Large-size hologram rapid generation method based on wavefront recording plane optimization

Abstract

The invention provides a large-size hologram rapid generation method based on wavefront recording plane optimization. The method comprises the following three steps of: 1, dispersing a 3D object into point sources, calculating a central diffraction pattern of each depth plane based on a scalar diffraction theory and visual area characteristics, translating the central diffraction patterns to obtain diffraction patterns of other object points on the same layer, and superposing the diffraction patterns of all object points to obtain a hologram of a wavefront recording plane of the 3D object; 2, calculating diffraction from the wavefront recording plane to a holographic surface based on an angular spectrum diffraction theory to obtain a hologram of the 3D object on the holographic surface; and step 3, carrying out segmentation and zero padding on the obtained holograms to obtain a hologram 1 and a hologram 2, loading digital blazed gratings on the two holograms to obtain two final holograms, correspondingly loading the two final holograms to the two spatial light modulators, and splicing effective imaging areas of the two spatial light modulators together by using a beam splitter to obtain the hologram 1 and the hologram 2. And a large-size object reproduction image is obtained.

Description

1. Technical Field

[0001] The present invention relates to holographic display technology, and more specifically, to a method for quickly generating large-size holograms based on wavefront recording plane optimization. 2. Background Technology

[0002] With the rapid development of information technology, 3D display technology has received more and more attention. Among them, holographic 3D display technology based on spatial light modulators can not only record and reconstruct all wavefront information of 3D objects, but also avoid convergence adjustment conflicts, and is considered to be one of the most ideal 3D display technologies. However, 3D objects contain a large amount of light field information, which leads to slow calculation of holograms and makes it difficult to achieve real-time and fast calculation of holograms. In addition, the size and viewing angle of holographic display are also restricted by the parameters of spatial light modulators. In order to improve the calculation speed of holograms, researchers have proposed a lookup table method to simplify the calculation process of holograms by pre-calculating and storing the wavefront information of each object point. On this basis, some researchers have introduced a virtual wavefront recording plane, which reduces the area of ​​the wavefront information to be calculated, greatly improves the calculation speed while reducing the storage space required for the lookup table. In order to expand the viewing area of ​​the holographic reconstructed image, researchers have proposed different methods, including the high-order diffraction light method based on a single spatial light modulator, the equivalent spatial light modulator curved array method, and the curved array arrangement method and plane arrangement method based on multiple spatial light modulators. Among them, the spatial light modulator curved array arrangement method achieves the expansion of the viewing area of ​​the reproduced image, but the structure of the optical reproduction system is relatively complex, which is not conducive to integration. The spatial light modulator planar arrangement method uses a 4f imaging system composed of two concave lenses to achieve the expansion of the viewing angle of the reproduced image, but the reproduction distance and the size of the reproduced image are relatively small. Nowadays, how to use a simple system to achieve fast and large-scale holographic 3D display is an urgent problem to be solved. III. Summary of the invention

[0003] The present invention proposes a method for quickly generating large-size holograms based on wavefront recording plane optimization. Figure 1 As shown, the method includes three steps: the first step is to discretize the 3D object into independent point sources, and then calculate the central diffraction pattern of each depth plane object point based on the scalar diffraction theory and the field of view characteristics of the reconstructed image, obtain the diffraction patterns of other object points on the same layer by translating the central diffraction pattern, and then obtain the hologram of the 3D object on the wavefront recording plane by superimposing the diffraction patterns of all object points; the second step is to calculate the diffraction from the wavefront recording plane to the holographic surface based on the angular spectrum diffraction theory to obtain the hologram of the 3D object on the holographic surface; the third step is to divide and fill the obtained hologram in the horizontal direction to obtain holograms of the same size. Figure 1 and holographic Figure 2 , for holographic Figure 1 and holographic Figure 2The digital blazed gratings are loaded separately to obtain two final holograms, and then the two final holograms are loaded onto spatial light modulator 1 and spatial light modulator 2 respectively, and the effective imaging areas of the two spatial light modulators are spliced ​​together using a beam splitter to obtain a large-sized object reconstruction image.

