Volume 11 Issue 4
Jul.  2018
Turn off MathJax
Article Contents
HU Qi, WANG Zhe, LIU Hong-shun, XUE Zhi-wen, DENG Jia-chun. Step diffraction algorithm based on single fast Fourier transform algorithm[J]. Chinese Optics, 2018, 11(4): 568-575. doi: 10.3788/CO.20181104.0568
Citation: HU Qi, WANG Zhe, LIU Hong-shun, XUE Zhi-wen, DENG Jia-chun. Step diffraction algorithm based on single fast Fourier transform algorithm[J]. Chinese Optics, 2018, 11(4): 568-575. doi: 10.3788/CO.20181104.0568

Step diffraction algorithm based on single fast Fourier transform algorithm

doi: 10.3788/CO.20181104.0568

National Natural Science Foundation of China 11604243

National Natural Science Foundation of China 11504268

National Natural Science Foundation of China 11204213

Natural Science Found Project of Tianjin 16JCQNJC01600

More Information
  • Corresponding author: WANG Zhe, E-mail:snowleoperd@126.com
  • Received Date: 2017-12-14
  • Rev Recd Date: 2018-02-10
  • Publish Date: 2018-08-01
  • Due to the constraints of the sampling theorem, it is not possible to flexibly control the diffractive frame size of the single Fourier transform algorithm and the number of effective content pixels and it is highly likely that the size of the diffractive surface frame does not match the diffraction distance.To solve this problem, we propose a step diffraction algorithm.First, in the case of a fixed number of samples, the wavelength of the light, the size of the initial diffraction surface, and the final diffractive frame size can be controlled by the split diffraction distance ratio.Then, the single-diffraction calculation results are compared with the segmented diffraction calculation results for image similarity.Experiments show that the step diffraction algorithm can increase the number of effective pixels and the data volume increases by 2-3 orders of magnitude.In addition, the following conclusion is drawn:one of the main causes of errors is the difference between the distribution of details and the low-resolution pixel values after the resolution of the effective data is increased, and it is also known that the richer the image details, the greater the difference.Therefore, this difference should be regarded as a better result than that of direct calculation.Through this algorithm, clearer image details can be obtained, and the size of the diffraction surface frame can be flexibly adjusted, so that the S-FFT algorithm can exert its algorithm advantage in the calculation of the large diffraction distance problem.
  • loading
  • [1]
    石敬, 王新柯, 郑显华, 等.太赫兹数字全息术的研究进展[J].中国光学, 2017, 10(1):131-147. http://www.chineseoptics.net.cn/CN/abstract/abstract9504.shtml

    SHI J, WANG X K, ZHENG X H, et al..Recent advances in terahertz digital holography[J].Chinese Optics, 2017, 10(1):131-147.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9504.shtml
    马建设, 夏飞鹏, 苏萍, 等.数字全息三维显示关键技术与系统综述[J].光学 精密工程, 2012, 20(5):1141-1152. https://wenku.baidu.com/view/86e2f0c016fc700aba68fc9e.html

    MA J SH, XIA F P, SU P, et al..Survey on key techniques and systems of digital holographic 3D display[J].Opt.Precision Eng., 2012, 20(5):1141-1152.(in Chinese) https://wenku.baidu.com/view/86e2f0c016fc700aba68fc9e.html
    贾甲, 王涌天, 刘娟, 等.计算全息三维实时显示的研究进展[J].激光与光电子学进展, 2012, 49:050002. http://mall.cnki.net/magazine/Article/JGDJ201205003.htm

    JIA J, WANG Y T, LIU J, et al..Progress of dynamic 3D display of the computer-generated hologram[J].Laser & Optoelectronics Progress, 2012, 49(050002):1-9.(in Chinese) http://mall.cnki.net/magazine/Article/JGDJ201205003.htm
    万玉红, 满天龙, 淘世荃.非相干全息术成像特性及研究进展[J].中国激光, 2014, 41(2):0209004. http://mall.cnki.net/magazine/Article/JJZZ201402005.htm

