US 11,573,527 B2Granted

Calculation method, recording method, optical film, and phase modulation structure

AssigneeToppan Printing Co., Ltd.

InventorAkihito Kagotani

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Abstract

A phase modulation structure includes a recording surface including phase angle recording regions in a plurality of calculated element regions corresponding to reconstruction points of an image on a one-to-one basis, each phase angle recording region being formed of a plurality of unit blocks in each of which a phase angle is recorded, the phase angle being calculated based on a phase that is a sum of a plurality of phases of light from the corresponding reconstruction points; and a representative area that is one of divisions of the calculated element region, the representative area being obtained by radially dividing the calculated element region centered on a point on the calculated element region, the point being obtained by extending a normal line from the corresponding reconstruction point to the calculated element region on the recording surface.

Claims11

Dependent claims

A calculation method used for calculating phases of calculated element regions, the calculated element regions each being formed of a plurality of unit blocks for which phases of light are calculated and corresponding to reconstruction points on a one-to-one basis, the method comprising the steps of:

defining a point on each calculated element region as a center thereof by extending a normal line from the corresponding reconstruction point to the calculated element region arranged on a recording surface;
radially dividing the calculated element region into divisions centered on the center of the calculated element region to define one of the divisions as a representative area of the calculated element region;
calculating phases for unit blocks that are partially or entirely included in the representative area;
copying the phases calculated for the unit blocks that are partially or entirely included in the representative area to an area other than the representative area of the calculated element region by rotating the representative area about the center of the calculated element region during inversion of the representative area;
and, iterating the rotation and the inversion to calculate phases for all unit blocks in the calculated element region, wherein a phase angle is calculated according to the following formula:
W
⁡
(
x
,
y
)
=
∑
n
=
0
N
⁢
max
W
n
(
kx
,
ky
)
W
n
(
kx
,
ky
)
=
amp
n
·
exp
⁡
(
i
⁢
ϕ
n
(
kx
,
ky
)
)
ϕ
n
(
kx
,
ky
)
=
π
λ
·
O
n
(
z
)
⁢
{
(
O
n
(
x
)
-
kx
)
2
+
(
O
n
(
y
)
-
ky
)
2
}
where Wn(kx, ky) is a phase of a reconstruction point n at coordinates (kx, ky, 0) in a calculated element region for an nth reconstruction point, W(x, y) is a phase recorded at coordinates (x, y, 0), n is an nth reconstruction point (n=0 to Nmax), ampn is an amplitude of light of an nth reconstruction point, i is an imaginary number, λ is a wavelength of light when reproducing the reconstruction point, On(x) is an x-coordinate of the reconstruction point, On(y) is a y-coordinate of the reconstruction point, On(z) is a z-coordinate of the reconstruction point, (x, y, 0) is a coordinate of the unit block, and ϕn(kx, ky) is a phase angle of an nth reconstruction point.

89 more elements

A phase modulation structure, comprising:

a recording surface including phase angle recording regions in a plurality of calculated element regions corresponding to reconstruction points of an image on a one-to-one basis, each phase angle recording region being formed of a plurality of unit blocks in each of which a phase angle is recorded, the phase angle being calculated based on a phase that is a sum of a plurality of phases of light from the corresponding reconstruction points;
and
a representative area that is one of divisions of the calculated element region, the representative area being obtained by radially dividing the calculated element region centered on a point on the calculated element region, the point being obtained by extending a normal line from the corresponding reconstruction point to the calculated element region on the recording surface, wherein
the representative area produces the calculated element region by being rotated about the center of the calculated element region during inversion of the representative area;
and
with the representative area being rotated about the center of the calculated element region during inversion of the representative area, phases of unit blocks partially or entirely included in the representative area are defined in corresponding unit blocks of another calculated element region so as to be the same as the phases of the corresponding unit blocks of the representative area, wherein a phase angle is calculated according to the following formula:
W
⁡
(
x
,
y
)
=
∑
n
=
0
N
⁢
max
W
n
(
kx
,
ky
)
W
n
(
kx
,
ky
)
=
amp
n
·
exp
⁡
(
i
⁢
ϕ
n
(
kx
,
ky
)
)
ϕ
n
(
kx
,
ky
)
=
π
λ
·
O
n
(
z
)
⁢
{
(
O
n
(
x
)
-
kx
)
2
+
(
O
n
(
y
)
-
ky
)
2
}
where Wn(kx, ky) is a phase of a reconstruction point n at coordinates (kx, ky, 0) in a calculated element region for an nth reconstruction point, W(x, y) is a phase recorded at coordinates (x, y, 0), n is an nth reconstruction point (n=0 to Nmax), ampn is an amplitude of light of an nth reconstruction point, i is an imaginary number, λ is a wavelength of light when reproducing the reconstruction point, On(x) is an x-coordinate of the reconstruction point, On(y) is a y-coordinate of the reconstruction point, On(z) is a z-coordinate of the reconstruction point, (x, y, 0) is a coordinate of the unit block, and ϕn(kx, ky) is an nth phase angle.

90 more elements

Dependencies are inferred from the claim text.

Facts

Application: 16/442,181Filed 14 Jun 2019 · continuation
Priority: JP JP2016-24343315 Dec 2016
Published: US 2019/0293492 A126 Sep 2019
Granted: 7 Feb 2023
Term ends: Not estimatedThe source records don’t support an estimate.

Classification19 codes

G03H 1/0808
Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms: methods of numerical synthesis, e.g. coherent ray…
B42D 25/328
Identification or security features, e.g. for preventing forgery: diffraction gratings; Holograms
G01J 9/0246
By interferometric methods: measuring optical wavelength
G03H 1/0011
Adaptation of holography to specific applications: for security or authentication