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Adaptive mixed-constraint Gerchberg-Saxton algorithm for phase-only holographic display

Gao Qian-Cheng He Ze-Hao Liu Ke-Xuan Han Chao Cao Liang-Cai

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Adaptive mixed-constraint Gerchberg-Saxton algorithm for phase-only holographic display

Gao Qian-Cheng, He Ze-Hao, Liu Ke-Xuan, Han Chao, Cao Liang-Cai
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  • At present, spatial light modulators are incapable of modulating both the amplitude and phase of the wavefront simultaneously. Therefore, when a spatial light modulator is used for holographic display, it is necessary to encode the complex amplitude of the object wave into amplitude-only or phase-only computer-generated-hologram. The phase-only holographic display has attracted much attention of researchers due to its characteristics of high diffraction efficiency and no conjugate image. However, current optimization algorithms for generating phase-only hologram have the problems of iterative divergence, slow convergence speed, and poor reconstruction quality, which is difficult to satisfy the requirements for high-quality holographic display. In this work, we propose an accurate adaptive mixed constraint Gerchberg-Saxton algorithm by constraining the frequency bandwidth in the hologram plane and adaptively constraining the amplitude of the reconstructed image in the image plane based on the angular spectrum propagation theory. Firstly, we use the angular spectrum propagation model without paraxial approximation to simulate the forward and backward propagation of the light wave for ensuring the accuracy of the wavefront propagation. Secondly, dividing the image plane into signal area and noise area according to the spatial distribution of target image, and different adaptive feedback strategies are set up for the two regions based on the optimized effect of the phase-only hologram. The adaptive feedback strategy is established, which can accelerate the convergence speed of the proposed algorithm and enhance the hologram of freedom of the optimization. Finally, the frequency bandwidth constraint strategy is introduced in the hologram plane to optimize the edge pixels and compensate for the frequency information loss of the phase-only computer-generated hologram, which improves the reconstruction quality of the hologram. After 100 iterations, the average correlation coefficient of the holographic reconstructed image of the proposed algorithm is about 0.9857, and the average peak signal-to-noise ratio is about 31.02 dB. The correlation coefficient and the peak signal-to-noise ratio of the reconstructed images of the proposed algorithm are better than those of the Gerchberg-Saxton algorithm with only frequency bandwidth constraint strategy, and the proposed algorithm has clearer texture and better display effect. The results of numerical simulations and optical experiments show the feasibility and effectiveness of the proposed method. The proposed adaptive mixed constraint Gerchberg-Saxton algorithm is a promising technology for high-quality holographic display.
      Corresponding author: Han Chao, hanchaozh@126.com ; Cao Liang-Cai, clc@tsinghua.edu.cn
    • Funds: Project supported by the Regional Innovation and Development Joint Funds of the National Natural Science Foundation of China (Grant No. U22A2079), the Open Research Fund of Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University, China (Grant No. DTESD2020A06), the 2021 Anhui University Graduate Scientific Research Project, China (Grant No. YJS20210447), and the Science and Technology Planning Project of Wuhu City, China (Grant No. 2021cg21).
    [1]

    Goodman J W, Lawrence R W 1967 Appl. Phys. Lett. 11 77Google Scholar

    [2]

    Gabor D 1948 Nature 161 777Google Scholar

    [3]

    Zhang H, Zhao Y, Cao L C, Jin G F 2014 Chin. Opt. Lett. 12 060002Google Scholar

    [4]

    He Z H, Sui X M, Jin G F, Cao L C 2019 Appl. Opt. 58 A74Google Scholar

    [5]

    Ma Q G, Cao L C, He Z H, Zhang S D 2019 Chin. Opt. Lett. 17 111001Google Scholar

    [6]

    贾甲, 王涌天, 刘娟, 李昕, 谢敬辉 2012 激光与光电子学进展 49 050002Google Scholar

    Jia J, Wang Y T, Liu J, Li X, Xie J H 2012 Lasers Optoelectron. Prog. 49 050002Google Scholar

    [7]

    Chang C L, Bang Kiseung, Wetzstein Gordon, Lee Byoungho, Gao L 2020 Optica 7 1563Google Scholar

    [8]

    Zhang H, Xie J H, Liu J, Wang Y T 2009 Appl. Opt. 48 5834Google Scholar

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    王迪, 侯页好, 黄倩, 郑义微, 王琼华 2022 中国激光 49 1909001Google Scholar

    Wang D, Hou Y H, Huang Q, Zheng Y W, Wang Q H 2022 Chin. J. Lasers 49 1909001Google Scholar

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    王一同, 周宏强, 闫景逍, 合聪, 黄玲玲 2021 中国激光 48 1918004

    Wang Y T, Zhou H Q, Yan J X, He C, Huang L L 2021 Chin. J. Lasers 48 1918004

    [11]