    WAN Y H, MAN T L, TAO SH Q.Imaging characteristics and research progress of incoherent holography[J].Chinese Journal of Lasers, 2014, 41(2):0209004.(in Chinese) http://mall.cnki.net/magazine/Article/JJZZ201402005.htm
    沈川, 韦穗, 刘凯峰, 等.彩色全息显示方法与系统概述[J].激光与光电子学进展, 2014, 51:030005. http://mall.cnki.net/magazine/article/JGDJ201403005.htm

    SHEN C, WEI S, LIU K F, et al..Survey on methods and systems of color holographic display[J].Laser & Optoelectronics Progress, 2014, 51:030005.(in Chinese) http://mall.cnki.net/magazine/article/JGDJ201403005.htm
    曾飞, 张新.全息波导头盔显示技术[J].中国光学, 2014, 7(5):731-738. http://www.chineseoptics.net.cn/CN/abstract/abstract9169.shtml

    ZENG F, ZHANG X.Waveguide holographic head-mounted display technology[J].Chinese Optics, 2014, 7(5):731-738.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9169.shtml
    魏小红, 何宇航, 高波, 等.用计算全息法测量长焦透镜的透射波前[J].光学 精密工程, 2016, 24(12):3005-3011. https://wenku.baidu.com/view/f531d04559fb770bf78a6529647d27284b7337b1.html

    WEI X H, HE Y H, GAO B, et al..Measurement of transmissive wavefront of long-focal length lens by computer-generated holography[J].Opt.Precision Eng., 2016, 24(12):3005-3011.(in Chinese) https://wenku.baidu.com/view/f531d04559fb770bf78a6529647d27284b7337b1.html
    夏明亮, 李抄, 刘肇南, 等.Shack-Hartmann波前传感器图像自适应阈值的选取[J].光学 精密工程, 2010, 18(2):334-340. https://wenku.baidu.com/view/865fdd21a32d7375a4178090.html

    XIA M L, LI C, LIU Z N, et al..Adaptive threshold selection method for Shack-Hartmann wavefront sensors[J].Opt.Precision Eng., 2010, 18(2):334-340.(in Chinese) https://wenku.baidu.com/view/865fdd21a32d7375a4178090.html
    朱咸昌, 伍凡, 曹学东, 等.基于Hartmann-Shack波前检测原理的微透镜阵列焦距测量[J].光学 精密工程, 2013, 21(5):1122-1128. https://wenku.baidu.com/view/8e3ad73ab84ae45c3b358c87.html

    ZHU X CH, WU F, CAO X D, et al..Focal length measurement of microlens-array based on wavefront testing principle of Hartmann-Shack sensor[J].Opt.Precision Eng., 2013, 21(5):1122-1128.(in Chinese) https://wenku.baidu.com/view/8e3ad73ab84ae45c3b358c87.html
    CAO G R, YU X.Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object[J].Optical Engineering, 1994, 33(7):2331-2335. doi: 10.1117/12.169716
    LISA A.Poyneer, bruce macintosh.spatially filtered wave-front sensor for high-order adaptive optics[J].L.A.Poyneer and B.Macintosh, 2004, 21(5):810-819. https://www.researchgate.net/publication/8567402_Spatially_filtered_wave-front_sensor_for_high-order_adaptive_optics
    范广飞, 陈林森, 魏国军, 等.基于衍迹成像的集成成像重构算法[J].光学学报, 2016, 36(5):0511003. http://wuxizazhi.cnki.net/Sub/jcwl/a/GXXB201605010.html

    FAN G F CHEN L S, WEI G J, et al..Computer reconstruction algorithm for integral imaging based on diffraction tracing[J].Acta Optica Sinica, 2016, 36(5):0511003.(in Chinese) http://wuxizazhi.cnki.net/Sub/jcwl/a/GXXB201605010.html
    HAI GONG, OLEG SOLOVIEV, DEAN WILDING, et al..Holographic imaging with a Shack-Hartmann wavefront sensor[J].Optics Express, 2016, 24(13):13729-13737. doi: 10.1364/OE.24.013729
    李俊昌.角谱衍射公式的快速傅里叶变换计算在数字全息波面重建中的应用[J].光学学报, 2009, 29(5):1163-1167. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB200905007.htm