[0004] As attached Figure 2 As shown in Figure 1, in step 1, the recorded 3D object is regarded as a series of point light sources located at different depth planes, where the process of light emitted from the object point P to the boundary of the holographic surface is shown by the dotted arrow. Assuming that the propagation distance from the object point P to the wavefront recording plane is z1, and the propagation distance from the wavefront recording plane to the holographic surface is z2, according to the scalar diffraction theory, the complex amplitude distribution PFP(x,y) of the central diffraction pattern on the wavefront recording plane is:

[0005]

[0006] Where x and y are the coordinates on the plane of the central diffraction pattern, k = 2π / λ is the wave number, and λ is the wavelength. By translating the central diffraction pattern, the diffraction patterns of all object points can be obtained. The size of the diffraction pattern of each object point in the same depth plane is equal to the size of the central diffraction pattern of the layer.

[0007] The size H of the diffraction pattern on the wavefront recording plane w The size H of the diffraction pattern on the holographic surface p The relationship is:

[0008]

[0009] As attached Figure 3 As shown, in the process of holographic reconstruction using a single spatial light modulator, when parallel light illuminates the spatial light modulator, according to the diffraction principle, the maximum diffraction angle θ of the spatial light modulator is:

[0010]

[0011] Where p is the pixel pitch of the spatial light modulator. When the viewer is located at a distance R from the back of the spatial light modulator, within the maximum diffraction angle range of the reproduced image, only the AB area can display the complete reproduced image, and the AB area is called the effective viewing area. According to the principle of geometry, the maximum diffraction angle α1 of the complete reproduced image and the size V1 of the effective viewing area are:

[0012]

[0013] Where H is the size of the spatial light modulator, D is the size of the reconstructed image, and L is the reconstruction distance of the object. According to the geometric relationship, the size of the central diffraction pattern H p1 and resolution re(H p1 ) are:

[0014] H p1 =HD (6)

[0015]

[0016] Where int() represents a rounding operation. According to formula (6), the present invention requires that the size of the recorded object is smaller than the size of the spatial light modulator, and the size of the central diffraction pattern is equal to the difference between the size of the spatial light modulator and the size of the recorded object.

[0017] As attached Figure 4 As shown in Figure 1, when two spatial light modulators of the same model and with a resolution of M are seamlessly spliced, the overall imaging effect is equivalent to that of a spatial light modulator with a resolution of 2M. Figure 4 The effective viewing area is the CD area, and the maximum diffraction angle α2 of the complete reconstructed image based on two spatial light modulators and the size V2 of the effective viewing area are:

[0018]

[0019] α2>2α1 (10)

[0020] V2>2V1 (11)

[0021] According to equations (10) and (11), compared with the method of calculating the effective viewing area of ​​two reconstructed images separately and then stitching them together, the method proposed in the present invention has a larger reconstruction size and effective viewing area. After seamless stitching using two spatial light modulators, the size H of the central diffraction pattern is p2 and resolution re(H p2 ) are:

[0022] H p2 =2H-D (12)

[0023]

[0024] According to equations (2) and (12), after seamless splicing using two spatial light modulators, the size H of the central diffraction pattern on the wavefront recording plane is w2 for:

[0025]

[0026] In step 2, the diffraction from the wavefront recording plane to the holographic surface is calculated based on the angular spectrum diffraction theory to obtain the hologram on the holographic surface. The complex amplitude distribution U(x,y) on the holographic surface is:

[0027]

[0028] in, and They are Fourier transform and inverse Fourier transform, PFP w (x w ,y w ) is the coordinate on the wavefront recording plane (x w ,y w ) of the point source, (f x ,f y ) is the frequency domain coordinate, the transfer function H(f x ,f y ) is calculated as:

[0029]

[0030] In step 3, the hologram obtained in step 2 is firstly divided into two holograms of the same size in the horizontal direction, and the two holograms are respectively zero-filled to make their resolutions the same as the resolution of the spatial light modulator, thereby obtaining a hologram. Figure 1 and holographic Figure 2 Then, for the holographic Figure 1 and holographic Figure 2 The digital blazed grating is loaded separately to obtain two final holograms. Figure 1 and holographic Figure 2 The reconstructed images can be seamlessly spliced ​​together in space. IV. Description of the drawings

[0031] Attached Figure 1 The present invention is a flowchart of a method for rapidly generating a large-size hologram based on wavefront recording plane optimization.

[0032] Attached Figure 2 Schematic diagram of the principle of wavefront plane recording method.

[0033] Attached Figure 3 Schematic diagram of the geometric relationship between the effective viewing area of ​​the reproduced image and a single spatial light modulator.

[0034] Attached Figure 4 Schematic diagram of the geometric relationship between the effective viewing area of ​​the reproduced image and the two spatial light modulators.

[0035] Attached Figure 5 This is a composition diagram of a verification system for a method for rapidly generating large-size holograms based on wavefront recording plane optimization according to the present invention.

[0036] The diagram numbers in the above-mentioned drawings are:

[0037] (1) Wavefront recording plane, (2) Holographic surface, (3) 3D object, (4) Spatial light modulator 1, (5) Reconstructed image, (6) Viewing position, (7) Spatial light modulator 2, (8) Laser, (9) Filter, (10) Solid lens, (11) Beam splitter, (12) Computer, (13) Aperture, (14) 4f system, (15) CCD.

[0038] It should be understood that the above drawings are only schematic and are not drawn to scale. V. Specific implementation methods

[0039] The following will describe in detail a large-size hologram rapid generation method based on wavefront recording plane optimization proposed by the present invention in conjunction with the accompanying drawings and embodiments. It is necessary to point out that the following embodiments are only used to further illustrate the present invention and cannot be understood as limiting the scope of protection of the present invention. Personnel skilled in the art in this field may make some non-essential improvements and adjustments to the present invention based on the above invention content, which still fall within the scope of protection of the present invention.

[0040] One embodiment of the present invention is: the method proposed by the present invention is as follows Figure 5 The holographic display system shown in the figure is realized, and the system includes a laser, a filter, a solid lens, a beam splitter, a spatial light modulator 1, a spatial light modulator 2, a computer, an aperture and a CCD. The laser, the filter and the solid lens are used to generate a uniform parallel light beam. The beam splitter divides the light source beam into two mutually perpendicular light beams, so that the zero-order light modulated by the spatial light modulator can be seamlessly spliced ​​together, and the computer is used to load the hologram. The aperture and two lenses with the same focal length form a 4f system, and the 4f system is used to filter out stray light in the reproduced image. When the hologram is loaded into the spatial light modulator, a large-size holographic reproduced image is captured by using the CCD.

[0041] In the experiment, a green laser with a wavelength of 532nm is used as the light source. The focal length of the solid lens is 300mm, and the transmittance of the beam splitter is >80%. The two spatial light modulators are of the same model, with the number of pixels and pixel pitch of 1920×1080 and 6.4μm respectively. Therefore, the resolution and pixel pitch of the two spatial light modulators after horizontal splicing are 3840×1080 and 6.4μm respectively. An object with a resolution of 200×200 is selected as the recorded object. According to the calculation of the effective field of view, the resolution of the hologram is 2384×728, the calculation time of the hologram is 133.76s, and the average calculation time for each object point is 3.34ms. At the same time, when the new lookup algorithm is used for comparative experiments, the resolution of the hologram is 3840×1080, the calculation time of the hologram is 224.40s, and the average calculation time for each object point is 5.61ms. It can be seen that compared with the new table lookup algorithm, the method proposed in the present invention increases the calculation speed by 40.4%. After the generated hologram is segmented and zero-filled, the digital blazed grating is loaded to obtain the final hologram. Figure 1 and holographic Figure 2 . Figure 1 and holographic Figure 2 The holographic images are loaded onto spatial light modulator 1 and spatial light modulator 2 respectively, and a large-size holographic reconstructed image is received through CCD. Compared with imaging using a single spatial light modulator, this method doubles the horizontal resolution of the reconstructed image. Compared with the traditional holographic 3D display method of directly splicing two spatial light modulators, the method proposed by the present invention increases the effective viewing area while improving the calculation speed.

Claims

1. A method for rapidly generating large-size holograms based on wavefront recording plane optimization, characterized in that: The method comprises the following three steps: first, discretizing the 3D object into independent point sources, then calculating the central diffraction pattern of each depth plane object point based on the scalar diffraction theory and the field of view characteristics of the reproduced image, obtaining the diffraction patterns of other object points on the same layer by translating the central diffraction pattern, and then obtaining the hologram of the 3D object on the wavefront recording plane by superimposing the diffraction patterns of all object points; second, calculating the diffraction pattern from the wavefront recording plane to the holographic surface based on the angular spectrum diffraction theory, and obtaining the hologram of the 3D object on the holographic surface; third, dividing and zero-filling the obtained hologram in the horizontal direction, obtaining hologram 1 and hologram 2 of the same size, loading digital blazed gratings on hologram 1 and hologram 2 respectively, obtaining two final holograms, and then loading the two final holograms correspondingly onto spatial light modulator 1 and spatial light modulator 2, and splicing the effective imaging areas of the two spatial light modulators together by using a beam splitter, so as to obtain a large-sized object reproduction image.

2. The method for rapidly generating a large-size hologram based on wavefront recording plane optimization according to claim 1, characterized in that: In step 1, the recorded 3D object is regarded as a series of point light sources located at different depths. According to the scalar diffraction theory, the complex amplitude distribution PFP(x,y) of the central diffraction pattern on the wavefront recording plane is: where x and y are the coordinates on the central diffraction pattern plane, z1 is the propagation distance from the object point to the wavefront recording plane, and k = 2π / λ is the wave number, λ is the wavelength; by translating the central diffraction pattern, the diffraction patterns of all object points are obtained, and the size of the diffraction pattern of each object point in the same depth plane is equal to the size of the central diffraction pattern of the layer; at the same time, the effective viewing area of ​​the reconstructed image is analyzed. Based on the diffraction principle and geometric relationship, when two spatial light modulators of the same model and resolution M are seamlessly spliced, the overall imaging effect is equivalent to a spatial light modulator with a resolution of 2M. The maximum diffraction angle α2 and the size V2 of the effective viewing area of ​​the complete reconstructed image based on the two spatial light modulators are: Where H is the size of the spatial light modulator, D is the size of the reconstructed image, L is the reconstruction distance of the object, and R is the distance between the viewer and the spatial light modulator; the size of the central diffraction pattern H p2 and resolution re(H p2 ) are: H p2 =2H-D After seamless stitching using two spatial light modulators, the size H of the central diffraction pattern on the wavefront recording plane w2 for:

3. The method for rapidly generating a large-size hologram based on wavefront recording plane optimization according to claim 1, characterized in that: In step 2, the diffraction from the wavefront recording plane to the holographic surface is calculated based on the angular spectrum diffraction theory to obtain the hologram on the holographic surface. The complex amplitude distribution U(x,y) on the holographic surface is: in, and They are Fourier transform and inverse Fourier transform, PFP w (x w ,y w ) is the coordinate on the wavefront recording plane (x w ,y w ) of the point source, (f x ,f y ) is the frequency domain coordinate, the transfer function H(f x ,f y ) is calculated as:

4. The method for rapidly generating a large-size hologram based on wavefront recording plane optimization according to claim 1, characterized in that: In step three, the hologram obtained in step two is firstly divided into two holograms of the same size in the horizontal direction, and the two holograms are respectively zero-filled to make their resolutions the same as the resolution of the spatial light modulator, thereby obtaining hologram 1 and hologram 2; then, the digital blazed grating is loaded on hologram 1 and hologram 2 respectively to obtain two final holograms. The role of the digital blazed grating is to enable the reconstructed images of hologram 1 and hologram 2 to be seamlessly spliced ​​together in space.

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