    范爽, 张亚萍, 王帆, 高云龙, 钱晓凡, 张永安, 许蔚, 曹良才 2018 物理学报 67 094203Google Scholar

    Fan S, Zhang Y P, Wang F, Gao Y L, Qian X F, Zhang Y A, Xu W, Cao L C 2018 Acta Phys. Sin. 67 094203Google Scholar

    [12]

    席思星, 于娜娜, 王晓雷, 朱巧芬, 董昭, 王微, 刘秀红, 王华英 2019 物理学报 68 110502Google Scholar

    Xi S X, Yu N N, Wang X L, Zhu Q F, Dong Z, Wang W, Liu X H, Wang H Y 2019 Acta Phys. Sin. 68 110502Google Scholar

    [13]

    曹良才, 何泽浩, 刘珂瑄, 隋晓萌 2022 红外与激光工程 51 20210935Google Scholar

    Cao L C, He Z H, Liu K X, Sui X M 2022 Inf. Laser. Eng. 51 20210935Google Scholar

    [14]

    何泽浩, 隋晓萌, 曹良才, 金国藩 2021 中国激光 48 1209002Google Scholar

    He Z H, Sui X M, Cao L C, Jin G F 2021 Chin. J. Lasers 48 1209002Google Scholar

    [15]

    He Z H, Sui X M, Jin G F, Chu D P, Cao L C 2021 Opt. Express 29 119Google Scholar

    [16]

    Liu K X, He Z H, Cao L C 2021 Chin. Opt. Lett. 19 50501Google Scholar

    [17]

    Sui X M, He Z H, Jin G F, Chu D P, Cao L C 2021 Opt. Express 29 2597Google Scholar

    [18]

    Liu K, He Z H, Cao L C 2022 Appl. Phys. Lett. 120 061103Google Scholar

    [19]

    Wu J C, Liu K X, Sui X M, Cao L C 2021 Opt. Lett. 46 2908Google Scholar

    [20]

    Gerchberg R W, Saxton W O 1972 Optik 35 237

    [21]

    Zhou P C, Bi Y, Sun M Y, Wang H, Li F, Qi Y 2014 Appl. Opt. 53 G209Google Scholar

    [22]

    Chang C L, Xia J, Yang L, Lei W, Yang Z M, Chen J H 2015 Appl. Opt. 54 6994Google Scholar

    [23]

    Chen L Z, Zhang H, He Z H, Wang X Y, Cao L C, Jin G F 2020 Appl. Sci. 10 3652Google Scholar

    [24]

    Wu Y, Wang J, Chen C, Liu C J, Jin F M, Chen N 2021 Opt. Express 29 1412Google Scholar

  • 图 1  AMCGS算法中的信号区与噪声区

    Figure 1.  Signal area and noise area on the reconstruction plane in the AMCGS algorithm.

    图 2  AMCGS算法原理图

    Figure 2.  Schematic of AMCGS algorithm.

    图 3  目标图像(a)—(d)及其AMCGS反馈策略仿真重建结果(e)—(h) (a), (e) 狒狒; (b), (f) 船; (c), (g) 芭芭拉; (d), (h) 女人

    Figure 3.  Target images (a)–(d) and corresponding simulation results by the proposed AMCGS feedback (e)–(h): (a), (e) Baboon;(b), (f) ship; (c), (g) barbara; (d), (h) women.

    图 4  AMCGS算法与RSGS算法仿真重建结果CC值随迭代次数的变化曲线 (a) 狒狒; (b) 船; (c) 芭芭拉; (d) 女人

    Figure 4.  CCs under different iteration numbers of the reconstructions by the AMCGS algorithm and RSGS algorithm: (a) Baboon; (b) ship; (c) barbara; (d) women.

    图 5  AMCGS算法与RSGS算法仿真重建结果PSNR值随迭代次数的变化曲线 (a) 狒狒; (b) 船; (c) 芭芭拉; (d) 女人

    Figure 5.  PSNRs under different iteration numbers of the reconstructions by the AMCGS algorithm and RSGS algorithm: (a) Baboon; (b) ship; (c) barbara; (d) women.

    图 6  全息再现仿真结果对比 (a)—(d) 传统随机相位法; (e)—(h) AMCGS算法

    Figure 6.  Comparison of holographic reconstructions simulation results: (a)–(d) Traditional random-phase method; (e)–(h) AMCGS algorithm.

    图 7  光学实验系统结构

    Figure 7.  Schematic of optical experimental setup.

    图 8  光学实验结果对比 (a)—(d) 传统随机相位法; (e)—(h) AMCGS算法

    Figure 8.  Comparison of optics experimental results: (a)–(d) Conventional random phase method; (e)–(h) AMCGS algorithm.

    表 1  传统GS算法, RSGS算法以及AMCGS算法迭代100次所需时间

    Table 1.  Time required for 100 iterations of GS algorithm, RSGS algorithm and AMCGS algorithm.

