A high-quality and high-efficiency hologram generation method based on complex amplitude constraint algorithm

Abstract

The application provides a high-quality and high-efficiency hologram generation method based on a complex amplitude constraint algorithm. The method comprises three steps: first, based on the intensity map and the depth map of the three-dimensional scene, the three-dimensional scene is processed in layers to obtain a set of layered images. Second, the inverse wavefront propagation calculation is performed on the layered images to generate the initial complex amplitude field on the hologram plane; then the wavefront propagation calculation is performed on the initial complex amplitude field on the hologram plane to generate the target complex amplitude field on the target plane. Third, the hologram is initialized by using the initial complex amplitude field on the hologram plane, and the wavefront propagation calculation is performed on the hologram to generate the reconstructed complex amplitude field of the hologram on the target plane; then the reconstructed complex amplitude field is constrained by using the target complex amplitude field on the target plane, and the reconstructed complex amplitude field is iteratively optimized to finally generate a high-quality hologram.

Description

I. Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a high-quality and efficient hologram generation method based on a complex amplitude constraint algorithm. II. Background Technology

[0002] Computational holography has garnered widespread attention for its ability to realistically reconstruct 3D scenes and provide viewers with a comfortable visual experience. However, achieving ideal holographic displays remains challenging, primarily due to the wavefront propagation process from the 3D scene to the hologram plane, and the phase encoding process from the complex amplitude distribution on the hologram plane to the pure phase hologram. These two processes jointly determine the computation time and image quality of the hologram reconstruction. In recent years, iterative algorithms have been widely applied to the computation of pure phase holograms. However, most existing iterative algorithms fail to consider the relationship between wavefront propagation and phase encoding, nor do they fully account for the crucial role and influence of phase information in hologram generation, resulting in poor image quality in the hologram reconstruction. Furthermore, while iterative algorithms can also be used to compute holograms of 3D scenes, the computation time of existing algorithms is affected by the complexity of the 3D scene, leading to excessively long computation times when handling complex 3D scenes. Therefore, reducing the computation time of holograms and improving the quality of hologram reconstruction—that is, efficiently generating high-quality pure phase holograms—is a pressing issue in the field of holographic displays. III. Summary of the Invention

[0003] This invention proposes a high-quality and efficient hologram generation method based on a complex amplitude constraint algorithm. (See attached diagram) Figure 1 As shown, the method of this invention includes three steps: First, the 3D scene is layered based on the intensity map and depth map of the 3D scene to obtain a set of layered images. Second, inverse wavefront propagation calculation is performed on the layered images to generate an initial complex amplitude field on the hologram plane; then, wavefront propagation calculation is performed on the initial complex amplitude field on the hologram plane to generate a target complex amplitude field on the target plane. Third, the hologram is initialized using the initial complex amplitude field on the hologram plane, and wavefront propagation calculation is performed on the hologram to generate a reconstructed complex amplitude field of the hologram on the target plane; then, the reconstructed complex amplitude field is constrained using the target complex amplitude field on the target plane, and the reconstructed complex amplitude field is iteratively optimized to finally generate a high-quality hologram. This invention reconstructs the complex amplitude field on the target plane based on complex amplitude constraints, which helps to recover all wavefront information of the 3D scene, thereby improving the quality of holographic reconstruction. In each iteration, only two wavefront propagation calculations are performed, and the number of calculations is independent of the number of layers in the 3D scene, thus significantly improving the computational efficiency of holograms of complex 3D scenes.

[0004] In step one, the intensity map of the 3D scene is a color image with three channels: red, green, and blue, while the depth map of the 3D scene is a single-channel grayscale image. Based on the different depth distributions of different parts of the 3D scene, the intensity map of the 3D scene is divided into a group of layered images located at different depths, with scenes within the same depth range located in the same layered image.

[0005] In step two, since the distance between each layered image and the hologram plane is different, a wavefront propagation method considering occlusion is used to generate the target complex amplitude field on the target plane. Specifically, firstly, a binarized mask is generated for each layered image, where the pixel values ​​corresponding to the non-zero regions of the layered image are 0, and the pixel values ​​of the remaining regions are 1. Then, inverse wavefront propagation is performed on the first layered image to obtain its complex amplitude distribution at the location of the second layered image. This complex amplitude distribution is then multiplied by the mask of the second layer to obtain the complex amplitude distribution after being occluded by the second layer. Next, the occluded complex amplitude distribution is added to the second layered image, and inverse wavefront propagation is continued to obtain its complex amplitude distribution at the location of the third layered image. The above process of occlusion using a binarized mask and layer-by-layer wavefront propagation is repeated until the inverse wavefront propagation calculation of all layers is completed, resulting in the initial complex amplitude field on the hologram plane. Finally, wavefront propagation calculation is performed on the initial complex amplitude field on the hologram plane to obtain the target complex amplitude field on the target plane. Preferably, the wavefront propagation method in this invention is the angular spectrum method.

