Abstract

Ptychography is an imaging method whereby a coherent beam is scanned across an object, and an image is obtained by iterative phasing of the set of diffraction patterns. It is able to be used to image extended objects at a resolution limited by scattering strength of the object and detector geometry, rather than at an optics-imposed limit. As technical advances allow larger fields to be imaged, computational challenges arise for reconstructing the correspondingly larger data volumes, yet at the same time there is also a need to deliver reconstructed images immediately so that one can evaluate the next steps to take in an experiment. Here we present a parallel method for real-time ptychographic phase retrieval. It uses a hybrid parallel strategy to divide the computation between multiple graphics processing units (GPUs) and then employs novel techniques to merge sub-datasets into a single complex phase and amplitude image. Results are shown on a simulated specimen and a real dataset from an X-ray experiment conducted at a synchrotron light source.

© 2014 Optical Society of America

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References

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2014 (4)

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using eiger: scanning x-ray nano-imaging of extended regions,” Opt. Express 22, 14859–14870 (2014).
[Crossref] [PubMed]

X. Huang, H. Yan, R. Harder, Y. Hwu, I. K. Robinson, and Y. S. Chu, “Optimization of overlap uniformness for ptychography,” Opt. Express 22, 12634–12644 (2014).
[Crossref] [PubMed]

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
[Crossref]

2013 (2)

2012 (4)

A. M. Maiden, M. J. Humphry, and J. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29, 1606–1614 (2012).
[Crossref]

D. Claus, A. M. Maiden, F. Zhang, F. G. Sweeney, M. J. Humphry, H. Schluesener, and J. M. Rodenburg, “Quantitative phase contrast optimised cancerous cell differentiation via ptychography,” Opt. Express 20, 9911–9918 (2012).
[Crossref] [PubMed]

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14, 063004 (2012).
[Crossref]

2011 (1)

2010 (3)

F. R. Maia, T. Ekeberg, D. Van Der Spoel, and J. Hajdu, “Hawk: the image reconstruction package for coherent x-ray diffractive imaging,” J. Appl. Crystallogr. 43, 1535–1539 (2010).
[Crossref]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[Crossref]

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

2008 (6)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
[Crossref]

P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33, 309–311 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
[Crossref] [PubMed]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

2007 (4)

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” International J. Comp. Vis. 74, 59–73 (2007).
[Crossref]

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[Crossref] [PubMed]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[Crossref]

2006 (3)

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
[Crossref] [PubMed]

2005 (1)

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151, 250–262 (2005).
[Crossref] [PubMed]

2004 (2)

H. Faulkner and J. 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. 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, 342–344 (1999).
[Crossref]

1994 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref] [PubMed]

W. Saxton and W. Baumeister, “The correlation averaging of a regularly arranged bacterial cell envelope protein,” J. Microsc. 127, 127–138 (1982).
[Crossref] [PubMed]

1980 (1)

1969 (1)

W. Hoppe, “Beugung im inhomogenen primarstrahlwellenfeld. i. prinzip einer phasenmessung von elektronen-beungungsinterferenzen,” Acta Crystallogr., Sect. A 25, 495–501 (1969).
[Crossref]

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Argyriou, V.

V. Argyriou and T. Vlachos, “Using gradient correlation for sub-pixel motion estimation of video sequences,” in “Acoustics, Speech, and Signal Processing, 2004. Proceedings.(ICASSP’04). IEEE International Conference on,”, vol. 3 (IEEE, 2004), vol. 3, pp. iii–329.

Bao, P.

Barty, A.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nature Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Baumeister, W.

W. Saxton and W. Baumeister, “The correlation averaging of a regularly arranged bacterial cell envelope protein,” J. Microsc. 127, 127–138 (1982).
[Crossref] [PubMed]

Bean, R.

Beetz, T.

Berenguer, F.

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Bolbat, M.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
[Crossref]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).
[Crossref]

Breiby, D. W.

T. L. Falch, J. B. Fløystad, A. C. Elster, and D. W. Breiby, “Optimization and parallelization of ptychography reconstruction code,” Norsk informatikkonferanse2012 (2012).

Brister, K.

S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
[Crossref]

Brown, M.

