Reconstructing a complex field from a series of its near-field diffraction patterns

doi:10.1088/1674-1056/21/10/104202

Abstract We propose a method for reconstructing a complex field from a series of its near-field diffraction patterns. This method is based on the paraxial Fresnel diffraction equation without making further approximations. Numerical simulations are presented showing that a complex field can even be reconstructed with moderate qualities from its two near-field diffraction patterns and almost exact reconstructions can be obtained when three or more diffraction patterns are used. We also show by numerical simulation that the correct diffraction distances can be recovered in case only coarsely measured values are available. This method may be applied to phase imaging of weak-absorption objects.

Keywords: phase imaging near field phase retrieval

Received: 05 February 2012
Revised: 15 February 2012
Accepted manuscript online:

PACS:	42.25.Fx	(Diffraction and scattering)
	42.30.Rx	(Phase retrieval)

Fund: Project supported by the National Basic Research Program of China (Grant Nos. 2012CB825800 and 2009CB930804), the Key Important Project of the National Natural Science Foundation of China (Grant No. 10734070), the National Natural Science Foundation of China (Grant Nos. 11179004 and 10979055), and the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX2-YW-N42).

Corresponding Authors: hu Pei-Ping, Wu Zi-Yu
E-mail: zhupp@ihep.ac.cn; wuzy@ustc.edu.cn

Cite this article:

Hong You-Li (洪友丽), Zhang Kai (张凯), Wang Zhi-Li (王志立), Zhu Zhong-Zhu (朱中柱), Zhao Xue-Jiao (赵雪娇), Huang Wan-Xia (黄万霞), Yuan Qing-Xi (袁清习), Zhu Pei-Ping (朱佩平), Wu Zi-Yu (吴自玉) Reconstructing a complex field from a series of its near-field diffraction patterns 2012 Chin. Phys. B 21 104202

