is a Young's modulus of the substrate, vs is a Poisson's ratio of the substrate, dH is a total film thickness of the high refractive index layer, dL is a total film thickness of the low refractive index layer, σH is intrinsic stress of the high refractive index layer, and σL is intrinsic stress of the low refractive index layer.

166 more elements

An optical product bending prediction program configured to form, through execution thereof by a computer, control means capable of referring to storage of the following Expressions (A1) to (I) in which a is set as a first fitting parameter and Td is set as a second fitting parameter, and these parameters have been optimized in each coating condition using a plurality of samples, the control means being configured to predict bending δ of a substrate having a film through calculation of the Expressions (A1) to (I),

[
Mathematical
⁢
⁢
6
]
δ
=
3
⁢
l
2
b
2
⁢
(
1
-
v
s
E
s
)
⁢
d
⁢
⁢
σ
(
A1
)
σ
=
a
⁢
⁢
σ
int
+
(
α
s
-
a
f
)
⁢
(
E
f
1
-
v
f
)
⁢
(
T
-
T
d
)
(
B1
)
d
=
d
H
+
d
L
(
C
)
σ
i
⁢
n
⁢
t
=
d
~
H
⁢
σ
H
+
d
~
L
⁢
σ
L
(
D
)
d
~
H
=
d
H
/
d
(
E
)
d
~
L
=
d
L
/
d
(
F
)
E
f
=
d
~
H
⁢
E
H
+
d
~
L
⁢
E
L
(
G
)
v
f
=
d
~
H
⁢
v
H
+
d
~
L
⁢
v
L
(
H
)
α
f
=
d
~
H
⁢
α
H
+
d
~
L
⁢
α
L
(
I
)
where σint is intrinsic stress, Ef is a Young's modulus of a multilayer film, EH is a Young's modulus of a high refractive index layer, EL is a Young's modulus of a low refractive index layer, vf is a Poisson's ratio of the multilayer film, vH is a Poisson's ratio of the high refractive index layer, vL is a Poisson's ratio of the low refractive index layer, αf is a coefficient of linear expansion of the multilayer film, αH is a coefficient of linear expansion of the high refractive index layer, αL is a coefficient of linear expansion of the low refractive index layer, αs is a coefficient of linear expansion of the substrate, T is a room temperature, d is a film thickness, b is a thickness of the substrate, 1 is a radius of the substrate, Es is a Young's modulus of the substrate, vs is a Poisson's ratio of the substrate, dH is a total film thickness of the high refractive index layer, dL is a total film thickness of the low refractive index layer, σH is intrinsic stress of the high refractive index layer, and σL is intrinsic stress of the low refractive index layer.

175 more elements

An optical product bending prediction program configured to form, through execution thereof by a computer, control means capable of referring to storage of the following Expressions (A1) to (I) in which aH is set as a first primary fitting parameter, aL is set as a first secondary fitting parameter, and Td is set as a second fitting parameter, and these parameters have been optimized in each coating condition using a plurality of samples, the control means being configured to predict bending δ of a substrate having a film through calculation of the Expressions (A1) to (I),

[
Mathematical
⁢
⁢
7
]
δ
=
3
⁢
l
2
b
2
⁢
(
1
-
v
s
E
s
)
⁢
d
⁢
⁢
σ
(
A1
)
σ
=
a
H
⁢
σ
H
⁢
d
~
H
+
a
L
⁢
σ
L
⁢
d
~
L
+
(
α
s
-
α
f
)
⁢
(
E
f
1
-
v
f
)
⁢
(
T
-
T
d
)
(
B2
)
d
=
d
H
+
d
L
(
C
)
d
~
H
=
d
H
/
d
(
E
)
d
~
L
=
d
L
/
d
(
F
)
E
f
=
d
~
H
⁢
E
H
+
d
~
L
⁢
E
L
(
G
)
v
f
=
d
~
H
⁢
v
H
+
d
~
L
⁢
v
L
(
H
)
α
f
=
d
~
H
⁢
α
H
+
d
~
L
⁢
α
L
(
I
)
where σint is intrinsic stress, Ef is a Young's modulus of a multilayer film, EH is a Young's modulus of a high refractive index layer, EL is a Young's modulus of a low refractive index layer, vf is a Poisson's ratio of the multilayer film, vH is a Poisson's ratio of the high refractive index layer, vL is a Poisson's ratio of the low refractive index layer, αf is a coefficient of linear expansion of the multilayer film, αH is a coefficient of linear expansion of the high refractive index layer, αL is a coefficient of linear expansion of the low refractive index layer, αs is a coefficient of linear expansion of the substrate, T is a room temperature, d is a film thickness, b is a thickness of the substrate, 1 is a radius of the substrate, Es is a Young's modulus of the substrate, vs is a Poisson's ratio of the substrate, dH is a total film thickness of the high refractive index layer, dL is a total film thickness of the low refractive index layer, σH is intrinsic stress of the high refractive index layer, and σL is intrinsic stress of the low refractive index layer.

166 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/305,611Filed 12 Jul 2021
Priority: JP 2019-00636817 Jan 2019
Published: 4 Nov 2021
Term ends: Not estimatedThe source records don’t support an estimate.

Classification6 codes

G02B 27/0012
Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00: optical design, e.g. procedures, algorithms,…
G02B 1/10
Optical elements characterised by the material of which they are made; Optical coatings for optical elements: optical coatings produced by…
G06F 30/20
Computer-aided design [CAD]: design optimisation, verification or simulation
G06F 2111/10
Details relating to CAD techniques: numerical modelling

Family

Application17/305,611Continuation
US 12,216,274 B2Related patent
US 2021/0341733 A1This patent

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