自然光条件下基于Green函数的相位检索方法
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摘要
基于强度测量的确定性相位检索技术将光学与计算结合起来,通过求解强度传输方程恢复相位信息,理论和实验证明是相位检索的可行途径.论文将Green函数应用于强度传输方程的求解中,给出Neumann和Dirichlet边界条件下新的推导方法.该方法中,Green函数的偏导数是四维矩阵,随着图像分辨率的提高,直接求解所占的内存空间比较大,提出了数值化处理方法,并推广到自然光条件下的相位检索中.同时,搭建了图像数据采集光学平台.模拟和真实实验验证了算法的正确性和实用性.
The transport of intensity equation is solved to recover the phase information through the combination of optics and calculation in the method of phase retrieval based on the intensity measurement.This method is proved to be a feasible way to obtain phase information theoretically and experimentally.A new derivation of Green function method in Neumann and Dirichlet boundary conditions is deduced.Because the partial derivative of Green′s function is a four-dimensional matrix,large memory space will be occupied with the improvement of image resolution by solving the function directly.The numerical processing method is presented and extended to natural light conditions.At same time,an optical data collection platform is built.Simulation and actual experimental results verify this new phase retrieval method is reasonable and correct.
The transport of intensity equation is solved to recover the phase information through the combination of optics and calculation in the method of phase retrieval based on the intensity measurement.This method is proved to be a feasible way to obtain phase information theoretically and experimentally.A new derivation of Green function method in Neumann and Dirichlet boundary conditions is deduced.Because the partial derivative of Green′s function is a four-dimensional matrix,large memory space will be occupied with the improvement of image resolution by solving the function directly.The numerical processing method is presented and extended to natural light conditions.At same time,an optical data collection platform is built.Simulation and actual experimental results verify this new phase retrieval method is reasonable and correct.
引文
[1]Yiying Pu,Jianwen Dong,Bingchu Chen,Yuanzhi,Liu,Hezhou Wang.Three-dimensional imaging with monocular cues using holographic stereography[J].Opt Lett,2010,35(19):3279-3281.
[2]李海,吴仁彪,廖桂生.基于相关系数加权观测矢量的InSAR干涉相位估计方法[J].电子学报,2012,40(3):453-458.Li Hai,Wu Ren-biao,Liao Gui-sheng,Estimation of interferometric phase for inSAR based on correlation coefficient weight data vector[J].Acta Electronica Sinica,2012,40(3):453-458.(in Chinese)
[3]应娜,赵晓晖,董婧,方昕.一种谐波正弦语音模型的最佳相位估计算法[J].电子学报,2009,37(4):860-863.Ying Na,Zhao Xiao-hui,Dong Jing,Fang Xin.An algorithm of optimal phase estimation in Harmonic sinusoidal speech model[J].Acta Electronica Sinica,2009,37(4):860-863.(in Chinese)
[4]S McVitie,D TNgo.Quantitative measurements of phase using the transport of intensity equation[J].Journal of Physics:Conference Series,2008,126:012041.
[5]S Marchesini.Phase retrieval and saddle-point optimization[J].J Opt Soc Am A,2007,24(10):3289-3296.
[6]C T Yong.Wavefront senors in adaptive optics[D].New Zealand:University of Canterbury,2008.
[7]T E Gureyev,A Roberts,K A Nugent.Phase retrieval with the transport of intensity equation:matrix solution with use of Zernike polynomials[J].J OPTSOC AM A,1995,12(9):1932-1942.
[8]T E Gureyev,K A Nugent.Rapid quantitative phase imaging using the transport of intensity equation[J].Opt Commun,1997,133(1-6):339-346.
[9]L J Allen,M POxley.Phase retrieval fromseries of images obtained by defocus variation[J].Opt Commun,2001,199(1-4):65-75.
[10]薛斌党,郑世玲,姜志国.完全多重网格法求解光强度传播方程的相位检索方法[J].光学学报,2009,29(6):1514-1518.Xue Bindang,Zheng Shiling,Jiang Zhiguo.Phase retrieval using transport of intensity equation solved by full multigrid method[J].Acta Optica Sinica,2009,29(6):1514-1518.(in Chinese)
[11]李永华.X射线类同轴法及光栅法相衬成像的相位复原算法研究[D].北京:清华大学,2010.Li Hua-yong.Study on phase retrieval algorithms of X-ray inline and grating-based phase-contrast imaging[D].Beijing:Tsinghua University,2010.(in Chinese)
[12]M RTeague.Deterministic phase retrieval:A Green′s function solution[J].J Opt Soc Am,1983,73(11):1434-1441.
[13]S C Woods,AHGreenaway.Wave-frontsensing by use of a Green′s function solutionto the intensity transport equation:reply to comment[J].J OPT SOC AM A,2003:24(8):2482-2484.
[14]J Frank,S Altmeyer,G Wernicke.Non-interferometric,non-iterative phase retrieval by Green′s functions[J].J.OPT.SOC.AM.A,2010,27(10):2244-2251.
