A large-size hologram fast generation method based on wavefront recording plane optimization

Abstract

The application provides a large-size hologram fast generation method based on wave front recording plane optimization. The method comprises three steps: in the first step, a 3D object is discretized into point sources, a central diffraction diagram of each depth plane is calculated based on a scalar diffraction theory and a viewing zone characteristic, a diffraction diagram of other object points on the same layer is obtained by translating the central diffraction diagram, and a hologram of the wave front recording plane of the 3D object is obtained by superimposing diffraction diagrams of all object points; in the second step, diffraction from the wave front recording plane to a holographic surface is calculated based on an angular spectrum diffraction theory, and a hologram of the 3D object on the holographic surface is obtained; and in the third step, the obtained hologram is segmented and zero-filled to obtain a hologram 1 and a hologram 2, digital blazed gratings are loaded on the two holograms to obtain two final holograms, the two final holograms are loaded on two spatial light modulators, effective imaging areas of the two spatial light modulators are spliced together by means of a beam splitter, and a large-size object reconstruction image is obtained.

Description

I. TECHNICAL FIELD

[0001] The present application relates to holographic display technology, more particularly, the present application relates to a large-size hologram fast generation method based on wavefront recording plane optimization. II. BACKGROUND

[0002] With the rapid development of information technology, 3D display technology has attracted more and more attention. Among them, the holographic 3D display technology based on spatial light modulator not only can record and reconstruct the whole wavefront information of 3D object, but also can avoid vergence-accommodation conflict, and is considered as one of the most ideal 3D display technologies. However, 3D object contains a large amount of light field information, which leads to slow hologram calculation speed and makes it difficult to realize real-time fast calculation of hologram. In addition, the size and viewing angle of holographic display are also restricted by the parameters of spatial light modulator. In order to improve the calculation speed of hologram, researchers have proposed a lookup table method, which simplifies the calculation process of hologram 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 to-be-calculated region of the wavefront information, and at the same time, greatly improves the calculation speed while reducing the storage space required by the lookup table. In order to expand the viewing area of the reconstructed image, researchers have proposed different methods, including high-order diffraction light method based on a single spatial light modulator, equivalent spatial light modulator curved array method, and curved array arrangement method and plane arrangement method based on multiple spatial light modulators. Among them, the spatial light modulator curved array arrangement method realizes the expansion of the viewing area of the reconstructed image, but the structure of the optical reconstruction system is relatively complex, which is not conducive to integration. The spatial light modulator plane arrangement method uses a 4f imaging system composed of two concave lenses to realize the expansion of the viewing angle of the reconstructed image, but the reconstruction distance and the size of the reconstructed image are relatively small. Today, how to use a simple system to realize fast large-size holographic 3D display is a problem to be solved. III. SUMMARY

[0003] The present application proposes a large-size hologram fast generation method based on wavefront recording plane optimization. As shown in the accompanying drawings, the method includes three steps: first, discretize the 3D object into independent point sources, then calculate the center diffraction pattern of each depth plane object point based on the scalar diffraction theory and the viewing area characteristics of the reconstructed image, obtain the diffraction patterns of other object points on the same layer by translating the center 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; second, calculate the diffraction from the wavefront recording plane to the holographic surface based on the angular spectrum diffraction theory, and obtain the hologram of the 3D object on the holographic surface; third, segment and zero-fill the obtained hologram in the horizontal direction to obtain holograms with the same size. Figure 1 and holographic Figure 1 , holographic Figure 2 , and holographic Figure 1 , and holographic Figure 2Two final holograms are obtained by loading digital blazed gratings separately. Then, the two final holograms are loaded onto spatial light modulator 1 and spatial light modulator 2 respectively. The effective imaging areas of the two spatial light modulators are stitched together by a beam splitter to obtain a large-size object reconstruction image.

[0004] As attached Figure 2 As shown, in step one, the 3D object to be recorded is considered as a series of point light sources located on surfaces of different depths. The process of light rays emitted from object point P reaching the boundary of the holographic surface is shown by the dashed arrow. Let the propagation distance from object point P to the wavefront recording plane be z1, and the propagation distance from the wavefront recording plane to the holographic surface be z2. According to 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 central diffraction plane, k = 2π / λ is the wavenumber, and λ is the wavelength. By translating the central diffraction pattern, the diffraction patterns of all points can be obtained. The size of the diffraction pattern of each point in the same depth plane is equal to the size of the central diffraction pattern of that layer.