[1]	Davis T J, Gao D, Gureyev T E, Stevenson A W and Wilkins S W 1995 Nature 373 595
[2]	Gao D C, Pogany A, Stevenson A W, Gureyev T, Wilkins S W and Mai Z 2000 Acta Phys. Sin. 49 2357 (in Chinese)
[3]	Huang W X, Tian Y L, Zhu P P, Mai Z H and Hu X F 2002 Acta Phys. Sin. 51 1040 (in Chinese)
[4]	Hwu Y, Tsai W, Je J, Seol S, Kim B, Groso A, Margaritondo G, Lee K and Seong J 2004 Phys. Med. Biol. 49 501
[5]	Chen M, Xiao T Q, Luo Y Y, Lu L X, Wei X, Du G H and Xu H J 2004 Acta Phys. Sin. 53 2953 (in Chinese)
[6]	Liu L X, Du G H, Hu W, Luo Y Y, Xie H L, Chen M and Xiao T Q 2006 Acta Phys. Sin. 55 6387 (in Chinese)
[7]	Tian Y, Li W, Chen J, Liu L, Liu G, Tkachuk A, Tian J, Xiong Y, Gelb J, Hsu G et al. 2008 Rev. Sci. Instrum. 79 103708
[8]	Shi S M, Chen R C, Xue Y L, Ren Y Q, Du G H, Deng B, Xie H L and Xiao T Q 2008 Acta Phys. Sin. 57 6319 (in Chinese)
[9]	Zhu P, Zhang K, Wang Z, Liu Y, Liu X, Wu Z, McDonald S, Marone F and Stampanoni M 2010 Proc. Natl. Acad. Sci. USA 107 13576
[10]	Xue Y L, Xiao T Q, Wu L H, Chen C, Guo R Y, Du G H, Xie H L, Deng B, Ren Y Q and Xu H J 2010 Acta Phys. Sin. 59 5496 (in Chinese)
[11]	Bonse U and Hart M 1965 Appl. Phys. Lett. 6 155
[12]	Liu X, Guo J C and Niu H B 2010 Chin. Phys. B 19 070701
[13]	Gerchberg R W and Saxton W O 1972 Optik 35 237
[14]	Fienup J R 1978 Opt. Lett. 3 27
[15]	Miao J, Charalambous P, Kirz J and Sayre D 1999 Nature 400 342
[16]	Zhou G Z, Tong Y J, Chen C, Ren Y Q, Wang Y D and Xiao T Q 2011 Acta Phys. Sin. 60 028701 (in Chinese)
[17]	Zhou G Z, Wang Y D, Ren Y Q, Chen C, Ye L L and Xiao T Q 2012 Acta Phys. Sin. 61 018701 (in Chinese)
[18]	Williams G J, Pfeifer M A, Vartanyants I A and Robinson I K 2003 Phys. Rev. Lett. 90 175501
[19]	Xiao X and Shen Q 2005 Phys. Rev. B 72 33103
[20]	Zhang F and Rodenburg J 2010 Phys. Rev. B 82 121104
[21]	Chen C C, Miao J, Wang C W and Lee T K 2007 Phys. Rev. B 76 064113
[22]	Li E, Liu Y, Liu X, Zhang K, Wang Z, Hong Y, Yuan Q, Huang W, Marcelli A, Zhu P and Wu Z 2008 J. Opt. Soc. Am. A 25 2651
[23]	Cheng J and Han S 1999 Opt. Commun. 172 17
[24]	Cheng J and Han S 1999 Opt. Lett. 24 175
[25]	Li E, Hwu Y, Chien D, Wang C L and Margaritondo G 2011 J. Opt. 13 035712
[26]	Teague M R 1982 J. Opt. Soc. Am. 72 1199
[27]	Gureyev T, Mayo S, Wilkins S, Paganin D and Stevenson A 2001 Phys. Rev. Lett. 86 5827
[28]	Yu B, Peng X, Tian J and Niu H 2005 Acta Phys. Sin. 54 2034 (in Chinese)
[29]	Zhang D, Li Z, Huang Z F, Yu A M and Sha W 2006 Chin. Phys. 15 1731
[30]	Liu L X, Du G H, Wen H, Xie H L and Xiao T Q 2007 Acta Phys. Sin. 56 4556 (in Chinese)
[31]	Li C, Li Z, Li C Q and Yu A M 2007 Chin. Phys. Lett. 24 2823
[32]	Nugent K A, Peele A G, Chapman H N and Mancuso A 2003 Phys. Rev. Lett. 91 203902
[33]	Gureyev T, Pogany A, Paganin D and Wilkins S 2004 Opt. Commun. 231 53
[34]	Cloetens P, Ludwig W, Baruchel J, Van Dyck D, Van Landuyt J, Guigay J and Schlenker M 1999 Appl. Phys. Lett. 75 2912
[35]	Allen L and Oxley M 2001 Opt. Commun. 199 65
[36]	Allen L J, Faulkner H M L, Nugent K A, Oxley M P and Paganin D 2001 Phys. Rev. E 63 37602
[37]	Zhang F, Pedrini G and Osten W 2007 Phys. Rev. A 75 043805
[38]	Liu Y J, Chen B, Li E R, Wang J Y, Marcelli A, Wilkins S W, Ming H, Tian Y C, Nugent K A, Zhu P P and Wu Z Y 2008 Phys. Rev. A 78 023817
[39]	Liu Y, Andrews J C, Wang J, Meirer F, Zhu P, Wu Z and Pianetta P 2011 Opt. Express 19 540
[40]	Song C, Ramunno-Johnson D, Nishino Y, Kohmura Y, Ishikawa T, Chen C, Lee T and Miao J 2007 Phys. Rev. B 75 12102

