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Ptychographic iterative engine (PIE) method can provide high-resolution amplitude and phase distributions in short-wavelength imaging,such as electron beam and X-ray imaging.Traditional PIE relies on the sub field of view (sub-FoV) scanning,and the coincidence between these adjacent sub-FoVs is required in order to ensure the high accuracy in sample information retrieval.However,in the applications of electron beam imaging,attachments or contaminants on the sample surface will be dragged with the probe light during the sub-FoV scanning due to the adsorption of charges,and the inevitable attachment and contaminant shifting will change the probe light,therefore generating inconsistent probe light,and reducing the imaging resolution and accuracy,since the deteriorated probe light destroys the PIE scanning demands.In order to maintain the high resolution and accuracy in the electron beam imaging,the attachment and contaminant shifting during the sub-FoV scanning should be avoided.Here,a shearing interference based PIE using Mllenstedt biprism is proposed in this paper.Mllenstedt biprism is widely used in the electron beam imaging,and by applying the voltage to the wire,the generated electrical field can control the deflection of the electron beam,working similarly to a biprism modulating the wavefront passing through it.In the proposed approach,setting the Mllenstedt biprism after the sample,and changing the voltage on the Mllenstedt biprism,the beam deflection angle proportional to the added voltage can generate a series of interferograms with different fringe densities.Because the traditional sub-FoV scanning is replaced by wide-field scanning by changing the voltage on the Mllenstedt biprism,the proposed method can maintain the stable probe light,avoiding the inevitable attachment and contaminant shifting,and both the amplitude and phase can be retrieved from these interferograms by using a modified PIE algorithm.In order to verify the proposed PIE method,besides the theoretical analysis,numerical calculations are provided.The biprism phase distribution is adopted to simulate the electron beam deflection caused by the Mllenstedt biprism.Additionally,by changing the voltage on the wire,different biprism phase distributions are generated to produce various interferograms.By the modified PIE method,accurate amplitude and phase distribution within error less than 0.2% can be obtained through using less than 50 iterations,indicating a rapid convergence rate.Moreover,the errors in the imaging system, such as phase deviation,position shifting,and rotation are also quantitatively analyzed.Numerical computation proves that the direction of the biprism can be precisely determined according to the frequency distribution of the fringe,and the accurate sample information can still be retrieved even with a deviation of 30% in phase deviation and 30 m in position shifting,proving the deviations of the direction and position of the Mllenstedt biprism,as well as the phase distribution can be corrected automatically in the iterative process.Finally,the modified PIE relying on the lensfree configuration can reach the resolution of the diffraction limit in imaging similar to those PIE approaches.The proposed technique can overcome difficulties of current PIE in using electron beam,thus promoting the development and application of PIE in electron microscopy.
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Keywords:
- Mllenstedt biprism /
- coherent diffraction imaging /
- phase retrieval /
- electron beam interference
[1] Tian X, Yu W, Meng X, Sun A, Xue L, Liu C, Wang S 2016 Opt. Lett. 41 1427
[2] Tsai E H R, Diaz A, Menzel A, Guizar-Sicairos M 2016 Opt. Express 24 6441
[3] Yu W, Tian X, He X, Song X, Xue L, Liu C, Wang S 2016 Appl. Phys. Lett. 109 071112
[4] Nomarski G 1955 J. Phys. Radium 16 9
[5] Miao J, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[6] Thibault P, Dierolf M, Bunk O, Menzel A, Pfeiffer F 2009 Ultramicroscopy 109 338
[7] Thibault P, Dierolf M, Menzel A, Bunk O, David C, Pfeiffer F 2008 Science 321 379
[8] Abbey B, Nugent A K, Willianms G J, Clark J N, Peele A G, Pfeiffer M A, Jonge M, McNulty I 2008 Nat. Phys. 4 394
[9] Maiden M A, Rodenburg J M 2009 Ultramicroscopy 109 1256
[10] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[11] Miao J, Sayre D, Chapman H N J 1998 J. Opt. Soc. Am. A 15 1662
