Method for optically realizing 360-degree spherical holographic display

Abstract

The invention relates to a method for optically realizing 360-degree spherical holographic display. The invention provides a method for optically realizing 360-degree spherical holographic display by using a planar spatial light modulator to solve the problem that spherical holographic display cannot be optically realized due to the absence of a spherical spatial light modulator in the market. According to the method, a convex parabolic mirror is used, the characteristic that the convex parabolic mirror converts incident plane waves into spherical waves is utilized, and a diffraction field of a plane hologram is converted to a convex paraboloid and then converted to a spherical surface. According to the method, the problem that spherical holographic display cannot be realized optically is solved for the first time, 360-degree spherical holographic display is realized optically by using the planar spatial light modulator, and the method has a great application prospect in the fields of medical treatment, geology, astronomy and the like.

Description

Technical Field

[0001] The present invention relates to a holographic display technology, in particular to a 360° holographic display method. Background Art

[0002] Holographic display can provide viewers with complete three-dimensional object depth perception without the need for additional auxiliary equipment, and has attracted more and more attention. Traditional planar holography can only provide a limited viewing angle, while spherical computer holography has become a research hotspot recently because it has a 360-degree field of view in the horizontal and vertical directions. However, there are currently no spherical spatial light modulators on the market, and spherical holographic display has not been optically realized. Therefore, optically realizing 360° spherical holographic display is an urgent problem to be solved. Summary of the invention

[0003] The present invention aims at the difficulty of optically realizing 360° spherical holographic display, and provides a method for optically realizing spherical holographic display. The method is performed in the following steps: (i) A hologram reconstruction method for optically realizing 360° spherical holographic display: Step 1, load the computerized hologram Holo onto a planar spatial light modulator, the radius of the hologram is a, and the convex parabolic mirror can be regarded as composed of N layers of planes with different radii, and the radius of each layer corresponding to the holographic plane is a i , i ranges from 1 to N, after different propagation distances z i , the holographic plane HP diffracts to the convex paraboloids CP at different heights i ; Step 2, the focal length of the convex parabola is d, and the i-th layer of the convex parabola is transformed into the layered inner sphere IS intersecting with the convex parabola through coordinate transformation i , the radius of the inner sphere of the layer is r i ; Step 3, N layered inner spherical surfaces intersecting with the convex paraboloid are all diffracted to the outer spherical surface OS with a radius of R, and the diffraction fields are added to finally obtain the optical reconstruction image U0 of the 360° spherical hologram, that is, the original object light wave; the mathematical process of this reconstruction method is expressed as: U0= , i ranges from 1 to N. Among them, HP2CP_Prop((), z i , a i ) indicates that the propagation distance is z i The diffraction propagation process from the holographic plane to the i-th convex paraboloid; CP2IS_Tran[(), r i , d], indicating that the radius of the i-th layer convex parabola is transformed to the convex parabola that intersects with the radius r i The conversion process of layered sphere; IS2OS_Prop{[], r i , R} represents the radius r iThe diffraction process from the layered inner sphere to the outer sphere with a radius of R; the distribution of the diffraction field on the outer sphere is equal to the sum of the diffraction fields from N layered inner spheres intersecting the convex parabola to the outer sphere with a radius of R.

[0004] (ii) A method for calculating and generating a hologram for optically realizing 360° spherical holographic display: To realize the hologram reproduction of the above-mentioned method for optical spherical holographic display, a computer is used to simulate the hologram generation process, which is the opposite process of the hologram reproduction process. The specific steps are as follows: Step 1, the object light wave U0 located on the outer spherical surface OS with a radius of R is diffracted to the radius r intersecting with the convex parabola i Layered inner sphere IS i , the convex paraboloid can be regarded as composed of N planes, i ranges from 1 to N; step 2, radius r i The diffraction field distribution CP of the i-th layer of the layered inner sphere is transformed into a convex parabola after coordinate transformation i , the focal length of the convex parabola is d; Step 3, the radius of the convex parabola of the i-th layer is r i , the diffraction field of the i-th convex parabola passes through the diffraction distance z i , the diffraction process to the holographic plane HP, the radius of the holographic plane corresponding to the i-th convex parabola is a i , N layers of convex paraboloids are diffracted to the holographic plane at different diffraction distances, and the diffraction field distribution of the holographic plane is the sum of the diffraction fields of N layers of planes, and the radius of the holographic plane is a; finally, through the hologram encoding algorithm, the complex amplitude distribution of the diffraction field on the holographic plane is encoded into a hologram that can be loaded and modulated by the spatial light modulator; the mathematical process of the calculation generation method is expressed as: Holo=Encode{ }, where i ranges from 1 to N. OS2IS_Prop([], R, r i ) represents the radius r from the outer sphere with radius R to the intersection with the convex parabola i The diffraction process of the inner sphere, IS2CP_Tran[(), r i , d] represents the radius r that will intersect the convex parabola with focal length d i The inner sphere of is converted into the diffraction field distribution of the i-th convex parabola, CP2HP_Prop{[], z i , a i} represents the diffraction field of the i-th convex parabola through the diffraction distance z i The diffraction process to a radius a iThe holographic plane process; the diffraction field distribution of the holographic plane is the sum of the diffraction fields of N layers of convex paraboloids diffracted to the holographic plane; Encode{} represents the hologram encoding process. The method uses a convex parabolic mirror to convert the diffraction field of the plane hologram to a spherical surface through a coordinate transformation function. The method of the invention can realize 360° optical spherical holographic display; the invention breaks through the limitation that there is no spherical spatial light modulator on the market, and provides a method for optically realizing spherical holographic display using a convex parabolic mirror, which has great application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Attached Figure 1 It is a schematic diagram of the holographic display method of the present invention.