[1]	Deep-learning-based cryptanalysis of two types of nonlinear optical cryptosystems Xiao-Gang Wang(汪小刚) and Hao-Yu Wei(魏浩宇). Chin. Phys. B, 2022, 31(9): 094202.
[2]	Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique Fang Xue(薛芳), Ya-Xuan Duan(段亚轩), Xiao-Yi Chen(陈晓义), Ming Li(李铭), Suo-Chao Yuan(袁索超), and Zheng-Shang Da(达争尚). Chin. Phys. B, 2021, 30(8): 084209.
[3]	Real time high accuracy phase contrast imaging with parallel acquisition speckle tracking Zhe Hu(胡哲), Wen-Qiang Hua(滑文强), and Jie Wang(王劼). Chin. Phys. B, 2021, 30(6): 064201.
[4]	Convolutional neural network for transient grating frequency-resolved optical gating trace retrieval and its algorithm optimization Siyuan Xu(许思源), Xiaoxian Zhu(朱孝先), Ji Wang(王佶), Yuanfeng Li(李远锋), Yitan Gao(高亦谈), Kun Zhao(赵昆), Jiangfeng Zhu(朱江峰), Dacheng Zhang(张大成), Yunlin Chen(陈云琳), and Zhiyi Wei(魏志义). Chin. Phys. B, 2021, 30(4): 048402.
[5]	Phase retrieval algorithm for optical information security Shi-Qing Wang(王诗晴), Xiang-Feng Meng(孟祥锋), Yu-Rong Wang(王玉荣), Yong-Kai Yin(殷永凯), Xiu-Lun Yang(杨修伦). Chin. Phys. B, 2019, 28(8): 084203.
[6]	Theory and method of dual-energy x-ray grating phase-contrast imaging Feng Rong(荣锋), Yan Gao(高艳), Cui-Juan Guo(郭翠娟), Wei Xu(徐微), Wei Xu(徐伟). Chin. Phys. B, 2019, 28(10): 108702.
[7]	Rapid measurement of transmission matrix with the sequential semi-definite programming method Zhenfeng Zhang(张振峰), Bin Zhang(张彬), Qi Feng(冯祺), Huimei He(何惠梅), Yingchun Ding(丁迎春). Chin. Phys. B, 2018, 27(8): 084201.
[8]	Modified physical optics algorithm for near field scattering Bin Chen(陈彬), Chuangming Tong(童创明). Chin. Phys. B, 2018, 27(11): 114102.
[9]	Phase-only stereoscopic hologram calculation based on Gerchberg-Saxton iterative algorithm Xinyi Xia(夏心怡), Jun Xia(夏军). Chin. Phys. B, 2016, 25(9): 094204.
[10]	Application of optical diffraction method in designing phase plates Ze-Min Lei(雷泽民), Xiao-Yan Sun(孙晓艳), Feng-Nian Lv(吕凤年), Zhen Zhang(张臻), Xing-Qiang Lu(卢兴强). Chin. Phys. B, 2016, 25(11): 114201.
[11]	Three-dimensional coherent diffraction imaging of Mie-scatteringspheres by laser single-orientation measurement Zhang Jian (张剑), Fan Jia-Dong (范家东), Zhang Jian-Hua (张建华), Sun Zhi-Bin (孙智斌), Huang Qing-Jie (黄庆捷), Jiang Huai-Dong (江怀东). Chin. Phys. B, 2015, 24(9): 094201.
[12]	Influence of the illumination coherency and illumination aperture on the ptychographic iterative microscopy Liu Cheng (刘诚), Zhu Jian-Qiang (朱健强), John Rodenburg. Chin. Phys. B, 2015, 24(2): 024201.
[13]	Improvement and error analysis of quantitative information extraction in diffraction-enhanced imaging Yang Hao (杨浩), Xuan Rui-Jiao (轩瑞娇), Hu Chun-Hong (胡春红), Duan Jing-Hao (段敬豪). Chin. Phys. B, 2014, 23(4): 048701.
[14]	Polarization dependence of the light coupling to surface plasmons in an Ag nanoparticle & Ag nanowire system Yang Chao-Jie (杨超杰), Zhao Hua-Bo (赵华波), Wang Pei-Pei (王培培), Li Jie (李洁), Tang Peng (唐鹏), Qu Sheng-Chun (曲胜春), Lin Feng (林峰), Zhu Xing (朱星). Chin. Phys. B, 2014, 23(11): 117302.
[15]	A general phase retrieval algorithm based on ptychographicaliterative engine for coherent diffractive imaging Fu Jian (傅健), Li Peng (李鹏). Chin. Phys. B, 2013, 22(1): 014204.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Reconstructing a complex field from a series of its near-field diffraction patterns

Cite this article:

Online attention