[0006] In step three, the hologram is first initialized by taking the phase of the initial complex amplitude field on the hologram plane. The phase distribution range of the initialized hologram is [0, 2π]. Next, the complex amplitude field reconstructed from the initialized hologram on the target plane is obtained through wavefront propagation. Specifically, the target plane can be divided into a signal region and a noise region, where the size of the signal region is controlled by a shearing factor c.

[0007] p signal =(p hologram -p image ) / c+p image (1)

[0008] Where, p signal p image and p hologram These represent the number of pixels in the signal region, image region, and the entire hologram region, respectively. Then, the reconstructed complex amplitude field is constrained using the target complex amplitude field generated in step two. The complex amplitude constraint algorithm is expressed as follows:

[0009]

[0010] Among them, U (n+1) and U (n)Let A represent the complex amplitude fields reconstructed on the target plane in the (n+1)th and nth iterations, respectively, where n>1. t and Let represent the amplitude and phase of the target complex amplitude field, respectively. The signal region is the signal area, and the free region is the noise area. w represents the weight of the complex amplitude constraint, expressed as:

[0011] w = exp(A t -A (n) (3)

[0012] Among them, A (n) This represents the amplitude on the target plane during the nth iteration.

[0013] After completing a single complex amplitude constraint, the reconstructed complex amplitude field on the target plane is propagated in reverse wavefront to obtain the complex amplitude field on the hologram plane. Then, only the phase of this complex amplitude field is retained as the newly generated hologram. Finally, the above wavefront propagation and complex amplitude constraint process is repeated between the hologram plane and the target plane until the iteration ends and the final hologram is generated. IV. Description of the attached drawings

[0014] Appendix Figure 1 This is a flowchart of a high-quality and efficient hologram generation method based on a complex amplitude constraint algorithm according to the present invention.

[0015] Appendix Figure 2 This is a comparison diagram of the amplitude reconstruction results of the holographic method of the present invention and the traditional amplitude constraint method.

[0016] Appendix Figure 3 This is a comparison diagram of the phase results of holographic reconstruction using the method of this invention and the traditional amplitude constraint method.

[0017] Appendix Figure 4 This is a comparison chart showing the change in holographic reconstruction quality between the method of this invention and the traditional amplitude constraint method as a function of computation time.

[0018] Appendix Figure 5 This is a comparison chart showing the computation time of the method of this invention and the traditional amplitude constraint method as a function of the number of layers in a 3D scene. V. Detailed Implementation Methods

[0019] The following detailed embodiments of the high-quality and efficient hologram generation method based on the complex amplitude constraint algorithm proposed in this invention further illustrate the invention. It is important to note that the following embodiments are for illustrative purposes only 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.

[0020] An embodiment of the present invention uses a spatial light modulator with a resolution of 1920×1080 and a pixel pitch of 4.5μm to load a hologram. Color lasers with wavelengths of 638nm, 520nm, and 450nm are used as coherent light sources. The emitted lasers are collimated and then illuminate the spatial light modulator. Time-division multiplexing is used to achieve color holographic display. A three-dimensional scene with a resolution of 1300×730 is used as the target scene. Based on the intensity and depth maps of the three-dimensional scene, it is divided into 256 layers, with a depth interval of 0.02mm between each layer. Wavefront propagation is performed using the angular spectral method, and the distance between the hologram plane and the target plane is 8cm. The shearing factor c, which controls the signal region size on the target plane, is set to 8.

[0021] The amplitude of the holographic reconstruction based on the above embodiments is shown in the appendix. Figure 2 As shown, where Figure 2 (a) and 2(b) show the reconstruction results of the traditional amplitude constraint method focusing on the foreground and background parts of the 3D scene, respectively. Figure 2 (c) and 2(d) show the reconstruction results of the foreground and background parts of a 3D scene using the method of the present invention. (See appendix) Figure 2 The peak signal-to-noise ratio (PSNR) of each reconstruction result is indicated. The holographic reconstruction method of this invention achieves a PNR of 21.96 dB for amplitude, compared to 13.55 dB for the traditional method, representing an improvement in quality of approximately 62%. The phase of the holographic reconstruction based on the above embodiments is shown in the attached figure. Figure 3 As shown, where Figure 3 (a) and (b) show the phase reconstructed in the target plane by the conventional method and the method of the present invention, respectively. Compared with the conventional method, the peak signal-to-noise ratio (PSNR) of the reconstructed phase by the method of the present invention is improved by approximately 60%. A comparison of the PSNR of the reconstructed amplitude of the present invention method and the conventional method as a function of iteration number based on the above embodiments is attached. Figure 4 As shown in the figure. This result demonstrates that the method of the present invention has a faster convergence speed and achieves higher image quality with fewer iterations.