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

[0008]

[0009] As attached Figure 3 As shown, during holographic reconstruction using a single spatial light modulator, when parallel light illuminates the spatial light modulator, according to the principle of diffraction, 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 behind the spatial light modulator, only region AB can display the complete reconstructed image within the maximum diffraction angle range of the reconstructed image. Region AB is called the effective viewing area. According to geometric principles, the maximum diffraction angle α1 of the complete reconstructed image and the size V1 of the effective viewing area are respectively:

[0012]

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

[0014] H p1 = H - D (6)

[0015]

[0016] where int() represents the rounding operation. According to equation (6), the size of the recorded object is required to be 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 shown in FIG. 1, when two spatial light modulators of the same model and resolution M are seamlessly spliced, the overall imaging effect is equivalent to that of a spatial light modulator with a resolution of 2M. Figure 4 As shown in FIG. 1, when two spatial light modulators of the same model and resolution M are seamlessly spliced, the overall imaging effect is equivalent to that of a spatial light modulator with a resolution of 2M. Figure 4 In the present application, the effective viewing area is the CD area, and the maximum diffraction angle a2 of the complete reconstruction image of the two spatial light modulators and the size V2 of the effective viewing area are respectively:

[0018]

[0019] a2 > 2a1 (10)

[0020] V2 > 2V1 (11)

[0021] According to equations (10) and (11), compared with the method of calculating the effective viewing area of two reconstruction images respectively and then splicing, the method proposed in the present application has a larger reconstruction size and effective viewing area. After seamlessly splicing two spatial light modulators, the size H p2 and the resolution re(H p2 ) of the central diffraction pattern on the wavefront recording plane are respectively:

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

[0023]

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

[0025]

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

[0027]

[0028] where, and are Fourier transform and inverse Fourier transform respectively, PFP w (x w ,y w ) is the complex amplitude distribution of a point source with coordinates (x w ,y w ) on the wavefront recording plane, (f x ,f y ) is the frequency domain coordinate, and the calculation formula of the transfer function H(f x ,f y ) is:

[0029]

[0030] In step three, firstly, the hologram obtained in step two is divided into two holograms with the same size in the horizontal direction, and zero padding operation is performed on the two holograms respectively, so that their resolutions are the same as the resolution of the spatial light modulator, thereby obtaining hologram Figure 1 and hologram Figure 2 . Then, digital blazed gratings are loaded on hologram Figure 1 and hologram Figure 2 respectively, thereby obtaining two final holograms. The function of the digital blazed grating is to make the reconstructed images of hologram Figure 1 and hologram Figure 2 be seamlessly spliced together in space. IV. BRIEF DESCRIPTION OF DRAWINGS

[0031] Fig. 1 is a flowchart of a wavefront recording plane optimization-based large-size hologram fast generation method according to the present application. Figure 1 Fig. 2 is a schematic diagram of the principle of the wavefront recording plane method.

[0032] Fig. 3 is a schematic diagram of the geometric relationship between the effective view area of the reconstructed image and a single spatial light modulator. Figure 2 Fig. 4 is a schematic diagram of the geometric relationship between the effective view area of the reconstructed image and two spatial light modulators.

[0033] Figure 3 Fig. 5 is a composition diagram of a verification system of a wavefront recording plane optimization-based large-size hologram fast generation method according to the present application.

[0034] The figure reference numbers in the above-mentioned drawings are as follows: Figure 4

[0035] Figure 5

[0036]

[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 figures are only schematic and are not drawn to scale. V. Detailed Implementation Methods

[0039] The following will describe in detail, with reference to the accompanying drawings and embodiments, a method for rapid generation of large-size holograms based on wavefront recording plane optimization proposed in this invention. It is important to note that the following embodiments are only for further illustration of this invention and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description are still within the scope of protection of this invention.

[0040] One embodiment of the present invention is as follows: The method proposed in this invention is implemented through the appendix... Figure 5 The holographic display system shown includes a laser, a filter, a solid-state lens, a beam splitter, two spatial light modulators (1 and 2), a computer, an aperture, and a CCD. The laser, filter, and solid-state lens generate a uniform parallel beam. The beam splitter divides the light source beam into two mutually perpendicular beams, allowing the zero-order light modulated by the spatial light modulators to be seamlessly stitched together. The computer loads the hologram. The aperture and two lenses with the same focal length form a 4f system, which filters out stray light from the reconstructed image. When the hologram is loaded onto the spatial light modulators, a large-size holographic reconstructed image is captured using the CCD.