    LI J CH.FFT computation of angular spectrum diffraction formula and its application in wavefront reconstruction of digital holography[J].Acta Optica Sinica, 2009, 29(5):1163-1167.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB200905007.htm
    潘锋, 闫贝贝, 肖文, 等.基于数学形态学的数字全息再现像融合方法[J].中国光学, 2015, 8(1):60-67. http://www.chineseoptics.net.cn/CN/abstract/abstract9250.shtml

    PAN F, YAN B B, XIAO W, et al..Digital holographic reconstruction image fusion based on mathematical morphology[J].Chinese Optics, 2015, 8(1):60-67.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9250.shtml
    郑华东, 于瀛洁, 程维明.三维物体空间再现技术中的全息图计算[J].光学 精密工程, 2008, 16(5):917-924. http://mall.cnki.net/magazine/article/GXJM200805025.htm

    ZHENG H D, YU Y J, CHENG W M.Computer-generated hologram calculation for spatial reconstruction of three-dimensional object[J].Opt.Precision Eng., 2008, 16(5):917-924.(in Chinese) http://mall.cnki.net/magazine/article/GXJM200805025.htm
    赵金宇, 吴元昊, 贾建禄, 等.基于实时波前信息的图像复原[J].光学 精密工程, 2012, 20(6):1350-1356. http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201206028.htm

    ZHAO J Y, WU Y H, JIA J L, et al.Image restoration based on real time wave-front information[J].Opt.Precision Eng., 2012, 20(6):1350-1356.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201206028.htm
    古德曼. 傅里叶光学导论: 第3版[M]. 秦克诚, 刘培森, 陈家璧, 等, 译. 北京: 电子工业出版社, 2011: 17-20, 23-37.

    JOSEPH W GOODMAN. Introduction to Fourier Optics[M]. Third Edition. QIN K CH, LIU P S, CHEN J B, et al., Transl. Beijing: Publishing House of Electronics Industry, 2011: 2011: 17-20, 23-37. (in Chinese)
    钱晓凡.信息光学数字实验室(Matlab版)[M].北京:科学出版社, 2015:22-27.

    QIAN X F.Information Optics Digital Laboratory(Matlab Edition)[M].Beijing:Science Press, 2015:22-27.(in Chinese)
    李俊昌, 熊秉衡, 等.信息光学教程[M].北京:科学出版社, 2011:17-34, 48-51.

    LI J C, XIONG B H, et al.Information Optics Course[M].Beijing:Science Press, 2011:17-34, 48-51.(in Chinese)
    雅里夫. 光电子学导论[M]. 李宇琦, 译. 北京: 科学出版社, 1983: 6-11. A.

    YARIV. Introduction to Optoelectronics[M]. LI Y Q, Transl. Beijing: Science Press, 1983: 6-11. (in Chinese)
    马科斯·波恩, 埃米尔·沃耳夫. 光学原理: 光的传播、干涉和衍射的电磁理论[M]. 杨葭荪, 译. 北京: 电子工业出版社, 2016: 1-9.

    MAX BORN, EMIL WOLF. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Seventh Edition[M]. YANG J S, Transl. Beijing: Publishing House of Electronics Industry, 2016: 1-9. (in Chinese)
    李俊昌.衍射计算及数字全息(上册)[M].北京:科学出版社, 2014:78-93.

    LI J CH.Diffraction Calculation and Digital Holography(VOL 1)[M].Beijing:Science Press, 2014:78-93.(in Chinese)
    章毓晋.图像处理和分析技术[M].北京:高等教育出版社, 2014:98-100.

    ZHANG Y J.Image Processing and Analysis Technology[M].Beijing:Higher Education Press, 2014:98-100.(in Chinese)
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(7)  / Tables(2)

    Article views (1392) PDF downloads(218) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint