# US 2025/0164929 A1 · Large-depth metasurface polarization holographic 3d display method

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- Number: US 2025/0164929 A1
- Document ID: US20250164929A1
- Status: Published application
- Kind: A1
- Application number: 18/911,429
- Filed: 2024-10-10
- Published: 2025-05-22
- Earliest claimed: 2023-11-22
- Assignees: Beihang University
- Applicants: Beihang University
- Inventors: Qionghua WANG; Di WANG; Yilong LI; Qian HUANG
- Web page: https://patentgrep.com/patent/US20250164929A1

## CPC

- G03H 1/0808: {Methods of numerical synthesis, e.g. coherent ray tracing [CRT], diffraction specific}
- G02B 30/25: using polarisation techniques
- G03H 1/0443: {Digital holography, i.e. recording holograms with digital recording means (holobject computation G03H1/0866)}
- G03H 1/0866: {Digital holographic imaging, i.e. synthesizing holobjects from holograms}
- G03H 1/22: Processes or apparatus for obtaining an optical image from holograms (G03H1/26 - G03H1/34 take precedence)
- G03H 1/2294: {Addressing the hologram to an active spatial light modulator}
- G03H 2001/0088: {for video-holography, i.e. integrating hologram acquisition, transmission and display}
- G03H 2222/31: Polarised light
- G03H: HOLOGRAPHIC PROCESSES OR APPARATUS (holograms, e.g. point holograms, used as ordinary optical elements G02B5/32; producing stereoscopic or other three-dimensional effects G02B30/00; diffraction-grating systems G02B27/44; systems using moiré fringes G02B27/60; optical logic elements G02F3/00; stereo-photography G03B35/00; photosensitive materials or processes for photographic purposes G03C; {stereo-photographic or similar processes G03C9/00}; apparatus for processing exposed photographic materials G03D; analogue computers performing mathematical operations with the aid of optical elements G06E3/00; authentication by radiation, of concealed information carried by holograms or diffraction gratings G06K19/16; holographic storage G11B7/0065, G11C13/04; {stereoscopic or other three dimensional effects in television systems H04N13/00})
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

Disclosed is a large-depth metasurface polarization holographic 3D display method, including: performing calculations for a first 3D object and a second 3D object based on an angular spectrum diffraction theory to obtain a first metasurface hologram and a second metasurface hologram; performing interleaved row-by-row insertion of the first and the second metasurface holograms to encode into a synthetic hologram, optimizing phases of the synthetic hologram by using an error diffusion algorithm to obtain phase information required by metasurface structures, that is, meta-phase information; designing the metasurface structures based on the meta-phase information, and making a metasurface structure in odd rows sensitive to left-handed circularly polarized light, and a metasurface structure in even rows sensitive to right-handed circularly polarized light to achieve independent control over different polarization states; and performing holographic 3D reconstruction by illuminating the metasurface structures with laser.

## Claims

### Claim 1

A large-depth metasurface polarization holographic 3D display method, comprising:
for two different 3D objects, that is, a first 3D object and a second 3D object, performing calculations based on an angular spectrum diffraction theory to obtain a first metasurface hologram and a second metasurface hologram of the two 3D objects respectively, and performing left-handed circularly polarized light holographic reconstruction and right-handed circularly polarized light holographic reconstruction by using the first metasurface hologram and the second metasurface hologram, respectively;
performing interleaved row-by-row insertion of the first and the second metasurface holograms to encode into a synthetic hologram, optimizing phases of the synthetic hologram by using an error diffusion algorithm to obtain phase information required by metasurface structures, that is, meta-phase information;
designing the metasurface structures based on the meta-phase information, and making a metasurface structure in odd rows sensitive to left-handed circularly polarized light, and a metasurface structure in even rows sensitive to right-handed circularly polarized light; and
performing holographic 3D reconstruction by illuminating the metasurface structures with laser; when the metasurface structures are illuminated by the left-handed circularly polarized light, the metasurface structure only in the odd rows is sensitive to incident light, such that a phase of light field can be modulated, in which case, a large-depth holographic reconstruction image of the first 3D object can be seen; when the metasurface structures are illuminated by the right-handed circularly polarized light, the metasurface structure only in the even rows is sensitive to incident light such that the phase of light field can be modulated, in which case, a large-depth holographic reconstruction image of the second 3D object can be seen; and when the metasurface structures are illuminated by the left-handed circularly polarized light and the right-handed circularly polarized light simultaneously, the large-depth holographic reconstruction images of the first 3D object and the second 3D object can be seen at the same time.

