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Gerchberg-Saxton algorithm and angular-spectrum layer-oriented method for true color three-dimensional display

Fan Shuang Zhang Ya-Ping Wang Fan Gao Yun-Long Qian Xiao-Fan Zhang Yong-An Xu Wei Cao Liang-Cai

Gerchberg-Saxton algorithm and angular-spectrum layer-oriented method for true color three-dimensional display

Fan Shuang, Zhang Ya-Ping, Wang Fan, Gao Yun-Long, Qian Xiao-Fan, Zhang Yong-An, Xu Wei, Cao Liang-Cai
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  • Computer-generated hologram (CGH) makes possible the three-dimensional (3D) display of true stereo. It has characteristics of strong flexibility, small noise, easy replication, and computable virtual object. However, there are still some difficulties with the CGH 3D display presently, such as slow computation speed of complex object hologram, small size and small field angle of 3D scene, much noise of reconstruction image, and true color display. In this paper, the problem of reconstruction image noise and true color display of the CGH are studied, and the hologram of true color 3D object with complex morphologies is calculated. First of all, the angular-spectrum layer-oriented method can avoid error caused by the paraxial approximation and be used to accurately generate and calculate 3D object hologram. And it also has advantages of efficient computation, reduced complexity, and less storage memory. We achieve the true color display of a 3D object by using the angular-spectrum method based on intensity and depth maps. We also analyze the problem of multi-wavelength sampling, and mitigate the phenomenon of frequency mixing effectively. Then, we propose to use the Gerchberg-Saxton (GS) algorithm along with the angular-spectrum layer oriented method to reduce the speckle noise in the reconstruction image. The root mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) of the reconstruction image by angular-spectrum layer-oriented method with the GS algorithm are compared with those obtained in the case without using the GS algorithm. The RMSE and PSNR are the main methods of evaluating the image quality. Smaller RMSE and bigger PSNR correspond to higher quality of the image. The hologram and reconstruction image of the true color locomotive with complex morphologies are calculated using the method proposed in this paper and the locomotive is divided into three parts:head, middle and tail. The RMSE and the PSNR of reconstruction image of the head are approximately 0.77 and 65.7, respectively. The RMSE and the PSNR of reconstruction image of the middle are approximately 0.68 and 70.0, respectively, and so are those of the tail. Comparing with the traditional angular-spectrum layer-oriented method, the RMSE of the reconstruction images of the head, middle and tail are reduced approximately by 0.11, 0.40, 0.41, and the PSNR are increased approximately by 1.15, 5.70, 4.13, respectively. The simulation results show that the speckle noise is suppressed effectively and the quality of the reconstruction image is improved when the GS algorithm along with the angular-spectrum layer oriented method is used. The proposed method is more suitable for the calculation of complex 3D objects with true color.
      Corresponding author: Zhang Ya-Ping, yapingzhang11@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61007061, 61565010, 11762009).
    [1]

    Goodman J W, Lwrence R W 1967 Appl. Phys. Lett. 11 77

    [2]

    Adam K, David L K 1965 Appl. Opt. 4 387

    [3]

    Qian X F 2015 Information Optical Digital Laboratory (Beijing: Science Press) p200 (in Chinese) [钱晓凡 2015 信息光学数字实验室 (北京: 科学出版社) 第200页]

    [4]

    Gabor D 1948 Nature 161 777

    [5]

    Leith E N, Upatnieks J 1963 J. Opt. Soc. Am. 53 1377

    [6]

    Tan F 2012 Opt. Instrum. 34 16 (in Chinese) [覃芳 2012 光学仪器34 16]

    [7]

    Waters J P 1966 Appl. Phys. Lett. 9 405

    [8]

    Matsushima K, Nakahara S 2009 Appl. Opt. 48 H54

    [9]

    Pan Y J, Wang Y T, Liu J, Li X, Jia J 2014 Appl. Opt. 53 1354

    [10]

    Sun P, Xie J H, Zhou Y L 2004 Acta Opt. Sin. 24 110 (in Chinese) [孙萍, 谢敬辉, 周元林 2004 光学学报 24 110]