M. Brown and D. G. Lowe, “Automatic panoramic image stitching using invariant features,” International J. Comp. Vis. 74, 59–73 (2007).
[Crossref]

Bunk, O.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
[Crossref]

M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using eiger: scanning x-ray nano-imaging of extended regions,” Opt. Express 22, 14859–14870 (2014).
[Crossref] [PubMed]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[Crossref]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
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M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
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M. Guizar-Sicairos, I. Johnson, A. Diaz, M. Holler, P. Karvinen, H.-C. Stadler, R. Dinapoli, O. Bunk, and A. Menzel, “High-throughput ptychography using eiger: scanning x-ray nano-imaging of extended regions,” Opt. Express 22, 14859–14870 (2014).
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F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
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P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
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M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express 19, 21345–21357 (2011).
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M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
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M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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Miao, 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, 342–344 (1999).
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Nugent, K. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
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F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
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C. G. Schroer, S. Hnig, A. Goldschmidt, R. Hoppe, J. Patommel, D. Samberg, A. Schropp, F. Seiboth, S. Stephan, S. Schder, M. Burghammer, M. Denecke, G. Wellenreuther, and G. Falkenberg, “Hard x-ray nano-beam characterization by ptychographic imaging,” in “SPIE Optical Engineering+ Applications,” (International Society for Optics and Photonics, 2011), p. 814103.

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33, 309–311 (2008).
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F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
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B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
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T. Peterka, D. Goodell, R. Ross, H.-W. Shen, and R. Thakur, “A configurable algorithm for parallel image-compositing applications,” in “Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis,” (ACM, 2009), p. 4.

T. Peterka, R. Ross, A. Gyulassy, V. Pascucci, W. Kendall, H.-W. Shen, T.-Y. Lee, and A. Chaudhuri, “Scalable parallel building blocks for custom data analysis,” in “Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on,” (IEEE, 2011), pp. 105–112.

Peterson, I.

Pfeifer, M. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nature Phys. 4, 394–398 (2008).
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Pfeiffer, F.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
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M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
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Ritala, M.

M. Holler, A. Diaz, M. Guizar-Sicairos, P. Karvinen, E. Färm, E. Härkönen, M. Ritala, A. Menzel, J. Raabe, and O. Bunk, “X-ray ptychographic computed tomography at 16nm isotropic 3D resolution,” Sci. Rep. 4, 3857 (2014).
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Ross, R.

T. Peterka, D. Goodell, R. Ross, H.-W. Shen, and R. Thakur, “A configurable algorithm for parallel image-compositing applications,” in “Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis,” (ACM, 2009), p. 4.

T. Peterka, R. Ross, A. Gyulassy, V. Pascucci, W. Kendall, H.-W. Shen, T.-Y. Lee, and A. Chaudhuri, “Scalable parallel building blocks for custom data analysis,” in “Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on,” (IEEE, 2011), pp. 105–112.

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A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 64–72 (2012).
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M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151, 250–262 (2005).
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M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
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C. G. Schroer, S. Hnig, A. Goldschmidt, R. Hoppe, J. Patommel, D. Samberg, A. Schropp, F. Seiboth, S. Stephan, S. Schder, M. Burghammer, M. Denecke, G. Wellenreuther, and G. Falkenberg, “Hard x-ray nano-beam characterization by ptychographic imaging,” in “SPIE Optical Engineering+ Applications,” (International Society for Optics and Photonics, 2011), p. 814103.

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C. G. Schroer, S. Hnig, A. Goldschmidt, R. Hoppe, J. Patommel, D. Samberg, A. Schropp, F. Seiboth, S. Stephan, S. Schder, M. Burghammer, M. Denecke, G. Wellenreuther, and G. Falkenberg, “Hard x-ray nano-beam characterization by ptychographic imaging,” in “SPIE Optical Engineering+ Applications,” (International Society for Optics and Photonics, 2011), p. 814103.

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T. Peterka, D. Goodell, R. Ross, H.-W. Shen, and R. Thakur, “A configurable algorithm for parallel image-compositing applications,” in “Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis,” (ACM, 2009), p. 4.

T. Peterka, R. Ross, A. Gyulassy, V. Pascucci, W. Kendall, H.-W. Shen, T.-Y. Lee, and A. Chaudhuri, “Scalable parallel building blocks for custom data analysis,” in “Large Data Analysis and Visualization (LDAV), 2011 IEEE Symposium on,” (IEEE, 2011), pp. 105–112.

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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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T. Peterka, D. Goodell, R. Ross, H.-W. Shen, and R. Thakur, “A configurable algorithm for parallel image-compositing applications,” in “Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis,” (ACM, 2009), p. 4.

