Abstract

Three-dimensional (3D) x-ray microscopy by ptychographic tomography requires elaborate numerical reconstructions. We describe a coupled ptychography-tomography reconstruction algorithm and apply it to an experimental ptychographic x-ray computed tomography data set of a catalyst particle. Compared to the traditional sequential algorithm, in which ptychographic projections are reconstructed to serve as input for subsequent tomographic reconstruction, the coupled ptychography-tomography algorithm reconstructs the 3D volume with higher spatial resolution over a larger field of view. Coupling the data from different projections improves the overall reconstruction, and the ptychographic sampling in individual projections can be coarsened beyond the point of overlap between neighboring scan points, still leading to stable reconstructions.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (6)

S. Sala, D. J. Batey, A. Prakash, S. Ahmed, C. Rau, and P. Thibault, “Ptychographic x-ray computed tomography at a high-brilliance x-ray source,” Opt. Express 27, 533–542 (2019).
[Crossref]

S. Aslan, V. Nikitin, D. J. Ching, T. Bicer, S. Leyffer, and D. Gürsoy, “Joint ptycho-tomography reconstruction through alternating direction method of multipliers,” Opt. Express 27, 9128–9143 (2019).
[Crossref]

T. Ramos, B. E. Grønager, M. S. Andersen, and J. W. Andreasen, “Direct three-dimensional tomographic reconstruction and phase retrieval of far-field coherent diffraction patterns,” Phys. Rev. A 99, 023801 (2019).
[Crossref]

T. Weissenberger, R. Leonhardt, B. Apeleo Zubiri, M. Pitínová-Štekrová, T. L. Sheppard, B. Reiprich, J. Bauer, R. Dotzel, M. Kahnt, A. Schropp, C. G. Schroer, J.-D. Grunwaldt, J. Casci, J. Čejka, E. Spiecker, and W. Schwieger, “Synthesis and characterisation of hierarchically structured titanium silicalite‐1 zeolites with large intracrystalline macropores,” Chemistry 25, 03287 (2019).
[Crossref]

X. Huang, H. Yan, Y. He, M. Ge, H. Öztürk, Y.-L. L. Fang, S. Ha, M. Lin, M. Lu, E. Nazaretski, I. K. Robinson, and Y. S. Chu, “Resolving 500 nm axial separation by multi-slice X-ray ptychography,” Acta Crystallogr. A 75, 336–341 (2019).
[Crossref]

E. H. R. Tsai, F. Marone, and M. Guizar-Sicairos, “Gridrec-ms: an algorithm for multi-slice tomography,” Opt. Lett. 44, 2181–2184 (2019).
[Crossref]

2018 (11)

P. F. Tavares, E. Al-Dmour, Å. Andersson, F. Cullinan, B. N. Jensen, D. Olsson, D. K. Olsson, M. Sjöström, H. Tarawneh, S. Thorin, and A. Vorozhtsov, “Commissioning and first-year operational results of the MAX IV 3 GeV ring,” J. Synchrotron Rad. 25, 1291–1316 (2018).
[Crossref]

P. Li and A. Maiden, “Multi-slice ptychographic tomography,” Sci. Rep. 8, 2049 (2018).
[Crossref]

K. Shimomura, M. Hirose, T. Higashino, and Y. Takahashi, “Three-dimensional iterative multislice reconstruction for ptychographic x-ray computed tomography,” Opt. Express 26, 31199–31208 (2018).
[Crossref]

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

F. Wittwer, R. Hoppe, F. Seiboth, J. Reinhardt, M. Scholz, and C. G. Schroer, “Ptychography with a virtually enlarged illumination,” Microsc. Microanal. 24, 46–47 (2018).
[Crossref]

M. Odstrčil, M. Holler, and M. Guizar-Sicairos, “Arbitrary-path fly-scan ptychography,” Opt. Express 26, 12585–12593 (2018).
[Crossref]

H. Öztürk, H. Yan, Y. He, M. Ge, Z. Dong, M. Lin, E. Nazaretski, I. K. Robinson, Y. S. Chu, and X. Huang, “Multi-slice ptychography with large numerical aperture multilayer Laue lenses,” Optica 5, 601–607 (2018).
[Crossref]

D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Ródriguez-Pérez, and C. Rau, “Coherence branch at I13, DLS: the multiscale, multimodal, ptycho-tomographic end station,” Microsc. Microanal. 24, 40–41 (2018).
[Crossref]

M. A. Gilles, Y. S. G. Nashed, M. Du, C. Jacobsen, and S. M. Wild, “3D x-ray imaging of continuous objects beyond the depth of focus limit,” Optica 5, 1078–1086 (2018).
[Crossref]

Y.-S. Yu, M. Farmand, C. Kim, Y. Liu, C. P. Grey, F. C. Strobridge, T. Tyliszczak, R. Celestre, P. Denes, J. Joseph, H. Krishnan, F. R. N. C. Maia, A. L. D. Kilcoyne, S. Marchesini, T. P. C. Leite, T. Warwick, H. Padmore, J. Cabana, and D. A. Shapiro, “Three-dimensional localization of nanoscale battery reactions using soft x-ray tomography,” Nat. Commun. 9, 921 (2018).
[Crossref]

