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As an expansion of coherent diffraction imaging, ptychographic iterative engine (PIE) not only inherits advantages such as ultra-high resolution and compact optical system, but also expands the field of view in quantitative imaging, thus PIE is widely used in short wavelength imaging such as X-ray and electron beam imaging, and then extended to visible light field. However, PIE requires coherent illumination for both phase and amplitude retrieval, while traditional X-ray or electron beam sources often cannot satisfy this strict coherent condition, which leads to poor-quality information retrieval with low signal-to-noise ratio. Though several proposed methods such as multiple wavelength and multi-mode algorithms can eliminate incoherency influence to some extent, various details such as quantitative spectrum of illuminating source should be obtained before information retrieval, which complicates computing procedures. In addition, it is hard to acquire the spectrum of the illuminating source in most cases. In order to acquire high-quality information based on PIE with partially coherent illumination, a newly designed enhanced phase retrieval method for weakly scattering samples in PIE with partially coherent illumination is presented in this paper, in which only the bright field of the diffraction patterns is used in the iterative procedures mimicking the coherent cases especially for weakly scattering samples without any prior illuminating details. The bright field area can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. While the dark-field area generated by interference of diffracted beams cannot satisfy the requirement for coherence, therefore, dark-field diffraction patterns should be excluded in sample information extraction and only the bright field is used for phase retrieval via iterative process. Compared with the proposed multiple wavelength and multi-mode algorithms, the proposed method can simplify sample reconstructing procedures due to needing no prior knowledge. Moreover, in order to enhance the information of weakly scattering samples in retrieval, high order iteration method is also introduced in the paper. Since the bright field can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. For weakly scattering sample, the weakened diffracted beam is much lower than zeroth order beam, thus it is difficult to acquire high-contrast information with classical PIE algorithms. Introducing high order iterative tactic, the contrast of weakly scattering sample is obviously improved and the details of weakly scattering sample can be retrieved clearly. Both theoretical analysis and numerical simulations are illustrated in detail, proving the robustness and availability of the designed method: high-contrast phase information can be obtained with the proposed method, while traditional phase retrieval algorithm almost loses all details of the sample. In order to mimic the real experimental situation, a 30 dB white noise is added into the simulation, the details of weakly scattering sample phase information can also be retrieved clearly by using the bright field of the diffraction patterns with high order iteration method. With the newly designed enhanced phase retrieval method for weakly scattering samples with partially coherent illumination, sample retrieval via PIE can not only use ordinary X-ray source or electron beam as illumination source, thereby avoiding the dependence on complete coherent source, but also obviously improve the retrieval quality of the sample characteristics, which widely expands the application fields of the PIE.
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Keywords:
- ptychographic iterative engine /
- partially coherent illumination /
- weak scattering samples
[1] Raab E L, Tennant D M, Waskiewicz W K, MacDowell A A, Freeman R R 1991 J. Opt. Soc. Am. A 8 1614
[2] Bergin R 1964 J. Sci. Instrum. 41 558
[3] Montgomery W D 1978 Opt. Lett. 2 120
[4] Fienup J R 1978 Opt. Lett. 31 27
[5] Fienup J R 1982 Appl. Opt. 21 2578
[6] Miao J, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[7] Zuo J, Vartanyants I, Gao M, Zhang R, Nagahara L A 2003 Science 300 1419
[8] Williams G J, Quiney H M, Dhal B B, Tran C Q, Nugent K A, Peele A G, Paterson D, de Jonge M D 2006 Phys. Rev. Lett. 97 025506
[9] Elser V 2003 J. Opt. Soc. Am. A 20 40
[10] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[11] Faulkner H M A, Rodenburg J M 2004 Phy. Rev. Lett. 93 023903
[12] Maiden M A, Rodenburg J M 2009 Ultramicroscopy 109 1256
[13] 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
[14] Rodenburg J M 2008 Adv. Imag. Elect. Phys. 150 87
[15] Claus D, Maiden M A, Zhang F, Sweeney F, Humphry M, Rodenburg J M 2011 SPIE 8001 800109
[16] 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]
[17] Chen B, Dilanian R A, Teichmann S, Abbey B, Peele A G, Williams G J, Hannaford P, Dao L V, Quiney H M, Nugent K A 2009 Phys. Rev. A 79 023809
[18] Abbey B, Whitehead L W, Quiney H M, Vine D J, Cadenazzi G A, Henderson C A, Nugent K A, Balaur E, Putkunz C T, Peele A G, Williams G J, Mcnulty I 2011 Nat. Photonics 5 420
[19] Liu C, Zhu J Q, Rodenburg J M 2015 Chin. Phys. B 24 024201
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[1] Raab E L, Tennant D M, Waskiewicz W K, MacDowell A A, Freeman R R 1991 J. Opt. Soc. Am. A 8 1614
[2] Bergin R 1964 J. Sci. Instrum. 41 558
[3] Montgomery W D 1978 Opt. Lett. 2 120
[4] Fienup J R 1978 Opt. Lett. 31 27
[5] Fienup J R 1982 Appl. Opt. 21 2578
[6] Miao J, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[7] Zuo J, Vartanyants I, Gao M, Zhang R, Nagahara L A 2003 Science 300 1419
[8] Williams G J, Quiney H M, Dhal B B, Tran C Q, Nugent K A, Peele A G, Paterson D, de Jonge M D 2006 Phys. Rev. Lett. 97 025506
[9] Elser V 2003 J. Opt. Soc. Am. A 20 40
[10] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[11] Faulkner H M A, Rodenburg J M 2004 Phy. Rev. Lett. 93 023903
[12] Maiden M A, Rodenburg J M 2009 Ultramicroscopy 109 1256
[13] 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
[14] Rodenburg J M 2008 Adv. Imag. Elect. Phys. 150 87
[15] Claus D, Maiden M A, Zhang F, Sweeney F, Humphry M, Rodenburg J M 2011 SPIE 8001 800109
[16] 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]
[17] Chen B, Dilanian R A, Teichmann S, Abbey B, Peele A G, Williams G J, Hannaford P, Dao L V, Quiney H M, Nugent K A 2009 Phys. Rev. A 79 023809
[18] Abbey B, Whitehead L W, Quiney H M, Vine D J, Cadenazzi G A, Henderson C A, Nugent K A, Balaur E, Putkunz C T, Peele A G, Williams G J, Mcnulty I 2011 Nat. Photonics 5 420
[19] Liu C, Zhu J Q, Rodenburg J M 2015 Chin. Phys. B 24 024201
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