[0022] Based on the above embodiments, a comparison of the computation time of the method of the present invention and the conventional method as a function of the number of layers is attached. Figure 5 As shown, the computation time required by the traditional method increases exponentially with the number of layers, while the phase encoding time required by the present method is independent of the number of layers; the time increase mainly comes from the wavefront propagation process. When the number of layers is 256, the traditional method requires 11626 s, while the method of the present invention requires 317 s, reducing the computation time by approximately 97%. This result demonstrates the high efficiency of the present invention in terms of computation time.

Claims

1. A high-quality and efficient hologram generation method based on a complex amplitude constraint algorithm, characterized in that, The method includes the following three steps: First, the three-dimensional scene is processed into layers based on the intensity map and depth map of the three-dimensional scene to obtain a set of layered images; The second step is to perform inverse wavefront propagation calculations on the layered image to generate the initial complex amplitude field on the hologram plane; Then, wavefront propagation calculations are performed on the initial complex amplitude field on the hologram plane to generate the target complex amplitude field on the target plane; The third step involves initializing the hologram using the initial complex amplitude field on the hologram plane and performing wavefront propagation calculations on the hologram to generate the reconstructed complex amplitude field of the hologram on the target plane. Then, the reconstructed complex amplitude field is constrained using the target complex amplitude field on the target plane. By iteratively optimizing the reconstructed complex amplitude field, a high-quality hologram is finally generated. In step two, a wavefront propagation method considering occlusion is used to generate the target complex amplitude distribution on the target plane. First, a binary mask is generated for each layered image, where the pixel values ​​corresponding to the non-zero regions of the layered image are 0, and the pixel values ​​of the remaining regions are 1. Then, inverse wavefront propagation is performed on the layered image of the first layer to obtain its complex amplitude distribution at the second layer position. This complex amplitude distribution is then multiplied by the mask of the second layer to obtain the complex amplitude distribution after being occluded by the second layer. Next, the occluded complex amplitude distribution is added to the layered image of the second layer, and inverse wavefront propagation is continued to obtain its complex amplitude distribution at the third layer position. The above process using binary wavefront propagation is repeated. The process involves masking and wavefront propagation layer by layer until the reverse wavefront propagation calculations for all layers are completed, resulting in an initial complex amplitude field on the hologram plane. Finally, wavefront propagation calculations are performed on the initial complex amplitude field on the hologram plane to obtain the target complex amplitude field on the target plane. In step three, the hologram is first initialized with the phase of the initial complex amplitude field on the hologram plane, and the phase distribution range of the initialized hologram is [0, 2π]. Secondly, the complex amplitude field reconstructed from the initialized hologram on the target plane is obtained through wavefront propagation. Specifically, the target plane is divided into a signal region and a noise region, where the size of the signal region is controlled by a shearing factor c. p signal =(p hologram -p image ) / c+p image Where, p signal p image and p hologram Let represent the number of pixels in the signal region, image region, and the entire hologram region, respectively. Then, the reconstructed complex amplitude field is constrained using the target complex amplitude field generated in step two. The complex amplitude constraint algorithm is expressed as follows: Among them, U (n+1) and U (n) Let A represent the complex amplitude fields reconstructed on the target plane in the (n+1)th and nth iterations, respectively. t and Let represent the amplitude and phase of the target complex amplitude field, respectively; let signal region be the signal region; let free region be the noise region; and let w be the weight of the complex amplitude constraint, expressed as: w=exp[A t -A (n) ] Among them, A (n) This represents the amplitude on the target plane during the nth iteration. After completing the single complex amplitude constraint, the reconstructed complex amplitude field on the target plane is propagated in reverse wavefront to obtain the complex amplitude field on the hologram plane. Then, only the phase of this complex amplitude field is retained as the newly generated hologram. Finally, the above wavefront propagation and complex amplitude constraint process is repeated between the hologram plane and the target plane until the iteration ends and the final hologram is generated.

2. The high-quality and efficient hologram generation method based on the complex amplitude constraint algorithm according to claim 1, characterized in that, In step one, the intensity map of the 3D scene is a color image with three channels: red, green, and blue, and the depth map of the 3D scene is a grayscale image with a single channel. Based on the different depth distributions of different parts of the 3D scene, the intensity map of the 3D scene is divided into a group of layered images located at different depths, where scenes with the same depth range are located in the same layered image.

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