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P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
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M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
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S. Chen, J. Deng, Y. Yuan, C. Flachenecker, R. Mak, B. Hornberger, Q. Jin, D. Shu, B. Lai, J. Maser, C. Roehrig, T. Paunesku, S. C. Gleber, D. J. Vine, L. Finney, J. VonOsinski, M. Bolbat, I. Spink, Z. Chen, J. Steele, D. Trapp, J. Irwin, M. Feser, E. Snyder, K. Brister, C. Jacobsen, G. Woloschak, and S. Vogt, “The bionanoprobe: hard x-ray fluorescence nanoprobe with cryogenic capabilities,” J. Synchrotron Radiat. 21, 66–75 (2014).
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M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. Von Koenig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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Figures (8)

Fig. 1
Fig. 1 Simplified ptychography experiment setup showing a Cartesian grid used for the overlapping raster scan positions.
Fig. 2
Fig. 2 GPU memory layout of a 2D M×N matrix. The gray area represents the aligned matrix zero padding, where W = warp size (32 threads on most devices). The padded area is always ignored in matrix operations. CUDA blocks operate on matrix slices of size s such as the region outlined by the dashed red line. Memory requests for a row of the padded matrix are served by a single cache line.
Fig. 3
Fig. 3 The diffraction patterns are subdivided and distributed among available GPUs. Pairwise stitching is performed on the separate reconstructions attained by phase retrieval.
Fig. 4
Fig. 4 Object array sharing through neighborhood exchange between 16 GPUs. The overlap (halo), highlighted in blue, is defined in terms of additional scan points assigned to each GPU sub-dataset.
Fig. 5
Fig. 5 (a) Normalized RMS error of final reconstructions achieved by different GPU configurations using the asynchronous, synchronous, and synchronous with halo=2 implementations. (b) Magnitude and phase of the object wavefront retrieved from simulated data using the asynchronous version and 128 GPUs. (c) Magnitude and phase of the object wavefront retrieved from simulated data using the synchronous version and 32 GPUs. (d) Magnitude and phase of the object wavefront retrieved from simulated data using the synchronous version, 32 GPUs, and a halo region of 2 additional scan point rows and columns.
Fig. 6
Fig. 6 Performance plots on synthetic data. Left: Total running time (in seconds) of different GPU configurations. Right: The scaling efficiency plotted as a percentage of linear scaling.
Fig. 7
Fig. 7 (a) Phase image of the reconstructed object transmission function, with the 1 μm×1 μm scan region highlighted in red. (b) Fourier ring correlation (FRC) plot showing a spatial resolution of 16 nm in the phase of the exit surface wave. (c,d) The recovered illumination function of two probe modes.
Fig. 8
Fig. 8 Performance plots on real data. Left: Total running time (in seconds) of different GPU configurations. Right: The scaling efficiency plotted as a percentage of linear scaling.

Equations (21)

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ψ j ( r ) = P ( r R j ) O ( r )
I j ( u ) = | [ ψ j ( r ) ] | 2 ,
Ψ j ( u ) = I j ( u ) [ ψ j ( r ) ] | [ ψ j ( r ) ] | .
ψ j ( r ) = 1 [ Ψ j ( u ) ] .
O j ( r ) = O j ( r ) + P j * ( r R j ) [ ψ j ( r ) ψ j ( r ) ] max ( | P j ( r R j ) | 2 )
P j ( r ) = P j ( r ) + O j * ( r + R j ) [ ψ j ( r ) ψ j ( r ) ] max ( | O j ( r + R j ) | 2 ) ,
ψ j ( k ) ( r ) = 1 [ I j ( u ) [ ψ j ( k ) ( r ) ] k | [ ψ j ( k ) ( r ) ] | 2 ] ,
O j ( r ) = O j ( r ) + k P j ( k ) * ( r R j ) [ ψ j ( k ) ( r ) ψ j ( k ) ( r ) ] max ( k | P j ( k ) ( r R j ) | 2 )
P j ( k ) ( r ) = P j ( k ) + O j * ( r + R j ) [ ψ j ( k ) ( r ) ψ j ( k ) ( r ) ] max ( | O j ( r + R j ) | 2 ) .
g h ( x , y ) = f ( x + 1 , y ) f ( x 1 , y )
g v ( x , y ) = f ( x , y + 1 ) f ( x , y 1 ) ,
g ( x , y ) = g h ( x , y ) + j g v ( x , y ) .
g 1 ( r ) = [ | g 1 ( x , y ) | ]
g 2 ( r ) = [ | g 2 ( x , y ) | ]
S ( r ) = g 1 ( r ) g 2 * ( r ) | g 1 ( r ) | | g 2 * ( r ) | ,
Δ x , Δ y = argmax x , y ( | 1 [ S ( r ) ] | ) .
O 2 ( x , y ) = μ 1 O 2 ( x , y ) μ 2 ,
O ( x , y ) = { O 1 ( x , y ) if x < Δ x + ( M Δ x ) / 2 , y < Δ y + ( N Δ y ) / 2 O 2 ( x , y ) otherwise .
O t ( r ) = O ( r ) + l = 1 L N l ( r ) L + 1 ,
E 0 ( n ) = r | O ( r ) γ O n ( r ) | 2 | O ( r ) | 2
γ = r | O ( r ) O n * ( r ) | 2 r | O n ( r ) | 2 ,

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