Design of holographic reproduction images based on liquid crystal spatial light modulator
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摘要:
随着全息平视显示系统、虚拟现实增强显示等技术的广泛应用，全息场景对再现图像的质量要求将会更高，再现图像的尺寸将会更加符合人眼视觉特征。本文根据计算全息再现成像原理，采用Gerchberg-Saxton (GS) 算法对输入与输出平面光场分布进行正、逆傅里叶变换迭代求解原始仿真图像在不同特征参数（线宽、圆环直径）和不同计算采样间隔下的相位分布，并仿真计算得到相应的再现图像。利用液晶空间光调制器搭建全息再现实验光路，通过加载不同原始仿真图像的相位分布图进行再现实验，采用相机拍摄得到远场衍射全息再现图像并进行图像处理得到再现图像的实际特征尺寸，实验结果表明再现图像特征尺寸与原始仿真图像特征尺寸基本呈线性变化关系，再现图像尺寸与仿真计算采样间隔呈现非线性变化关系，且与推导的理论计算关系曲线一致。为了进一步验证结论的正确性，设计预期再现图像尺寸为圆环直径0.943 mm，中心十字线宽0.015 mm时，仿真计算得到预期目标原始仿真图像的特征尺寸和采样间隔分别为线宽3 pixel、圆环直径594 pixel、采样间隔25 μm，通过再现实验测量得到的全息再现图像圆环直径为0.93 mm，线宽为0.017 mm，误差精度在0.02 mm以内。研究结果对全息显示、AR/VR显示等应用场景提高虚拟显示图像尺寸真实性提供有益参考。
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关键词:
- 计算全息 /
- 傅里叶变换 /
- Gerchberg-Saxton算法 /
- 采样间隔 /
- 液晶空间光调制器
Abstract:With the wide application of holographic head-up display system and virtual reality augmented display technology, holographic reproduced images are required to be virtual images with higher quality, more realistic reproduction image size and more in line with human visual characteristics. Based on the principle of computer-generated holograms reproduction imaging, this paper used the Gerchberg-Saxton (GS) algorithm to iteratively solve the phase distribution of the original simulation images under different characteristic parameters (line width, ring diameter) and different calculated sampling intervals by performing direct and inverse Fourier transforms on the optical field distributions of the input and output planes, and the corresponding reproduced images were obtained by simulation calculation. The optical path of the holographic reproduction experiment was constructed by using the liquid crystal spatial light modulator, and the reproduction experiment was carried out by loading the phase distribution maps of different original simulation images, the holographic reproduction images of far-field diffraction were taken by the camera, and the actual feature size of the reproduced images was obtained by image processing. The experimental results show that the feature size of the reproduced images is basically linear with the characteristic size of the original simulation images. Furthermore, the reproduction image size shows a non-linear change relationship with the sampling intervals of the simulation calculation, which is consistent with the derived theoretical calculation relationship curve. In order to further verify the correctness of the conclusion, when the size of the expected reproduced image is designed as the ring diameter of 0.943mm and the line width of the central cross of 0.015mm. The characteristic size and sampling interval of the original simulation image of the expected target are obtained by the simulation calculation as the line width of 3pixel, the ring diameter of 594pixel and the sampling interval of 25μm, respectively. The ring diameter and line width of the holographic reproduction image, as measured by the reproduction experiment, are 0.93mm and 0.017mm, respectively. The error accuracy is within 0.02mm. The findings of this study provide an effective reference for application scenarios such as holographic display and AR/VR display to improve the authenticity of virtual display image size.
