CN112558451B - Two-dimensional angle multiplexing method based on spherical holography - Google Patents
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- G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
- G03H1/04—Processes or apparatus for producing holograms
- G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
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Abstract
The invention provides a two-dimensional angle multiplexing method based on spherical holography. The method comprises a spherical diffraction calculation model based on phase compensation and a two-dimensional angle multiplexing and reconstruction method. The method firstly obtains the diffraction field distribution of the target spherical segment rapidly through a phase compensation method. When two-dimensional angle multiplexing is carried out, the two-dimensional angle multiplexing can be realized only by utilizing the change of the field angle parameters of two dimensions of the spherical holography, and a plurality of holograms are directly superposed to obtain a final hologram; during reconstruction, different view angle images of the object can be obtained only by reproducing reconstruction according to different field angle parameters. The method has the beneficial effects that: compared with the traditional angle multiplexing method, the two-dimensional angle multiplexing method based on the spherical holography effectively improves the angle multiplexing efficiency, has high reconstruction quality, and is an effective way for expanding the reconstruction visual angle.
Description
Technical Field
The invention relates to a holographic display technology, in particular to a method for generating and reconstructing a computer generated hologram.
Background
Holographic display has been receiving great attention as an ideal true three-dimensional display technology. However, the computer generated hologram has been a recent research hotspot because it can record both real objects and virtual objects. However, the computer generated hologram has a technical problem to be solved, and the problem is that the computer generated hologram inevitably suffers from the reproduction viewing angle. The reason why the reproduction viewing angle is limited is that the pixels of the spatial light modulation device used at the time of reproduction have a certain physical size, which inevitably determines the reproduction viewing angle. Angular multiplexing of incident light has some effect on expanding the viewing angle, but is still not ideal. Therefore, in order to solve the problem of limited viewing angle in the generation and reconstruction of computer generated holograms, a new angle multiplexing method is needed.
Disclosure of Invention
The invention provides a two-dimensional angle multiplexing method based on spherical holography, aiming at the problem of angle multiplexing in the process of generating and reconstructing a computer generated hologram. The method comprises a spherical diffraction calculation model based on phase compensation and a two-dimensional angle multiplexing and reconstruction method.
The specific description of the spherical diffraction calculation model based on the phase compensation is as follows:
step A1, establishing a diffraction model from an object plane to a target spherical segment, wherein in the diffraction model, the object plane is vertical to the propagation direction, the center of the plane is positioned on the propagation optical axis, the center and the spherical center of the target spherical segment are positioned on the optical axis, the chordal plane and the object plane are parallel and have the same size, and the origin of coordinates is positioned on the spherical center;
step A2, calculating the diffraction process from the object plane to the tangent plane of the target spherical segment according to the scalar diffraction theory, which is expressed as: u1(x1, y1, z1) = FrT { U0(x0, y0, z0), zd }, where U0 and U1 respectively represent diffraction field distributions of an object plane and a chord tangent plane, (x0, y0, z0) and (x1, y1, z1) are coordinates in a rectangular coordinate system thereof, and a diffraction distance is zd = z1-z 0;
step a3, based on the diffraction field of the chord tangent plane, a phase compensation method is used to calculate the diffraction field u2(x2, y2, z2) = u1(x1, y1, z1) × exp (-j × k × zc), x2= x1, y2= y1, z2= R × cos θ × cos Φ, zc = z2-z1, where sin θ = x2/(R × cos θ), Φ = y2/R, θ Φ, and latitudinal direction angular coordinates of the spherical segment in the longitudinal direction and the latitudinal direction, respectively.
The two-dimensional angle multiplexing and reconstructing method is specifically described as follows:
b1, carrying out holographic encoding on a group of spherical segment diffraction fields with the maximum field angle of (theta 1, phi 1) to obtain a hologram H1;
step B2, multiplexing the two dimensions of the warp and weft field angles for n times, namely (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), obtaining n holograms multiplexed by two-dimensional angles, namely H2, H3 and … Hn, and then superposing the holograms to obtain the final hologram H = H1+ H2+ H3 … … + Hn;
and step B3, performing holographic reconstruction on the final hologram according to the opening angle condition sets multiplexed for n times, namely (theta 1, phi 1), (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), and obtaining different viewing angles of n objects.
The scalar diffraction theory can adopt, but is not limited to, a plane-to-plane diffraction calculation formula such as an angular spectrum diffraction theory or a Fresnel diffraction theory to calculate the diffraction field of the target plane.
The method has the beneficial effects that: compared with the traditional angle multiplexing method, the two-dimensional angle multiplexing method based on the spherical holography effectively improves the angle multiplexing efficiency, has high reconstruction quality, and is an effective way for expanding the reconstruction visual angle.
Drawings
FIG. 1 is a schematic diagram of the diffraction model from the object plane to the target spherical segment according to the present invention.
Fig. 2 is a schematic diagram of the coordinate relationship between the target spherical segment and its tangent plane in the diffraction model from the object plane to the target spherical segment of the present invention, where (a) and (b) are a top view and a side view, respectively.
FIG. 3 is a schematic diagram of two-dimensional angle multiplexing based on spherical holography according to the present invention.
FIG. 4 is a schematic diagram of a multi-view holographic reconstruction of the present invention.
FIG. 5 shows the digital simulation results of the angle multiplexing of the present invention, (a) - (c) are three different view angle images of the object, and (d) - (f) are the multi-view angle holographic reconstruction results.
Fig. 6 shows the results of the optical experiments of the angular multiplexing of the present invention, where (a) and (d) are 2 different view angle images of an object, (b) to (e) are the results of multi-view holographic reconstruction based on cylindrical holography, and (c) to (f) are the results of multi-view holographic reconstruction based on spherical holography.
Detailed Description
An exemplary embodiment of a two-dimensional angle multiplexing method based on spherical holography according to the present invention is described in detail below, and the method is further described in detail. It is to be noted that the following examples are given for the purpose of illustration only and are not to be construed as limiting the scope of the present invention, and that the skilled person will be able to make insubstantial modifications and adaptations of the method based on the teachings of the method described above and still fall within the scope of the invention.
The invention provides a two-dimensional angle multiplexing method based on spherical holography.
The phase compensation-based spherical diffraction calculation model is shown in fig. 1 and 2, and is specifically described as follows:
step A1, establishing a diffraction model from an object plane to a target spherical segment, wherein in the diffraction model, the object plane is vertical to the propagation direction, the center of the plane is positioned on the propagation optical axis, the center and the spherical center of the target spherical segment are positioned on the optical axis, the chordal plane and the object plane are parallel and have the same size, and the origin of coordinates is positioned on the spherical center;
step A2, calculating the diffraction process from the object plane to the tangent plane of the target spherical segment according to the scalar diffraction theory, which is expressed as: u1(x1, y1, z1) = FrT { U0(x0, y0, z0), zd }, where U0 and U1 respectively represent diffraction field distributions of an object plane and a chord tangent plane, (x0, y0, z0) and (x1, y1, z1) are coordinates in a rectangular coordinate system thereof, and a diffraction distance is zd = z1-z 0;
step a3, based on the diffraction field of the chord tangent plane, a phase compensation method is used to calculate the diffraction field u2(x2, y2, z2) = u1(x1, y1, z1) × exp (-j × k × zc), x2= x1, y2= y1, z2= R × cos θ × cos Φ, zc = z2-z1, where sin θ = x2/(R × cos θ), Φ = y2/R, θ Φ, and latitudinal direction angular coordinates of the spherical segment in the longitudinal direction and the latitudinal direction, respectively.
The two-dimensional angle multiplexing and reconstructing method is shown in fig. 3 and 4, and is specifically described as follows:
b1, carrying out holographic encoding on a group of spherical segment diffraction fields with the maximum field angle of (theta 1, phi 1) to obtain a hologram H1;
step B2, multiplexing the two dimensions of the warp and weft field angles for n times, namely (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), obtaining n holograms multiplexed by two-dimensional angles, namely H2, H3 and … Hn, and then superposing the holograms to obtain the final hologram H = H1+ H2+ H3 … … + Hn;
and step B3, performing holographic reconstruction on the final hologram according to the opening angle condition sets multiplexed for n times, namely (theta 1, phi 1), (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), and obtaining different viewing angles of n objects.
The scalar diffraction theory can adopt, but is not limited to, a plane-to-plane diffraction calculation formula such as an angular spectrum diffraction theory or a Fresnel diffraction theory to calculate the diffraction field of the target plane.
The angle spectrum diffraction calculation formula is specifically as follows: u (x, y) = AS { U0(x, y) } = IFT { FT [ U0(x, y)]X H (u, v) }, wherein H (u, v) = exp{j×k×z×sqrt[1-λ2×u2-λ2×v2]-k =2 pi/λ is the wavenumber, z is the diffraction distance, λ is the wavelength, (x, y) and (U, v) are the coordinates in space and frequency domain, respectively, and U0 and U are the complex amplitude distributions of the object plane and the diffraction plane, respectively.
In the example of the present invention, the object plane resolution is 512 × 512, the wavelength λ and the diffraction distance zd are 671 nm and 200 mm, respectively, and the spherical segment field angle parameters are: (π/4), (0.1+ π/4, π/6), (0.2+ π/4, π/12), the cylindrical fragment opening angle parameters for comparative experiments were: pi/4, pi/6, pi/12.