    [11]

    Li J C 2014 Diffraction Calculations and Digital Holography (Vol. 1) (Beijing: Science Press) p261 (in Chinese) [李俊昌 2014 衍射计算及数字全息(上册) (北京: 科学出版社)第261页]

    [12]

    Poon T C, Liu J P 2014 Introduction to Modern Digital Holography with MATLAB (London: Cambridge University Press) p5

    [13]

    Michal M, Maciei S, Andrzei K, Grzegorz M 2005 Opt. Eng. 44 125805

    [14]

    Cao X M, Sang X Z, Chen Z D, Leng J M, Zhang M, Guo N, Yu C X, Xu D X 2014 Chin. J. Lasers 41 0609002 (in Chinese) [曹雪梅, 桑新柱, 陈志东, 冷俊敏, 张明, 郭南, 余重秀, 徐大雄 2014中国激光41 0609002]

    [15]

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

    [16]

    Pang H, Wang J Z, Cao A X, Zhang M, Shi L F, Deng Q L 2017 IEEE Photon. J. 9 1

    [17]

    Zhao Y, Cao L C, Zhang H, Kong D Z, Jin G F 2015 Opt. Express 23 25440

    [18]

    Gerchberg R W, Saxton W O 1972 Optik 35 237

    [19]

    Xie J H, Liao N F, Cao L C 2007 Fundamentals of Fourier Optics and Contemporary Optics (Beijing: Beijing Polytechnic University Press) p79 (in Chinese) [谢景辉, 廖宁放, 曹良才 2007 傅里叶光学与现代光学基础(北京:北京理工大学出版社)第79页]

    [20]

    Shen C, Wei S, Liu K F, Zhang F, Li H, Wang Y 2014 Laser Optoelectr. Prog. 51 030005} (in Chinese) [沈川, 韦穗, 刘凯峰, 张芬, 李浩, 王岳 2014 激光与光电子学进展 51 030005]

    [21]

    Piao Y L, Kwon K C, Jeong J S, Kim N 2016 3D Image Acquisition and Display: Technology, Perception and Applications Heidelberg, Germany, July 25-28, 2016 JW4A. 29

    [22]

    Peng J M, Du S J, Jiang P Z 2013 High Power Laser and Particle Beams 25 315 (in Chinese) [彭金锰, 杜少军, 蒋鹏志 2013 强激光与粒子束 25 315]

    [23]

    Gu X, Xu K S 2000 J. Fudan Univ. (Natural Science) 39 205 (in Chinese) [顾翔, 徐克璹 2000 复旦学报(自然科学版) 39 205]

    [24]

    Wang J Y, Cao J H 2015 J. Tianjin Univ. Technol. Education 25 36 (in Chinese) [王金洋, 曹继华2015天津职业技术师范大学学报 25 36]

    [25]

    Li F, Bi Y, Wang H, Sun M Y, Kong X X 2012 Chin. J. Lasers 39 1009001

    [26]

    Zhou P H, Bi Y, Sun M Y, Wang H, Li F, Qi Y 2014 Appl. Opt. 53 G209

    [27]

    Pan Y C, Xu X W, Liang X N 2013 Appl. Opt. 52 6562

    [28]

    Liu J, Ma X, Wang Y T, Jia J, Zhang Y X 2015 CN104281490A (in Chinese) [刘娟, 马晓, 王涌天, 贾甲, 张迎曦 2015 CN104281490A]

    [29]

    Kwon M W, Kim S C, Yoon S E, Kim E S 2015 Opt. Express 23 2101

    [30]

    Chen H R, Fu S H, Wang Y Q 2014 Opto-Electron. Eng. 41 48 (in Chinese) [陈慧荣, 付胜豪, 王元庆2014光电工程41 48]

    [31]

    Fu S H, Wang Y Q, Bao X L, Fan K F 2013 Electron. Opt. Control 20 61 (in Chinese) [付胜豪, 王元庆, 鲍绪良, 范科峰 2013 电光与控制 20 61]