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图 7 不同线宽下原始图像的相位分布
Figure 7. Phase distribution of original images with different line widths
图 10 不同圆环直径下原始图像的相位分布
Figure 10. Phase distribution of original images with different ring diameters
图 11 不同圆环直径的仿真再现图像
Figure 11. Simulated reproduction images with different ring diameters
图 12 不同采样间隔下原始图像的相位分布
Figure 12. Phase distribution of original images with different sampling intervals
图 13 不同采样间隔的仿真再现图像
Figure 13. Simulated reproduction images with different sampling intervals
图 15 基于LC-SLM的全息再现实验系统。1-激光平行光管；2-偏振片；3-LC-SLM；4-带成像镜头的CCD相机；5-电脑1；6-电脑2
Figure 15. Holographic reproduction experimental system based on LC-SLM. 1-Laser collimated light tube; 2-Polarizer; 3-LC-SLM; 4-CCD camera with imaging lens; 5-Computer 1; 6-Computer 2
图 16 透射式相位型LC-SLM液晶显示屏的微结构
Figure 16. Microstructure of transmissive phase-type LC-SLM liquid crystal display
图 18 不同线宽的全息再现图像
Figure 18. Holographic reproduction images with different line widths
图 19 再现图像线宽随原始图像线宽的变化曲线
Figure 19. Curve of the line widths of the reproduction images with the line widths of the original images
图 20 不同圆环直径下的全息再现图像
Figure 20. Holographic reproduction images with different ring diameters
图 21 再现图像圆环直径随原始图像圆环直径的变化曲线
Figure 21. Curve of the ring diameters of reproduction images with ring diameters of original images
图 22 不同采样间隔下的全息再现图像
Figure 22. Holographic reproduction images with different sampling intervals
图 23 再现图像尺寸与相机镜头焦距的关系示意图
Figure 23. Schematic diagram of relationship between reproduction images and focal length of camera lens
图 24 再现图像尺寸随采样间隔的变化曲线
Figure 24. The curve of the size of reproduction images with sampling intervals
图 25 仿真设计的预期目标图像、相位分布图及再现图像
Figure 25. Expected target images and phase distribution map of the simulation design, and the reproduction image
表 1 不同原始图像线宽对应的仿真再现图像线宽值
Table 1. Line widths of simulated reproduction images corresponding to line widths of different original images
Line width of the original
images k0 (pixel)Line width of the simulated
reproduction images (pixel)Fitting
slope5 5 1 10 10 15 15 20 20 
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表 2 不同原始图像圆环直径对应的仿真再现图像圆环直径
Table 2. Simulated reproduction image ring diameters corresponding to different original image ring diameters
Ring diameter of the
original images D0 (pixel)Ring diameter in simulated
reproduction images (pixel)Fitting
slope400 400 1 500 500 600 600 700 700
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表 3 不同采样间隔对应的仿真再现图像圆环直径值
Table 3. Simulated reproduction image ring diameters corresponding to different sampling intervals
Ring diameter
of original
imagesSampling
coefficient
NSampling
interval d
(μm)Ring diameter of
simulated reproduction
images (pixel)Fitting
slope700 1 12.5 700 1 2 25 350 1/2 4 50 175 1/4 8 100 87 1/8
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表 4 LC-SLM的工作参数
Table 4. Operating parameters of LC-SLM
Project Parameter Effective area size 12.8 mm×9.6 mm Number of pixels 1024×768 Pixel size 12.5 μm×12.5 μm Pixel pitch 12.5 μm Fill factor 80% Gray scale range 0～255
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表 5 CCD相机及成像镜头的工作参数
Table 5. Operating parameters of CCD cameras and imaging lens
Project Parameter Camera operating parameters Number of pixels 2048×1536 Pixel size 2.8 μm×2.8 μm Lens operating parameters Focal length 50 mm Aperture range F/1.8～F/10
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表 6 实验测试的不同原始图像线宽对应的再现图像线宽值
Table 6. Reproduction images line widthscorresponding to different original images line widths tested experimentally
Line width of the
original images
k0 (pixel)Line width of the
reproduction images
in pixels (pixel)Line width of the
reproduction images
k (mm)Fitting
slope
(mm/pixel)5 10 0.0280 0.0030 10 16 0.0450 15 22 0.0620 20 26 0.0730
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表 7 实验测试的不同原始图像圆环直径对应的再现图像圆环直径值
Table 7. Ring diameters of the reproduction images corresponding to the ring diameters of the different original images tested experimentally
Ring diameter of
the original images
D0 (pixel)Pixel occupied by
ring diameters in
reproduction
images (pixel)Ring diameter of
reproduction images
D (mm)Fitting
slope
(mm/pixel)400 448 1.2544 0.0030 500 558 1.5624 600 667 1.8676 700 766 2.1448
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表 8 实验测试的不同采样间隔对应的再现图像圆环直径值
Table 8. The ring diameters values of the reproduction images corresponding to the different sampling intervals tested experimentally
Sampling
coefficient
NSampling
interval d
(μm)Pixel occupied by ring
diameters of reproduction
images (pixel)Ring diameter of
reproduction images
D (mm)1 12.5 702 2.1448 2 25 396 1.1088 4 50 241 0.6748 8 100 162 0.4536
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