[0006] Attached Figure 2 Schematic diagram of the method process of the present invention; (a) schematic diagram of N layers of convex parabolic mirror, (b) transformation of N layers of plane to spherical surface, (c) concentric sphere diffraction model.

[0007] Attached Figure 3 The optical reconstruction results of the method of the present invention are shown in Figure 1. (a) The result when 1-4 observers are located at the center of the sphere, (b) The result when the observers are located outside the sphere, and (c) The result of 360° at different latitudes.

[0008] Note: The above drawings are only schematic and not drawn to scale. DETAILED DESCRIPTION

[0009] A typical example of a method for optically realizing 360° spherical holographic display of the present invention is described in detail below, and the present invention is further described in detail. It is necessary to point out here that the following embodiments are only used to further illustrate the present invention and cannot be understood as limiting the protection scope of the present invention. Persons skilled in the art in this field may make some non-essential improvements and adjustments to the present invention based on the above content of the present invention, which still fall within the protection scope of the present invention.

[0010] The specific implementation of the method of the present invention is as follows: A method for optically realizing 360° spherical holographic display, such as Figure 1 As shown, there are several steps as follows: (i) A hologram reconstruction method for optically realizing 360° spherical holographic display: Step 1, load the computerized hologram Holo onto a planar spatial light modulator, the radius of the hologram is a, and the convex parabolic mirror can be regarded as composed of N layers of planes with different radii, and the radius of each layer corresponding to the holographic plane is a i , i ranges from 1 to N, after different propagation distances z i , the holographic plane HP diffracts to the convex paraboloids CP at different heights i; Step 2, the focal length of the convex parabola is d, and the i-th layer of the convex parabola is transformed into the layered inner sphere IS intersecting with the convex parabola through coordinate transformation i , the radius of the inner sphere of the layer is r i ; Step 3, N layered inner spherical surfaces intersecting with the convex paraboloid are all diffracted to the outer spherical surface OS with a radius of R, and the diffraction fields are added to finally obtain the optical reconstruction image U0 of the 360° spherical hologram, that is, the original object light wave; the mathematical process of this reconstruction method is expressed as: U0= , i ranges from 1 to N. Among them, HP2CP_Prop((), z i , a i ) indicates that the propagation distance is z i The diffraction propagation process from the holographic plane to the i-th convex paraboloid; CP2IS_Tran[(), r i , d], indicating that the radius of the i-th layer convex parabola is transformed to the convex parabola that intersects with the radius r i The conversion process of layered sphere; IS2OS_Prop{[], r i , R} represents the radius r i The diffraction process from the layered inner sphere to the outer sphere with a radius of R; the distribution of the diffraction field on the outer sphere is equal to the sum of the diffraction fields from N layered inner spheres intersecting the convex parabola to the outer sphere with a radius of R.

[0011] (ii) A method for calculating and generating a hologram for optically realizing 360° spherical holographic display: To realize the hologram reproduction of the above-mentioned method for optical spherical holographic display, a computer is used to simulate the hologram generation process, which is the opposite process of the hologram reproduction process. The specific steps are as follows: Step 1, the object light wave U0 located on the outer spherical surface OS with a radius of R is diffracted to the radius r intersecting with the convex parabola i Layered inner sphere IS i , the convex paraboloid can be regarded as composed of N planes, i ranges from 1 to N; step 2, radius r i The diffraction field distribution CP of the i-th layer of the layered inner sphere is transformed into a convex parabola after coordinate transformation i , the focal length of the convex parabola is d; Step 3, the radius of the convex parabola of the i-th layer is r i , the diffraction field of the i-th convex parabola passes through the diffraction distance z i , the diffraction process to the holographic plane HP, the radius of the holographic plane corresponding to the i-th convex parabola is a i, N layers of convex paraboloids are diffracted to the holographic plane at different diffraction distances, and the diffraction field distribution of the holographic plane is the sum of the diffraction fields of N layers of planes, and the radius of the holographic plane is a; finally, through the hologram encoding algorithm, the complex amplitude distribution of the diffraction field on the holographic plane is encoded into a hologram that can be loaded and modulated by the spatial light modulator; the mathematical process of the calculation generation method is expressed as: Holo=Encode{ }, where i ranges from 1 to N. OS2IS_Prop([], R, r i ) represents the radius r from the outer sphere with radius R to the intersection with the convex parabola i The diffraction process of the inner sphere, IS2CP_Tran[(), r i , d] represents the radius r that will intersect the convex parabola with focal length d i The inner sphere of is converted into the diffraction field distribution of the i-th convex parabola, CP2HP_Prop{[], z i , a i} represents the diffraction field of the i-th convex parabola through the diffraction distance z i The diffraction process to a radius a i holographic plane process; the diffraction field distribution of the holographic plane is the addition of the diffraction fields diffracted to the holographic plane by N layers of convex paraboloids; Encode{} represents the hologram encoding process.