  • [1]

    Goodman J W, Lwrence R W 1967 Appl. Phys. Lett. 11 77

    [2]

    Adam K, David L K 1965 Appl. Opt. 4 387

    [3]

    Qian X F 2015 Information Optical Digital Laboratory (Beijing: Science Press) p200 (in Chinese) [钱晓凡 2015 信息光学数字实验室 (北京: 科学出版社) 第200页]

    [4]

    Gabor D 1948 Nature 161 777

    [5]

    Leith E N, Upatnieks J 1963 J. Opt. Soc. Am. 53 1377

    [6]

    Tan F 2012 Opt. Instrum. 34 16 (in Chinese) [覃芳 2012 光学仪器34 16]

    [7]

    Waters J P 1966 Appl. Phys. Lett. 9 405

    [8]

    Matsushima K, Nakahara S 2009 Appl. Opt. 48 H54

    [9]

    Pan Y J, Wang Y T, Liu J, Li X, Jia J 2014 Appl. Opt. 53 1354

    [10]

    Sun P, Xie J H, Zhou Y L 2004 Acta Opt. Sin. 24 110 (in Chinese) [孙萍, 谢敬辉, 周元林 2004 光学学报 24 110]

    [11]

    Li J C 2014 Diffraction Calculations and Digital Holography (Vol. 1) (Beijing: Science Press) p261 (in Chinese) [李俊昌 2014 衍射计算及数字全息(上册) (北京: 科学出版社)第261页]

    [12]

    Poon T C, Liu J P 2014 Introduction to Modern Digital Holography with MATLAB (London: Cambridge University Press) p5

    [13]

    Michal M, Maciei S, Andrzei K, Grzegorz M 2005 Opt. Eng. 44 125805

    [14]

    Cao X M, Sang X Z, Chen Z D, Leng J M, Zhang M, Guo N, Yu C X, Xu D X 2014 Chin. J. Lasers 41 0609002 (in Chinese) [曹雪梅, 桑新柱, 陈志东, 冷俊敏, 张明, 郭南, 余重秀, 徐大雄 2014中国激光41 0609002]

    [15]

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

    [16]

    Pang H, Wang J Z, Cao A X, Zhang M, Shi L F, Deng Q L 2017 IEEE Photon. J. 9 1

    [17]

    Zhao Y, Cao L C, Zhang H, Kong D Z, Jin G F 2015 Opt. Express 23 25440

    [18]

    Gerchberg R W, Saxton W O 1972 Optik 35 237

    [19]

    Xie J H, Liao N F, Cao L C 2007 Fundamentals of Fourier Optics and Contemporary Optics (Beijing: Beijing Polytechnic University Press) p79 (in Chinese) [谢景辉, 廖宁放, 曹良才 2007 傅里叶光学与现代光学基础(北京:北京理工大学出版社)第79页]

    [20]

    Shen C, Wei S, Liu K F, Zhang F, Li H, Wang Y 2014 Laser Optoelectr. Prog. 51 030005} (in Chinese) [沈川, 韦穗, 刘凯峰, 张芬, 李浩, 王岳 2014 激光与光电子学进展 51 030005]

    [21]

    Piao Y L, Kwon K C, Jeong J S, Kim N 2016 3D Image Acquisition and Display: Technology, Perception and Applications Heidelberg, Germany, July 25-28, 2016 JW4A. 29

    [22]

    Peng J M, Du S J, Jiang P Z 2013 High Power Laser and Particle Beams 25 315 (in Chinese) [彭金锰, 杜少军, 蒋鹏志 2013 强激光与粒子束 25 315]

    [23]

    Gu X, Xu K S 2000 J. Fudan Univ. (Natural Science) 39 205 (in Chinese) [顾翔, 徐克璹 2000 复旦学报(自然科学版) 39 205]

    [24]

    Wang J Y, Cao J H 2015 J. Tianjin Univ. Technol. Education 25 36 (in Chinese) [王金洋, 曹继华2015天津职业技术师范大学学报 25 36]