[12] Gerchberg R W, Saxton W O 2007 Phy. Rev. A 75 043805
[13] Fienup J R 1978 Opt. Lett. 3 27
[14] Fienup J R 1982 Appl. Opt. 21 2758
[15] Zhang F, Pedrini G, Osten W 2007 Phy. Rev. A 75 043805
[16] Claus D, Maiden M A, Zhang F, Sweeney F, Humphry M, Rodenburg J M, Schluesener H, Humphry M J 2011 Ptychography:A Novel Phase Retrieval Technique, Advantages and its Application Braga, Portugal, May 3, 2011 p800109
[17] Liu C, Pan X C, Zhu J Q 2013 Acta Phys. Sin. 62 184204 (in Chinese)[刘诚, 潘兴臣, 朱健强 2013 物理学报 62 184204]
[18] Chen B, Dilanian R A, Teichmann S, Abbey B, Peele A G, Williams G J, Hannaford P, van Dao L, Quiney H M, Nugent K A 2009 Phys. Rev. A 79 023809
[19] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[20] Faulkner H M A, Rodenburg J M 2004 Phys. Rev. Lett. 93 023903
[21] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy 107 227
[22] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[23] Suzuki A, Takahashi Y 2015 Opt. Express 23 16429
[24] Yu W, He X L, Liu C, Zhu J Q 2015 Acta Phys. Sin. 64 244201 (in Chinese)[余伟, 何小亮, 刘诚, 朱健强 2015 物理学报 64 244201]
[25] Yu W, Wang S S, Veetil S, Gao S M, Liu C, Zhu J Q 2016 Phys. Rev. B 93 241105
[26] Mllenstedt G, Dker H 1956 Zeitschrift fr Physik 145 377
[27] Cowley J M 1992 Ultramicroscopy 41 335
[28] Tonomura A, Matsuda T, Endo J, Todokoro H, Komoda T 2004 Appl. Phys. Lett. 84 3229
[29] Harada K, Tonomura A 2004 Appl. Phys. Lett. 84 3229
[30] Rder F, Lubk A 2014 Ultramicroscopy 146 103
[31] Chen J W 2012 J. Opt. Soc. Am. A 29 1606
[32] Fu S F 1985 Acta Opt. Sin. 5 435 (in Chinese) [傅淑芬1985 光学学报5 435]
[33] Fu S F 1987 Acta Opt. Sin. 7 558 (in Chinese) [傅淑芬1987 光学学报7 558]
[34] Maiden A M, Humphry M J, Rodenburg J M 2012 J.Opt. Soc. Am. A 29 1606
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[1] Tian X, Yu W, Meng X, Sun A, Xue L, Liu C, Wang S 2016 Opt. Lett. 41 1427
[2] Tsai E H R, Diaz A, Menzel A, Guizar-Sicairos M 2016 Opt. Express 24 6441
[3] Yu W, Tian X, He X, Song X, Xue L, Liu C, Wang S 2016 Appl. Phys. Lett. 109 071112
[4] Nomarski G 1955 J. Phys. Radium 16 9
[5] Miao J, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[6] Thibault P, Dierolf M, Bunk O, Menzel A, Pfeiffer F 2009 Ultramicroscopy 109 338
[7] Thibault P, Dierolf M, Menzel A, Bunk O, David C, Pfeiffer F 2008 Science 321 379
[8] Abbey B, Nugent A K, Willianms G J, Clark J N, Peele A G, Pfeiffer M A, Jonge M, McNulty I 2008 Nat. Phys. 4 394
[9] Maiden M A, Rodenburg J M 2009 Ultramicroscopy 109 1256
[10] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[11] Miao J, Sayre D, Chapman H N J 1998 J. Opt. Soc. Am. A 15 1662
[12] Gerchberg R W, Saxton W O 2007 Phy. Rev. A 75 043805
[13] Fienup J R 1978 Opt. Lett. 3 27
[14] Fienup J R 1982 Appl. Opt. 21 2758
[15] Zhang F, Pedrini G, Osten W 2007 Phy. Rev. A 75 043805
[16] Claus D, Maiden M A, Zhang F, Sweeney F, Humphry M, Rodenburg J M, Schluesener H, Humphry M J 2011 Ptychography:A Novel Phase Retrieval Technique, Advantages and its Application Braga, Portugal, May 3, 2011 p800109
[17] Liu C, Pan X C, Zhu J Q 2013 Acta Phys. Sin. 62 184204 (in Chinese)[刘诚, 潘兴臣, 朱健强 2013 物理学报 62 184204]
[18] Chen B, Dilanian R A, Teichmann S, Abbey B, Peele A G, Williams G J, Hannaford P, van Dao L, Quiney H M, Nugent K A 2009 Phys. Rev. A 79 023809
[19] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[20] Faulkner H M A, Rodenburg J M 2004 Phys. Rev. Lett. 93 023903
[21] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy 107 227
[22] Rodenburg J M, Hurst A C, Cullis A G, Dobson B R, Pfeiffer F, Bunk O, David C, Jefimovs K, Johnson I 2007 Phys. Rev. Lett. 98 034801
[23] Suzuki A, Takahashi Y 2015 Opt. Express 23 16429
[24] Yu W, He X L, Liu C, Zhu J Q 2015 Acta Phys. Sin. 64 244201 (in Chinese)[余伟, 何小亮, 刘诚, 朱健强 2015 物理学报 64 244201]
[25] Yu W, Wang S S, Veetil S, Gao S M, Liu C, Zhu J Q 2016 Phys. Rev. B 93 241105
[26] Mllenstedt G, Dker H 1956 Zeitschrift fr Physik 145 377
[27] Cowley J M 1992 Ultramicroscopy 41 335
[28] Tonomura A, Matsuda T, Endo J, Todokoro H, Komoda T 2004 Appl. Phys. Lett. 84 3229
[29] Harada K, Tonomura A 2004 Appl. Phys. Lett. 84 3229
[30] Rder F, Lubk A 2014 Ultramicroscopy 146 103
[31] Chen J W 2012 J. Opt. Soc. Am. A 29 1606
[32] Fu S F 1985 Acta Opt. Sin. 5 435 (in Chinese) [傅淑芬1985 光学学报5 435]
[33] Fu S F 1987 Acta Opt. Sin. 7 558 (in Chinese) [傅淑芬1987 光学学报7 558]
[34] Maiden A M, Humphry M J, Rodenburg J M 2012 J.Opt. Soc. Am. A 29 1606
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