Abstract

A single-shot phase retrieval algorithm based on a random aperture and partially saturated diffraction pattern is proposed. The diffraction pattern in the saturated area could be retrieved during the iterative process, which circumvents the problem of limited dynamic range of the detector. Besides, the random aperture is easier to be manufactured and if the accuracy of the random aperture is high enough, the design value could be used directly for iterations. It has the potential to be adapted for different wavelengths without additional transmission measurement of the wave modulator. The validity has been demonstrated by simulations and experiment.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (4)

2016 (5)

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

H. Tao, S. P. Veetil, X. Pan, C. Liu, and J. Zhu, “Lens-free coherent modulation imaging with collimated illumination,” Chin. Opt. Lett. 14, 071203 (2016).

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

2015 (7)

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

R. Horisaki, R. Egami, and J. Tanida, “Experimental demonstration of single-shot phase imaging with a coded aperture,” Opt. Express 23, 28691–28697 (2015).
[Crossref] [PubMed]

Z.-J. Cheng, B.-Y. Wang, Y.-Y. Xie, Y.-J. Lu, Q.-Y. Yue, and C.-S. Guo, “Phase retrieval and diffractive imaging based on babinet’s principle and complementary random sampling,” Opt. Express 23, 28874–28882 (2015).
[Crossref] [PubMed]

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

M. H. Seaberg, A. d’Aspremont, and J. J. Turner, “Coherent diffractive imaging using randomly coded masks,” Appl. Phys. Lett. 107, 231103 (2015).
[Crossref]

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

2014 (2)

R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39, 6466–6469 (2014).
[Crossref] [PubMed]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

2013 (1)

R. M. Glaeser, “Invited review article: Methods for imaging weak-phase objects in electron microscopy,” Rev. Sci. Instruments 84, 312 (2013).
[Crossref]

2012 (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

2011 (3)

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

2010 (1)

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104 (2010).
[Crossref]

2008 (1)

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

2007 (1)

2004 (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342 (1999).
[Crossref]

1982 (1)

Aino, M.

Almoro, P.

Anand, A.

Andrés, P.

Barbour, A.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Bian, F.

Bunk, O.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Burdet, N.

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342 (1999).
[Crossref]

Chen, B.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

Chen, S.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Cheng, Z.-J.

Chu, Y. S.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

Clark, J. N.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

Clemente, P.

d’Aspremont, A.

M. H. Seaberg, A. d’Aspremont, and J. J. Turner, “Coherent diffractive imaging using randomly coded masks,” Appl. Phys. Lett. 107, 231103 (2015).
[Crossref]

Dallal, Y.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

David, C.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

de Jonge, M. D.

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

Deng, J.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Diaz, A.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Dierolf, M.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Dudovich, N.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

Egami, R.

Elgass, K. D.

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

Estandarte, A. K.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Fienup, J. R.

Flachenecker, C.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Glaeser, R. M.

R. M. Glaeser, “Invited review article: Methods for imaging weak-phase objects in electron microscopy,” Rev. Sci. Instruments 84, 312 (2013).
[Crossref]

Gleber, S. C.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Gray, J.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Guizar-Sicairos, M.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

Guo, C.-S.

Han, L.

Harder, R.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Hirose, M.

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

Horisaki, R.

Hornberger, B.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Hua, W.

Huang, X.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Humphry, M. J.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

Ishikawa, T.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Jacobsen, C.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

Jefimovs, K.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Jin, Q.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Johnson, I.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Jones, M. W. M.

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

Junker, M. D.

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342 (1999).
[Crossref]

Kohmura, Y.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Komanicky, V.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

Lai, B.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Lancis, J.

Lauer, K.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

Leshem, B.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

Li, X.

Liu, C.

H. Tao, S. P. Veetil, X. Pan, C. Liu, and J. Zhu, “Lens-free coherent modulation imaging with collimated illumination,” Chin. Opt. Lett. 14, 071203 (2016).

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

Liu, Y.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Lu, Y.-J.

Maiden, A. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

Mak, R.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Maser, J.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Menzel, A.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Miao, J.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342 (1999).
[Crossref]

Morrison, G. R.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

Nadler, B.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

Nashed, Y. S. G.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

Nazaretski, E.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

Ogura, Y.

Ohashi, H.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Oron, D.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

Osten, W.

Pan, X.

H. Tao, S. P. Veetil, X. Pan, C. Liu, and J. Zhu, “Lens-free coherent modulation imaging with collimated illumination,” Chin. Opt. Lett. 14, 071203 (2016).

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

Parmar, N.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Pedrini, G.

Peng, C.

Pérez, D. G.

Peterka, T.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

Peters, E.

Pfeiffer, F.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Pierce, M. S.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Raz, O.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

Reese, M.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Renker, D.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Robinson, I. K.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Rodenburg, J. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104 (2010).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

J. M. Rodenburg, Ptychography and Related Diffractive Imaging Methods (Elsevier, 2008), vol. Volume 150, pp. 87–184.

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Salvador-Balaguer, E.

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342 (1999).
[Crossref]

Schwenke, J.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Seaberg, M. H.

M. H. Seaberg, A. d’Aspremont, and J. J. Turner, “Coherent diffractive imaging using randomly coded masks,” Appl. Phys. Lett. 107, 231103 (2015).
[Crossref]

Senba, Y.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, M. Reese, K. Giewekemeyer, S. C. Gleber, T. Salditt, and A. Rosenhahn, “Chemical contrast in soft x-ray ptychography,” Phys Rev Lett 107, 208101 (2011).
[Crossref] [PubMed]

Shemilt, L.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Shimomura, K.

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

Shu, D.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Suzuki, A.

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Tajahuerce, E.

Takahashi, Y.

A. Suzuki, K. Shimomura, M. Hirose, N. Burdet, and Y. Takahashi, “Dark-field x-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens,” Sci. Reports 6, 35060 (2016).
[Crossref]

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Tanida, J.

Tao, H.

Turner, J. J.

M. H. Seaberg, A. d’Aspremont, and J. J. Turner, “Coherent diffractive imaging using randomly coded masks,” Appl. Phys. Lett. 107, 231103 (2015).
[Crossref]

van Riessen, G. A.

M. W. M. Jones, K. D. Elgass, M. D. Junker, M. D. de Jonge, and G. A. van Riessen, “Molar concentration from sequential 2-d water-window x-ray ptychography and x-ray fluorescence in hydrated cells,” Sci. Reports 6, 24280 (2016).
[Crossref]

Veetil, S. P.

H. Tao, S. P. Veetil, X. Pan, C. Liu, and J. Zhu, “Lens-free coherent modulation imaging with collimated illumination,” Chin. Opt. Lett. 14, 071203 (2016).

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

Verbanis, E.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Vila-Comamala, J.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

Vine, D. J.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

Vogt, S.

J. Deng, D. J. Vine, S. Chen, Q. Jin, Y. S. G. Nashed, T. Peterka, S. Vogt, and C. Jacobsen, “X-ray ptychographic and fluorescence microscopy of frozen-hydrated cells using continuous scanning,” Sci. Reports 7, 445 (2017).
[Crossref]

Wang, B.

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

Wang, B.-Y.

Wang, J.

Wang, Y.

Xie, Y.-Y.

Xiong, G.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Xu, R.

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
[Crossref] [PubMed]

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Xu, W.

X. Huang, K. Lauer, J. N. Clark, W. Xu, E. Nazaretski, R. Harder, I. K. Robinson, and Y. S. Chu, “Fly-scan ptychography,” Sci. Reports 5, 9074 (2015).

Yamauchi, K.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Yang, S.

Yang, Y.

You, H.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Yuan, Y.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Yue, Q.-Y.

Yusuf, M.

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Zettsu, N.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[Crossref]

Zhang, F.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref] [PubMed]

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28, 604–612 (2011).
[Crossref]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104 (2010).
[Crossref]

Zhou, G.

Zhou, P.

Zhu, C.

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

Zhu, J.

H. Tao, S. P. Veetil, X. Pan, C. Liu, and J. Zhu, “Lens-free coherent modulation imaging with collimated illumination,” Chin. Opt. Lett. 14, 071203 (2016).

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

Appl. Opt. (1)

Appl. Phys. Lett. (3)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

C. Zhu, R. Harder, A. Diaz, V. Komanicky, A. Barbour, R. Xu, X. Huang, Y. Liu, M. S. Pierce, A. Menzel, and H. You, “Ptychographic x-ray imaging of surfaces on crystal truncation rod,” Appl. Phys. Lett. 106, 101604 (2015).
[Crossref]

M. H. Seaberg, A. d’Aspremont, and J. J. Turner, “Coherent diffractive imaging using randomly coded masks,” Appl. Phys. Lett. 107, 231103 (2015).
[Crossref]

Biophys. J. (1)

L. Shemilt, E. Verbanis, J. Schwenke, A. K. Estandarte, G. Xiong, R. Harder, N. Parmar, M. Yusuf, F. Zhang, and I. K. Robinson, “Karyotyping human chromosomes by optical and x-ray ptychography methods,” Biophys. J. 108, 706–713 (2015).
[Crossref] [PubMed]

Chin. Opt. Lett. (2)

J. Mod. Opt. (1)

X. Pan, S. P. Veetil, B. Wang, C. Liu, and J. Zhu, “Ptychographical imaging with partially saturated diffraction patterns,” J. Mod. Opt. 621–8 (2015).

