基于单次傅里叶变换的分段衍射算法
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摘要
针对单次傅里叶变换算法(S-FFT算法)受到采样定理的约束,衍射面画幅尺寸和有效内容像素数无法灵活控制,很容易出现衍射面画幅尺寸大小与衍射距离不匹配的情况,本文提出了一种分段衍射算法。首先,在采样数、光的波长、初始衍射面大小确定的情况下,利用拆分的衍射距离比控制最终衍射面画幅尺寸。然后,对单次衍射计算结果与分段衍射计算结果进行了图像相似度对比。实验表明,分段衍射算法可在画面强度分布不变的情况下,提高有效像素数目,数据量增加了2~3个数量级。此外,文章分析了造成误差的一个主要原因来自有效数据分辨率提高后,细节分布与低分辨率像素值之间的差别。在图像细节较丰富时,其差别较大。因此这种差别应视为优于直接计算的一种结果。本算法能够获得更加清晰的图像细节,灵活调整衍射面画幅尺寸,使得S-FFT算法在大衍射距离问题计算中能发挥其算法优势。
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 itis 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.
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 itis 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.
引文
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[18]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)
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[21]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)
[22]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)
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[2]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.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)
[3]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.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)
[4]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.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)
[5]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.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)
[6]曾飞,张新.全息波导头盔显示技术[J].中国光学,2014,7(5):731-738.ZENG F,ZHANG X.Waveguide holographic head-mounted display technology[J].Chinese Optics,2014,7(5):731-738.(in Chinese)
[7]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.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)
[8]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.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)
[9]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.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)
[10]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.
[11]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.
[12]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.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)
[13]HAI GONG,OLEG SOLOVIEV,DEAN WILDING,et al..Holographic imaging with a Shack-Hartmann wavefront sensor[J].Optics Express,2016,24(13):13729-13737.
[14]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.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)
[15]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.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)
[16]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.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)
[17]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.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)
[18]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)
[19]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)
[20]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)
[21]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)
[22]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)
[23]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)
[24]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)