[0012] In an example of the present invention, in a hologram calculation generation method for optically realizing a 360° spherical holographic display method, when calculating the diffraction field distribution from the outer sphere to the inner sphere of different radii intersecting with the convex parabolic mirror, the radius of the outer sphere is R, and the radius of the inner sphere is r i The point spread function h_OS2IS_Prop of the diffraction process can be expressed as: h_OS2IS_Prop(θ, ψ,R, r i )=[1 / (j*λ)]* exp{j*k* dh(θ, ψ, R, r i )} / dh(θ, ψ, R, r i ), where j is the imaginary unit, k=2π / λ, dh is the diffraction distance, λ is the wavelength, θ is the radial variable of the sphere, ψ is the vertical variable of the sphere, and i ranges from 1 to N. The specific calculation formula for the diffraction distance dh is: dh(θ, ψ, R, r i ) = sqrt[R 2 + r i 2 - 2R*r i *cos(θ0-θ1) *cos(ψ0-ψ1) 2 ], where r iis the radius of the inner sphere. Since the inner sphere intersects the convex parabola, the radius of the inner sphere is related to the focal length d of the convex parabola and the height g of the convex parabola mirror. i It can be expressed as: i =sqrt[4d(dg i )]. Then the diffraction field distribution U of the spherical surface with different radii is i The specific calculation formula is: i = , where U is the convolution operation, FT and IFT are Fourier transform and inverse Fourier transform respectively.

[0013] In an example of the present invention, in a hologram calculation generation method for optically realizing a 360° spherical holographic display method, when calculating the diffraction field distribution of the layered inner sphere, only a circle of inner spheres with different radii intersecting with the convex parabola is retained.

[0014] In an embodiment of the present invention, in a hologram calculation generation method for optically realizing a 360° spherical holographic display method, the layered inner sphere IS is calculated. i When converted to the convex parabola diffraction field distribution, the process is approximately the process of coordinate transformation, specifically expressed as U2 i [(x2 i ,y2 i ),g i ]=IS2CP_Tran[(), r i , d]. p(r,ө,ψ) is a point on the sphere, xp=r i × sinө × cosψ, yp = r i ×sinөsinψ,zp=r i ×cosө, the point on the sphere is obtained by reflection on a convex parabolic mirror, and the expression that the reflection point needs to satisfy at the same time is: i 2 +y2 i 2 +4d(z2 i -d)=0;y2 i -(yp / xp)×x2 i =0;z2 i -(zp / xp)×x2 i =0, and finally the coordinates of a circle in the plane of the ith layer on the convex parabola in the rectangular coordinate system are obtained (x2 i ,y2 i ).

[0015] In an example of the present invention, in a hologram calculation generation method for optically realizing a 360° spherical holographic display method, when calculating the propagation process from the convex parabola CP to the holographic recording plane HP, the diffraction field distribution on the holographic recording plane HP is: Uh(x1,y1)= Among them, H_CP2HP_Prop is the transfer function of the diffraction process, specifically expressed as H_CP2HP_Prop(f x2 ,f y2 )=exp{(ikz i )*[1-(λfx2 i ) 2 -(λfy2 i ) 2 ] 1 / 2}, where (x1,y1) represents the coordinates on the holographic surface, (fx2 i ,fy2 i ) represents the spatial coordinates (x2 i ,y2 i ) corresponds to the frequency domain coordinate, z i It represents the distance from the i-th plane of the convex parabola to the holographic plane after coordinate transformation. The diffraction field distribution of the holographic plane is the superposition of the diffraction fields of N layers of planes.

[0016] In an example of the present invention, in a hologram calculation generation method for optically realizing a 360° spherical holographic display method, the encoding process function Encode() of the holographic surface diffraction field is specifically a phase function.

[0017] The content of the present invention is further explained below in conjunction with embodiments and drawings: During the hologram calculation and generation process, the object resolution is 3840×960, the focal length of the convex parabola is 5 mm, the radius R of the outer spherical surface is 20 mm, the diffraction distance z1 is 295 mm, zN is 300 mm, and the wavelength λ is 671 nm; the resolution of the hologram is 1080×1080, and the pixel pitch of the planar spatial light modulator is 8.0 um. Figure 2 Schematic diagram of the principle of the method of the present invention. Figure 3 The optical reconstruction results of the method of the present invention are shown in Figure 1, where (a) the result when 1-4 observers are located at the center of the sphere, (b) the result when the observers are located outside the sphere, and (c) the result of 360° horizontal direction at different latitudes. From the results, the method of the present invention successfully realizes the optical 360° spherical holographic display.

[0018] Therefore, the present invention breaks through the limitation that there is no spherical spatial light modulator on the market, and provides a method for optically realizing spherical holographic display using a convex parabolic mirror, which has great application prospects.

Claims

1. A method for optically realizing 360° spherical holographic display, characterized in that: (i) A hologram reconstruction method for optically realizing 360° spherical holographic display: Step 1, load the computerized hologram Holo onto a planar spatial light modulator, the radius of the hologram is a, and the convex parabolic mirror can be regarded as composed of N layers of planes with different radii, and the radius of each layer corresponding to the holographic plane is a i , i ranges from 1 to N, after different propagation distances z i , the holographic plane HP diffracts to the convex paraboloids CP at different heights i ; Step 2, the focal length of the convex parabola is d, and the i-th layer of the convex parabola is transformed into the layered inner sphere IS intersecting with the convex parabola through coordinate transformation i , the radius of the inner sphere of the layer is r i ; Step 3, N layered inner spherical surfaces intersecting with the convex paraboloid are all diffracted to the outer spherical surface OS with a radius of R, and the diffraction fields are added to finally obtain the optical reconstruction image U0 of the 360° spherical hologram, that is, the original object light wave; the mathematical process of this reconstruction method is expressed as: U0= , i ranges from 1 to N; where HP2CP_Prop((), z i , a i ) indicates that the propagation distance is z i The diffraction propagation process from the holographic plane to the i-th convex paraboloid; CP2IS_Tran[(), r i , d], indicating that the radius of the i-th layer convex parabola is transformed to the convex parabola that intersects with the radius r i The conversion process of layered sphere; IS2OS_Prop{[], r i , R} represents the radius r i The diffraction process from the layered inner sphere to the outer sphere with a radius of R; the distribution of the diffraction field of the outer sphere is equal to the sum of the diffraction fields of N layered inner spheres intersecting with the convex paraboloid to the outer sphere with a radius of R; (ii) A method for calculating and generating a hologram for optically realizing 360° spherical holographic display: In order to realize the hologram reproduction of the above-mentioned optical spherical holographic display method, a computer is used to simulate the generation process of the hologram, and the process is the opposite of the hologram reproduction process. The specific steps are as follows: Step 1, the object light wave U0 located at the outer sphere OS with a radius of R is diffracted to the radius r intersecting with the convex paraboloid i Layered inner sphere IS i , the convex paraboloid can be regarded as composed of N planes, i ranges from 1 to N; step 2, radius r i The diffraction field distribution CP of the i-th layer of the layered inner sphere is transformed into a convex parabola after coordinate transformation i , the focal length of the convex parabola is d; Step 3, the radius of the convex parabola of the i-th layer is r i , the diffraction field of the i-th convex parabola passes through the diffraction distance z i , the diffraction process to the holographic plane HP, the radius of the holographic plane corresponding to the i-th convex parabola is a i , N layers of convex paraboloids are diffracted to the holographic plane at different diffraction distances, and the diffraction field distribution of the holographic plane is the sum of the diffraction fields of N layers of planes, and the radius of the holographic plane is a; finally, through the hologram encoding algorithm, the complex amplitude distribution of the diffraction field on the holographic plane is encoded into a hologram that can be loaded and modulated by the spatial light modulator; the mathematical process of the calculation generation method is expressed as: Holo=Encode{ }, where i ranges from 1 to N; OS2IS_Prop([], R, r i ) represents the radius r from the outer sphere with radius R to the intersection with the convex parabola i The diffraction process of the inner sphere, IS2CP_Tran[(), r i , d] represents the radius r that will intersect the convex parabola with focal length d i The inner sphere of is converted into the diffraction field distribution of the i-th convex parabola, CP2HP_Prop{[], z i , a i } represents the diffraction field of the i-th convex parabola through the diffraction distance z i The diffraction process to a radius a i holographic plane process; the diffraction field distribution of the holographic plane is the addition of the diffraction fields diffracted to the holographic plane by N layers of convex paraboloids; Encode{} represents the hologram encoding process.

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