    算法类型时间/s
    BaboonBarbaraShipWomen
    传统GS算法3.022.982.963.12
    RSGS算法10.0510.0310.0610.10
    AMCGS算法10.4710.1110.0810.26
    DownLoad: CSV
  • [1]

    Goodman J W, Lawrence R W 1967 Appl. Phys. Lett. 11 77Google Scholar

    [2]

    Gabor D 1948 Nature 161 777Google Scholar

    [3]

    Zhang H, Zhao Y, Cao L C, Jin G F 2014 Chin. Opt. Lett. 12 060002Google Scholar

    [4]

    He Z H, Sui X M, Jin G F, Cao L C 2019 Appl. Opt. 58 A74Google Scholar

    [5]

    Ma Q G, Cao L C, He Z H, Zhang S D 2019 Chin. Opt. Lett. 17 111001Google Scholar

    [6]

    贾甲, 王涌天, 刘娟, 李昕, 谢敬辉 2012 激光与光电子学进展 49 050002Google Scholar

    Jia J, Wang Y T, Liu J, Li X, Xie J H 2012 Lasers Optoelectron. Prog. 49 050002Google Scholar

    [7]

    Chang C L, Bang Kiseung, Wetzstein Gordon, Lee Byoungho, Gao L 2020 Optica 7 1563Google Scholar

    [8]

    Zhang H, Xie J H, Liu J, Wang Y T 2009 Appl. Opt. 48 5834Google Scholar

    [9]

    王迪, 侯页好, 黄倩, 郑义微, 王琼华 2022 中国激光 49 1909001Google Scholar

    Wang D, Hou Y H, Huang Q, Zheng Y W, Wang Q H 2022 Chin. J. Lasers 49 1909001Google Scholar

    [10]

    王一同, 周宏强, 闫景逍, 合聪, 黄玲玲 2021 中国激光 48 1918004

    Wang Y T, Zhou H Q, Yan J X, He C, Huang L L 2021 Chin. J. Lasers 48 1918004

    [11]

    范爽, 张亚萍, 王帆, 高云龙, 钱晓凡, 张永安, 许蔚, 曹良才 2018 物理学报 67 094203Google Scholar

    Fan S, Zhang Y P, Wang F, Gao Y L, Qian X F, Zhang Y A, Xu W, Cao L C 2018 Acta Phys. Sin. 67 094203Google Scholar

    [12]

    席思星, 于娜娜, 王晓雷, 朱巧芬, 董昭, 王微, 刘秀红, 王华英 2019 物理学报 68 110502Google Scholar

    Xi S X, Yu N N, Wang X L, Zhu Q F, Dong Z, Wang W, Liu X H, Wang H Y 2019 Acta Phys. Sin. 68 110502Google Scholar

    [13]

    曹良才, 何泽浩, 刘珂瑄, 隋晓萌 2022 红外与激光工程 51 20210935Google Scholar

    Cao L C, He Z H, Liu K X, Sui X M 2022 Inf. Laser. Eng. 51 20210935Google Scholar

    [14]

    何泽浩, 隋晓萌, 曹良才, 金国藩 2021 中国激光 48 1209002Google Scholar

    He Z H, Sui X M, Cao L C, Jin G F 2021 Chin. J. Lasers 48 1209002Google Scholar

    [15]

    He Z H, Sui X M, Jin G F, Chu D P, Cao L C 2021 Opt. Express 29 119Google Scholar

    [16]

    Liu K X, He Z H, Cao L C 2021 Chin. Opt. Lett. 19 50501Google Scholar

    [17]

    Sui X M, He Z H, Jin G F, Chu D P, Cao L C 2021 Opt. Express 29 2597Google Scholar

    [18]

    Liu K, He Z H, Cao L C 2022 Appl. Phys. Lett. 120 061103Google Scholar

    [19]

    Wu J C, Liu K X, Sui X M, Cao L C 2021 Opt. Lett. 46 2908Google Scholar

    [20]

    Gerchberg R W, Saxton W O 1972 Optik 35 237

    [21]

    Zhou P C, Bi Y, Sun M Y, Wang H, Li F, Qi Y 2014 Appl. Opt. 53 G209Google Scholar

    [22]

    Chang C L, Xia J, Yang L, Lei W, Yang Z M, Chen J H 2015 Appl. Opt. 54 6994Google Scholar

    [23]

    Chen L Z, Zhang H, He Z H, Wang X Y, Cao L C, Jin G F 2020 Appl. Sci. 10 3652Google Scholar

    [24]

    Wu Y, Wang J, Chen C, Liu C J, Jin F M, Chen N 2021 Opt. Express 29 1412Google Scholar

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Publishing process
  • Received Date:  25 August 2022
  • Accepted Date:  14 October 2022
  • Available Online:  11 November 2022
  • Published Online:  20 January 2023

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