US 12,216,274 B2Granted

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 i ⁢ n ⁢ t + ( α s - α f ) ⁢ ( E f 1 - v f ) ⁢ ( T - T d ) ( B1 )

Claims8

Dependent claims

A computer implemented optical product bending prediction program configured to predict a bending δ of a substrate having a film by execution thereof by a computer,

wherein the computer includes a non-transitory, computer-readable storage medium storing the optical product bending prediction program and an integrated film designing program, and control means capable of referring to the non-transitory computer-readable storage medium to execute the optical product bending prediction program and the integrated film designing program stored therein,
wherein the optical product bending prediction program stored in the non-transitory, computer-readable medium includes 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, the fitting parameters having been optimized for each coating condition using a plurality of samples,
wherein the control means is configured to execute the optical product bending prediction program to perform calculations to predict the bending δ of the substrate having the film using the Expressions (A1) to (I),
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
)
wherein 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, and
wherein the film designing program stored in the non-transitory, computer-readable medium, automatically passes values determined by the film designing program to the bending prediction program, whereby an accurate bending δ of the substrate can be determined during or at the completion of executing the film designing program.

174 more elements

A computer implemented optical product bending prediction program configured to predict a bending δ of a substrate having a film by execution thereof by a computer,

wherein the computer includes a non-transitory, computer-readable storage medium storing the optical product bending prediction program and an integrated film designing program, and control means capable of referring to the non-transitory, computer-readable storage medium to execute the optical product bending prediction program and the integrated film designing program stored therein,
wherein the optical product bending prediction program stored in the non-transitory, computer-readable storage medium includes 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, the fitting parameters having been optimized for each coating condition using a plurality of samples,
wherein the control means is configured to execute the optical product bending prediction program to perform calculations to predict the bending δ of the substrate having a film using the Expressions (A1) to (I),
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
)
wherein 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, and
wherein the film designing program stored in the non-transitory, computer-readable medium, automatically passes values determined by the film designing program to the bending prediction program, whereby an accurate bending δ of the substrate is determined during or at the completion of the execution of the film designing program.

165 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/305,611Filed 12 Jul 2021 · continuation
Priority: JP 2019-00636817 Jan 2019
Published: US 2021/0341733 A14 Nov 2021
Granted: 4 Feb 2025
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

PCT/JP2019/050662Parent of this continuation · filed 24 Dec 2019
US 2021/0341733 A1Pre-grant publication · published 4 Nov 2021
US 12,216,274 B2This patent

From the US filing history. Foreign family members aren’t listed.

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