    [25]

    Li F, Bi Y, Wang H, Sun M Y, Kong X X 2012 Chin. J. Lasers 39 1009001

    [26]

    Zhou P H, Bi Y, Sun M Y, Wang H, Li F, Qi Y 2014 Appl. Opt. 53 G209

    [27]

    Pan Y C, Xu X W, Liang X N 2013 Appl. Opt. 52 6562

    [28]

    Liu J, Ma X, Wang Y T, Jia J, Zhang Y X 2015 CN104281490A (in Chinese) [刘娟, 马晓, 王涌天, 贾甲, 张迎曦 2015 CN104281490A]

    [29]

    Kwon M W, Kim S C, Yoon S E, Kim E S 2015 Opt. Express 23 2101

    [30]

    Chen H R, Fu S H, Wang Y Q 2014 Opto-Electron. Eng. 41 48 (in Chinese) [陈慧荣, 付胜豪, 王元庆2014光电工程41 48]

    [31]

    Fu S H, Wang Y Q, Bao X L, Fan K F 2013 Electron. Opt. Control 20 61 (in Chinese) [付胜豪, 王元庆, 鲍绪良, 范科峰 2013 电光与控制 20 61]

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  • Received Date:  16 November 2017
  • Accepted Date:  15 January 2018
  • Published Online:  05 May 2018

Gerchberg-Saxton algorithm and angular-spectrum layer-oriented method for true color three-dimensional display

    Corresponding author: Zhang Ya-Ping, yapingzhang11@qq.com
  • 1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;
  • 2. Architectural Engineering Institute, Kunming University of Science and Technology, Kunming 650500, China;
  • 3. State Key Laboratory of Precision Measurement Technology and Instruments, Tsinghua University, Beijing 100084, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61007061, 61565010, 11762009).

Abstract: Computer-generated hologram (CGH) makes possible the three-dimensional (3D) display of true stereo. It has characteristics of strong flexibility, small noise, easy replication, and computable virtual object. However, there are still some difficulties with the CGH 3D display presently, such as slow computation speed of complex object hologram, small size and small field angle of 3D scene, much noise of reconstruction image, and true color display. In this paper, the problem of reconstruction image noise and true color display of the CGH are studied, and the hologram of true color 3D object with complex morphologies is calculated. First of all, the angular-spectrum layer-oriented method can avoid error caused by the paraxial approximation and be used to accurately generate and calculate 3D object hologram. And it also has advantages of efficient computation, reduced complexity, and less storage memory. We achieve the true color display of a 3D object by using the angular-spectrum method based on intensity and depth maps. We also analyze the problem of multi-wavelength sampling, and mitigate the phenomenon of frequency mixing effectively. Then, we propose to use the Gerchberg-Saxton (GS) algorithm along with the angular-spectrum layer oriented method to reduce the speckle noise in the reconstruction image. The root mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) of the reconstruction image by angular-spectrum layer-oriented method with the GS algorithm are compared with those obtained in the case without using the GS algorithm. The RMSE and PSNR are the main methods of evaluating the image quality. Smaller RMSE and bigger PSNR correspond to higher quality of the image. The hologram and reconstruction image of the true color locomotive with complex morphologies are calculated using the method proposed in this paper and the locomotive is divided into three parts:head, middle and tail. The RMSE and the PSNR of reconstruction image of the head are approximately 0.77 and 65.7, respectively. The RMSE and the PSNR of reconstruction image of the middle are approximately 0.68 and 70.0, respectively, and so are those of the tail. Comparing with the traditional angular-spectrum layer-oriented method, the RMSE of the reconstruction images of the head, middle and tail are reduced approximately by 0.11, 0.40, 0.41, and the PSNR are increased approximately by 1.15, 5.70, 4.13, respectively. The simulation results show that the speckle noise is suppressed effectively and the quality of the reconstruction image is improved when the GS algorithm along with the angular-spectrum layer oriented method is used. The proposed method is more suitable for the calculation of complex 3D objects with true color.

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