Fig. 5 shows the result of digital simulation of angular multiplexing, (a) - (c) are three different view angle images of an object, and (d) - (f) are the result of multi-view angle holographic reconstruction. Fig. 6 shows the results of optical experiments of angular multiplexing, (a) and (d) are 2 different viewing angle images of an object, (b) to (e) are the results of multi-view holographic reconstruction based on cylindrical holography, and (c) to (f) are the results of multi-view holographic reconstruction based on spherical holography. The result shows that the method can effectively realize angle multiplexing and has obvious effect of expanding the visual angle; compared with the one-dimensional angle multiplexing based on cylindrical holography, the two-dimensional angle multiplexing based on spherical holography has the advantages of high reconstruction quality and high multiplexing efficiency.
Claims (2)
1. The two-dimensional angle multiplexing method based on the spherical holography is characterized by comprising a spherical diffraction calculation model based on phase compensation and a two-dimensional angle multiplexing and reconstructing method; the specific description of the spherical diffraction calculation model based on the phase compensation is as follows: step A1, establishing a diffraction model from an object plane to a target spherical segment, wherein in the diffraction model, the object plane is vertical to the propagation direction, the center of the plane is positioned on the propagation optical axis, the center and the spherical center of the target spherical segment are positioned on the optical axis, the chordal plane and the object plane are parallel and have the same size, and the origin of coordinates is positioned on the spherical center; step A2, calculating the diffraction process from the object plane to the tangent plane of the target spherical segment according to the scalar diffraction theory, which is expressed as: u1(x1, y1, z1) = FrT { U0(x0, y0, z0), zd }, where U0 and U1 respectively represent diffraction field distributions of an object plane and a chord tangent plane, (x0, y0, z0) and (x1, y1, z1) are coordinates in a rectangular coordinate system thereof, and a diffraction distance is zd = z1-z 0; step a3, calculating a diffraction field u2(x2, y2, z2) = u1(x1, y1, z1) × exp (-j × k × zc) of the target spherical segment by using a phase compensation method based on the diffraction field of the chord tangent plane, where x2= x1, y2= y1, z2= R × cos θ × cos Φ, and zc = z2-z1, and satisfies: sin θ = x2/(R × cos θ), sin Φ = y2/R, θ and Φ being the angular orientation of the spherical segment in the warp and weft directions, respectively; the two-dimensional angle multiplexing and reconstructing method is specifically described as follows: b1, carrying out holographic encoding on a group of spherical segment diffraction fields with the maximum field angle of (theta 1, phi 1) to obtain a hologram H1; step B2, multiplexing the two dimensions of the warp and weft field angles for n times, namely (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), obtaining n holograms multiplexed by two-dimensional angles, namely H2, H3 and … Hn, and then superposing the holograms to obtain the final hologram H = H1+ H2+ H3 … … + Hn; and step B3, performing holographic reconstruction on the final hologram according to the opening angle condition sets multiplexed for n times, namely (theta 1, phi 1), (theta 2, phi 2), (theta 3, phi 3) and … … (theta n, phi n), and obtaining different viewing angles of n objects.
2. The two-dimensional angle multiplexing method based on spherical holography according to claim 1, wherein the scalar diffraction theory adopts a diffraction calculation formula of an angular spectrum diffraction theory or a Fresnel diffraction theory to calculate the diffraction field of the target plane.
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| CN101206878A (en) * | 2006-12-22 | 2008-06-25 | 汤姆森特许公司 | Reference beam coupler for an apparatus for reading from and/or writing to holographic storage media |
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| CN111538223A (en) * | 2020-04-30 | 2020-08-14 | 北京大学 | Holographic projection method based on light beam deflection |
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| EP1008919A1 (en) * | 1998-12-09 | 2000-06-14 | Communauté Européenne (CE) | Computer assisted holographic method and apparatus for reproducing three-dimensional images |
| US7092133B2 (en) * | 2003-03-10 | 2006-08-15 | Inphase Technologies, Inc. | Polytopic multiplex holography |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US4968108A (en) * | 1983-10-03 | 1990-11-06 | Fujitsu Limited | Method for constructing and reconstructing hologram |
| CN101206878A (en) * | 2006-12-22 | 2008-06-25 | 汤姆森特许公司 | Reference beam coupler for an apparatus for reading from and/or writing to holographic storage media |
| CN101819401A (en) * | 2010-04-02 | 2010-09-01 | 中山大学 | Holography-based great-visual angle three-dimensional image display method and system |
| CN111538223A (en) * | 2020-04-30 | 2020-08-14 | 北京大学 | Holographic projection method based on light beam deflection |
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