[15]K Ishizuka,B Allman.Phase measurement in electron microscopy using the transport of intensity equation[J].Microscopy Today,2005:22-24.
[16]程鸿,章权兵,韦穗,基于整体变分的相位恢复[J].中国图象图形学报,2010,15(10):1425-1429.Cheng Hong,Zhang Quan-bing,Wei Sui,Phase retrieval based on total variation[J].Journal of Image and Graphics,2010,15(10):1425-1429.(in Chinese)
[17]I Lyuboshenko,H.Maitre.Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the firstGreen′s identity[J].J OptSoc Am A,1999,16(2):378-395.
[18]程鸿,张成,韦穗,汪伟.自然光条件下的相位检索方法与系统设计[J].光电子·激光,2012,23(7):1411-1417.Cheng Hong,Zhang Cheng,Wei Sui,Wang Wei,Phase retrieval method and design of the system in natural light imaging,Journal of Optoelectronics Laser,2012,23(7):1411-1417.(in Chinese)
[2]李海,吴仁彪,廖桂生.基于相关系数加权观测矢量的InSAR干涉相位估计方法[J].电子学报,2012,40(3):453-458.Li Hai,Wu Ren-biao,Liao Gui-sheng,Estimation of interferometric phase for inSAR based on correlation coefficient weight data vector[J].Acta Electronica Sinica,2012,40(3):453-458.(in Chinese)
[3]应娜,赵晓晖,董婧,方昕.一种谐波正弦语音模型的最佳相位估计算法[J].电子学报,2009,37(4):860-863.Ying Na,Zhao Xiao-hui,Dong Jing,Fang Xin.An algorithm of optimal phase estimation in Harmonic sinusoidal speech model[J].Acta Electronica Sinica,2009,37(4):860-863.(in Chinese)
[4]S McVitie,D TNgo.Quantitative measurements of phase using the transport of intensity equation[J].Journal of Physics:Conference Series,2008,126:012041.
[5]S Marchesini.Phase retrieval and saddle-point optimization[J].J Opt Soc Am A,2007,24(10):3289-3296.
[6]C T Yong.Wavefront senors in adaptive optics[D].New Zealand:University of Canterbury,2008.
[7]T E Gureyev,A Roberts,K A Nugent.Phase retrieval with the transport of intensity equation:matrix solution with use of Zernike polynomials[J].J OPTSOC AM A,1995,12(9):1932-1942.
[8]T E Gureyev,K A Nugent.Rapid quantitative phase imaging using the transport of intensity equation[J].Opt Commun,1997,133(1-6):339-346.
[9]L J Allen,M POxley.Phase retrieval fromseries of images obtained by defocus variation[J].Opt Commun,2001,199(1-4):65-75.
[10]薛斌党,郑世玲,姜志国.完全多重网格法求解光强度传播方程的相位检索方法[J].光学学报,2009,29(6):1514-1518.Xue Bindang,Zheng Shiling,Jiang Zhiguo.Phase retrieval using transport of intensity equation solved by full multigrid method[J].Acta Optica Sinica,2009,29(6):1514-1518.(in Chinese)
[11]李永华.X射线类同轴法及光栅法相衬成像的相位复原算法研究[D].北京:清华大学,2010.Li Hua-yong.Study on phase retrieval algorithms of X-ray inline and grating-based phase-contrast imaging[D].Beijing:Tsinghua University,2010.(in Chinese)
[12]M RTeague.Deterministic phase retrieval:A Green′s function solution[J].J Opt Soc Am,1983,73(11):1434-1441.
[13]S C Woods,AHGreenaway.Wave-frontsensing by use of a Green′s function solutionto the intensity transport equation:reply to comment[J].J OPT SOC AM A,2003:24(8):2482-2484.
[14]J Frank,S Altmeyer,G Wernicke.Non-interferometric,non-iterative phase retrieval by Green′s functions[J].J.OPT.SOC.AM.A,2010,27(10):2244-2251.
[15]K Ishizuka,B Allman.Phase measurement in electron microscopy using the transport of intensity equation[J].Microscopy Today,2005:22-24.
[16]程鸿,章权兵,韦穗,基于整体变分的相位恢复[J].中国图象图形学报,2010,15(10):1425-1429.Cheng Hong,Zhang Quan-bing,Wei Sui,Phase retrieval based on total variation[J].Journal of Image and Graphics,2010,15(10):1425-1429.(in Chinese)
[17]I Lyuboshenko,H.Maitre.Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the firstGreen′s identity[J].J OptSoc Am A,1999,16(2):378-395.
[18]程鸿,张成,韦穗,汪伟.自然光条件下的相位检索方法与系统设计[J].光电子·激光,2012,23(7):1411-1417.Cheng Hong,Zhang Cheng,Wei Sui,Wang Wei,Phase retrieval method and design of the system in natural light imaging,Journal of Optoelectronics Laser,2012,23(7):1411-1417.(in Chinese)
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