[0041] Green laser with wavelength of 532 nm was used as light source in the experiment. The focal length of the solid lens was 300 mm, and the transmittance of the beam splitter was >80%. The two spatial light modulators were of the same type, and the pixel number and pixel pitch were 1920x1080 and 6.4 μm, respectively. Therefore, the resolution and pixel pitch of the two spatial light modulators after lateral splicing were 3840x1080 and 6.4 μm, respectively. The object with resolution of 200x200 was selected as the recorded object. According to the calculation of the effective viewing area, the resolution of the hologram was 2384x728, the calculation time of the hologram was 133.76 s, and the average calculation time of each object point was 3.34 ms. At the same time, when the new lookup table algorithm was used for comparison experiment, the resolution of the hologram was 3840x1080, the calculation time of the hologram was 224.40 s, and the average calculation time of each object point was 5.61 ms. It can be seen that, compared with the new lookup table algorithm, the calculation speed of the method proposed in the application was increased by 40.4%. After the generated hologram was subjected to segmentation and zero padding operation, the digital blazed grating was loaded to obtain the final holographic Figure 1 and holographic Figure 2 . The holographic Figure 1 and holographic Figure 2 were loaded onto the spatial light modulator 1 and the spatial light modulator 2, respectively, and the large-size holographic reconstruction image was received by the CCD. Compared with the imaging using a single spatial light modulator, the horizontal resolution of the reconstruction image was doubled by the method. Compared with the traditional holographic 3D display method using two spatial light modulators for direct splicing, the method proposed in the application increased the effective viewing area while improving the calculation speed.

Claims

1. A method for rapid generation of large-size holograms based on wavefront recording plane optimization, characterized in that, The method comprises the following three steps: First, the 3D object is discretized into independent point sources. Then, based on scalar diffraction theory and the viewing area characteristics of the reconstructed image, the center diffraction pattern of each point in the depth plane is calculated. The diffraction patterns of other points on the same layer are obtained by translating the center diffraction pattern. Finally, the hologram of the 3D object on the wavefront recording plane is obtained by superimposing the diffraction patterns of all points. Second, the diffraction pattern from the wavefront recording plane to the holographic plane is calculated based on angular spectrum diffraction theory to obtain the hologram of the 3D object on the holographic plane. Third, the obtained hologram is segmented and zero-padding is performed in the horizontal direction. Holograms 1 and 2 of the same size are obtained. Digital blazed gratings are then loaded onto holograms 1 and 2 respectively to obtain two final holograms. These two final holograms are then loaded onto spatial light modulators 1 and 2 respectively. A beam splitter is used to stitch together the effective imaging regions of the two spatial light modulators, thus obtaining a large-size object reconstruction image. In step one, the 3D object to be recorded is considered as a series of point light sources located on planes of different depths. According to 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 plane, z1 is the propagation distance from the object point to the wavefront recording plane, and k = 2π / λ Here, λ is the wave number and λ is the wavelength. By translating the central diffraction pattern, the diffraction patterns of all object points are 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 that layer. Simultaneously, the effective viewing area of ​​the reconstructed image is analyzed. Based on the diffraction principle and geometric relationships, when two identical spatial light modulators with a resolution of M are seamlessly stitched together, the overall imaging effect is equivalent to a spatial light modulator with a resolution of 2M. The maximum diffraction angle α2 and the effective viewing area size V2 of the complete reconstructed image based on the two spatial light modulators are respectively: 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 is H. p2 and resolution re(H) p2 They are respectively: H p2 =2H-D The size H of the central diffraction pattern on the wavefront recording plane after seamless stitching using two spatial light modulators. w2 for:

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

3. The method for rapid generation of large-size holograms based on wavefront recording plane optimization according to claim 1, characterized in that, In step three, the hologram obtained in step two is first divided into two holograms of the same size in the horizontal direction, and zero-padding is performed on the two holograms to make their resolution the same as that of the spatial light modulator, thus obtaining hologram 1 and hologram 2. Then, digital blazed gratings are loaded onto hologram 1 and hologram 2 respectively to obtain two final holograms. The function of the digital blazed gratings is to enable the reconstructed images of hologram 1 and hologram 2 to be seamlessly stitched together in space.

Images