J. Opt. Soc. Am. A (1)

J. Synchro. Radiat. (1)

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, and J. Maser, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchro. Radiat. 21, 66–75 (2014).
[Crossref]

Nat Commun (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat Commun 3, 730 (2012).
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Nat. Commun. (2)

B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz, “Direct single-shot phase retrieval from the diffraction pattern of separated objects,” Nat. Commun. 7, 10820 (2016).
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Nature (1)

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Phys Rev Lett (1)

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Phys. Rev. B (2)

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104 (2010).
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J. M. Rodenburg, Ptychography and Related Diffractive Imaging Methods (Elsevier, 2008), vol. Volume 150, pp. 87–184.

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Figures (6)

Fig. 1
Fig. 1 (a) Illustration of the scattering properties of a random aperture; (b) complete power spectrum of the random aperture; (c) power spectrum of the random aperture after setting the low-frequency components to zero.
Fig. 2
Fig. 2 (a) Basic scheme for single-shot phase retrieval based on a random aperture; (b) amplitude of the specimen exit wave and the amplitude of the incident wave on the specimen is illustrated by the up-right inset; (c) phase of the specimen while the phase of the incident wave is illustrated by the up-right inset. (d) and (e) are the retrieved amplitude of exit wave and phase map of specimen respectively without considering any noise and saturations. The red dashed circle in (d) indicates the constraints in the specimen plane. Scale bar in (b), 1 mm and (b)(d) share the same scale bar. The color bars of (c) and (e) indicate phase in radians.
Fig. 3
Fig. 3 Results of the numerical simulations. (a)–(d) are the results of CAMI while the results of CMI are shown in (e)–(h). (a1)–(d1) and (e1)–(h1) are the diffraction patterns recorded for CAMI and CMI respectively with different exposure time. The red sections indicate the saturated area and the amplified views are illustrated by the corresponding up-right insets. The number of saturated pixels, indicated by N, for each column is approximately the same for fair comparisons. The random phase plate, providing binary phase delay 0 or π for CMI, has the same basic size S with the random aperture for CAMI. After 200 iterations, the retrieved exit waves and phase maps of the specimen with CAMI and CMI are shown by (a2)–(d2), (a3)–(d3) and (e2)–(h2), (e3)–(h3) respectively. The red dashed circles in (a2)–(d2) and (e2)–(h2) indicate the constraints in the specimen plane. (a1)–(d1) and (e1)–(h1) share the same scale bar. (a2)–(d2), (a3)–(d3), (e2)–(h2) and (e3)–(h3) share the same scale bar. The color bars of the third and sixth rows indicate phase in radians.
Fig. 4
Fig. 4 Variation of the error ER of the simulations shown in Fig. 3. The solid lines and dashed lines represent the results of CAMI and CMI respectively. (a) The variation of the error with iteration number and the curves with same color has approximate amounts of saturated pixels in the diffraction patterns. (b) The comparisons of final ER between CAMI and CMI after 200 iterations.
Fig. 5
Fig. 5 (a), 5(d), 5(g) The partially saturated diffraction patterns when S = 6μm, 8 μm and 12 μm respectively. The center part of the random apertures are shown in the corresponding up-right insets. The corresponding amplitude of exit wave and the phase map of specimen are illustrated by (b)–(c), (e)–(f) and (h)–(i) respectively. The color bars of (c) (f) (i) indicate phase in radians.
Fig. 6
Fig. 6 (a) The photo of a chrome silica plate used as a random aperture in the experiment. (b) The comparison between the micro-graph of (a) and the design value, the grayscale map is the micro-graph and the red map above the micro-graph is the corresponding design value. The sections without chrome for red map is transparent. (c) Diffraction pattern recorded by the CCD. (d) Reconstructed amplitude of the specimen exit wave, the top-right inset shows the phase distribution. (e) The phase map the specimen after subtract the phase of illumination, which is retrieved from the diffraction pattern without specimen. The red dashed circles are the constraints in the specimen plane. The color bars of (d) and (e) indicate phase in radians.

Equations (3)

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ER ( k ) = ( | E k | 2 I ) 2 / ( I ) 2 .
E ˜ k = { I e j ω k S E k S ,
I = { round [ Poisson ( n I 0 ) + rand × 50 ] S 4095 S ,

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