### Claim 2 (depends on 1)

The large-depth metasurface polarization holographic 3D display method according to claim 1,
wherein, for any of the 3D objects, complex amplitude distributions of the 3D object and a hologram plane are expressed as:
T
0
(
x
0
,
y
0
;
0
)
=
∫
∫
-
∞
∞
A
0
(
f
x
,
f
y
;
0
)
⁢
exp
[
j
⁢
2
⁢
π
⁡
(
x
0
⁢
f
x
+
y
0
⁢
f
y
)
]
⁢
df
x
⁢
df
y
T
⁡
(
x
,
y
;
z
)
=
∫
∫
-
∞
∞
A
⁡
(
f
x
,
f
y
;
z
)
⁢
exp
[
j
⁢
2
⁢
π
⁡
(
xf
x
+
yf
y
)
]
⁢
df
x
⁢
df
y
in the formulae, T0 and T are the complex amplitude distributions of the 3D object and the hologram plane, respectively; x0 and y0 are position coordinates of the 3D object; x and y are position coordinates of the hologram plane; fx and fy are spatial frequencies of the light field in an x direction and a y direction, respectively; j is an imaginary unit; z is a distance between the 3D object and the hologram plane; and A0(fx, fy; 0) and A(fx, fy; z) are spatial spectra of the 3D object and the hologram plane, respectively, and the Helmholtz equation is solved to obtain the following formulae:
A
⁡
(
f
x
,
f
y
;
z
)
=
A
0
(
f
x
,
f
y
;
0
)
⁢
H
⁡
(
f
x
,
f
y
;
z
)
H
⁡
(
f
x
,
f
y
;
z
)
=
exp
⁡
(
j
⁢
φ
⁡
(
f
x
,
f
y
;
z
)
)
=
exp
⁡
(
j
⁢
2
⁢
π
⁢
z
⁢
λ
-
2
-
f
x
2
-
f
y
2
)
in the formulae, H(fx, fy; z) is a transfer function; φ(fx, fy; z) is a phase of the transfer function; and λ is a wavelength;
for the first 3D object and the second 3D object, the corresponding complex amplitude distributions on the hologram plane can be directly obtained:
T
LCP
=
ℱ
-
1
⁢
{
ℱ
[
T
1
(
x
,
y
;
0
)
]
·
H
LCP
(
f
x
,
f
y
;
z
)
}
T
RCP
=
ℱ
-
1
⁢
{
ℱ
[
T
2
(
x
,
y
;
0
)
]
·
H
RCP
(
f
x
,
f
y
;
z
)
}
in the formulae, TLCP is the complex amplitude distribution of the first 3D object on the hologram plane; TRCP is the complex amplitude distribution of the second 3D object on the hologram plane; F and F−1 denote Fourier transform and inverse Fourier transform, respectively; T1(x, y; 0) and T2(x, y; 0) the complex amplitude distributions of the first 3D object and the second 3D object, respectively; and HLCP(fx, fy; z) and HRCP(fx, fy; z) denote transfer functions of the first 3D object and the second 3D object, respectively;
a local signal frequency Mf and a sampling frequency Δfx of the transfer function need to meet the following conditions:
M
f
=
-
f
x
⁢
z
λ
-
2
-
f
x
2
-
f
y
2
Δ
⁢
f
x
≥
2
⁢
❘
"\[LeftBracketingBar]"
M
f
❘
"\[RightBracketingBar]"
when calculating a metasurface hologram, the sampling frequency is determined by the following formulae:
Δ
⁢
f
x
=
(
2
⁢
N
⁢
p
)
-
1
in the formulae, N is a number of pixels of the metasurface hologram in the x direction, p is a pixel pitch, wherein the transfer function can be a band-limited function, and the transfer function in the x direction should be constrained within the range shown in the following formula:
f
x
2
f
xlimit
2
+
f
y
2
λ
2
≤
1
f
xlimit
=
1
λ
⁢
(
z
N
⁢
p
)
2
+
1
in the formulae, fxlimit is a maximum frequency of the transfer function in the x direction, a bandwidth limit of the transfer function in the x direction forms a regular ellipse with a y-axis as a major axis, similarly, a bandwidth limit in a y direction forms a regular ellipse with an x-axis as the major axis, and an overlapping area of the two ellipses is a band-limited area of the transfer function; a depth of the metasurface holographic 3D display is extended by limiting high-frequency information of the transfer function, and finally the first and second metasurface holograms capable of achieving the function of large-depth deep holographic 3D display are generated, and pixel pitches of the two metasurface holograms in the x direction and the y direction are p and 2p, respectively.

### Claim 3 (depends on 1)

The large-depth metasurface polarization holographic 3D display method according to claim 1, wherein performing alternately inserting row by row of the first and the second metasurface holograms comprises: complex amplitude information of the first and the second metasurface holograms are synthesized by interleaved row-by-row insertion to obtain the complex amplitude distribution of the synthetic hologram, the synthetic hologram has a pixel pitch of p in both the x direction and the y direction, the odd rows in the y direction correspond to the complex amplitude of the first metasurface hologram, and the even rows in the y direction correspond to the complex amplitude of the second metasurface hologram; and all pixels of the synthetic hologram are scanned and optimized one by one using the error diffusion algorithm, so as to obtain meta-phase information required by the metasurface structures.

### Claim 4 (depends on 1)

The large-depth metasurface polarization holographic 3D display method according to claim 1, wherein the metasurface structure independently modulates a phase of each unit structure based on a principle of geometric phase control, each unit structure of the metasurface is composed of rectangular amorphous silicon nanorods fabricated on a quartz substrate; a rotation angle of each of the rectangular amorphous silicon nanorods relative to the x-axis is θ, the phase can be controlled by rotating an angle of each of the rectangular amorphous silicon nanorods, and a phase offset is φ1=±2θ; a positive sign is taken when the polarization state is the left-handed circularly polarized light, and a negative sign is taken when the polarization state is the right-handed circularly polarized light; and the metasurface structures are designed based on the meta-phase information generated, the metasurface structure in the odd rows is sensitive to the left-handed circularly polarized light, and the metasurface structure in the even rows is sensitive to the right-handed circularly polarized light, thereby achieving independent control over different polarization states.