F. Pfeiffer, “X-ray ptychography,” Nat. Photonics 12, 9–17 (2018).
[Crossref]

2017 (5)

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

J. C. da Silva, J. Haubrich, G. Requena, M. Hubert, A. Pacureanu, L. Bloch, Y. Yang, and P. Cloetens, “High energy near- and far-field ptychographic tomography at the ESRF,” Proc. SPIE 10391, 1039106 (2017).
[Crossref]

D. Gürsoy, “Direct coupling of tomography and ptychography,” Opt. Lett. 42, 3169–3172 (2017).
[Crossref]

C. G. Schroer, M. Seyrich, M. Kahnt, S. Botta, R. Döhrmann, G. Falkenberg, J. Garrevoet, M. Lyubomirskiy, M. Scholz, A. Schropp, and F. Wittwer, “PtyNAMi: ptychographic nano-analytical microscope at PETRA III—interferometrically tracking positions for 3D x-ray scanning microscopy using a ball-lens retroreflector,” Proc. SPIE 10389, 103890E (2017).
[Crossref]

J. Reinhardt, R. Hoppe, G. Hofmann, C. D. Damsgaard, J. Patommel, C. Baumbach, S. Baier, A. Rochet, J.-D. Grunwaldt, G. Falkenberg, and C. G. Schroer, “Beamstop-based low-background ptychography to image weakly scattering objects,” Ultramicroscopy 173, 52–57 (2017).
[Crossref]

2016 (4)

T. Gerzen and D. Minkwitz, “Simultaneous multiplicative column-normalized method (SMART) for 3-D ionosphere tomography in comparison to other algebraic methods,” Ann. Geophys. 34, 97–115 (2016).
[Crossref]

E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, “X-ray ptychography with extended depth of field,” Opt. Express 24, 29089–29108 (2016).
[Crossref]

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49, 1245–1252 (2016).
[Crossref]

P. Raimondi, “ESRF-EBS: the extremely brilliant source project,” Synchr. Rad. News 29(6), 8–15 (2016).
[Crossref]

2015 (6)

J. Deng, Y. S. G. Nashed, S. Chen, N. W. Phillips, T. Peterka, R. Ross, S. Vogt, C. Jacobsen, and D. J. Vine, “Continuous motion scan ptychography: characterization for increased speed in coherent x-ray imaging,” Opt. Express 23, 5438–5451 (2015).
[Crossref]

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

M. Soleimani and T. Pengpen, “Introduction: a brief overview of iterative algorithms in x-ray computed tomography,” Philos. Trans. A Math. Phys. Eng. Sci. 373, 20140399 (2015).
[Crossref]

A. G. Machoke, A. M. Beltrán, A. Inayat, B. Winter, T. Weissenberger, N. Kruse, R. Güttel, E. Spiecker, and W. Schwieger, “Micro/macroporous system: Mfi-type zeolite crystals with embedded macropores,” Adv. Mater. 27, 1066–1070 (2015).
[Crossref]

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref]

2014 (8)

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 16 nm 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]

Y. S. G. Nashed, D. J. Vine, T. Peterka, J. Deng, R. Ross, and C. Jacobsen, “Parallel ptychographic reconstruction,” Opt. Express 22, 32082–32097 (2014).
[Crossref]

P. M. Pelz, M. Guizar-Sicairos, P. Thibault, I. Johnson, M. Holler, and A. Menzel, “On-the-fly scans for x-ray ptychography,” Appl. Phys. Lett. 105, 251101 (2014).
[Crossref]

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22, 12513–12523 (2014).
[Crossref]

A. Suzuki, S. Furutaku, K. Shimomura, K. Yamauchi, Y. Kohmura, T. Ishikawa, and Y. Takahashi, “High-resolution multislice x-ray ptychography of extended thick objects,” Phys. Rev. Lett. 112, 053903 (2014).
[Crossref]

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104, 171104 (2014).
[Crossref]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

2013 (4)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref]

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, “Full spatial characterization of a nanofocused x-ray free-electron laser beam by ptychographic imaging,” Sci. Rep. 3, 1633 (2013).
[Crossref]

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).
[Crossref]

R. Hoppe, J. Reinhardt, G. Hofmann, J. Patommel, J.-D. Grunwaldt, C. D. Damsgaard, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, “High-resolution chemical imaging of gold nanoparticles using hard x-ray ptychography,” Appl. Phys. Lett. 102, 203104 (2013).
[Crossref]

2012 (3)

A. Schropp, R. Hoppe, J. Patommel, D. Samberg, F. Seiboth, S. Stephan, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, “Hard x-ray scanning microscopy with coherent radiation: beyond the resolution of conventional x-ray microscopes,” Appl. Phys. Lett. 100, 253112 (2012).
[Crossref]

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

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

2011 (1)

2009 (2)

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

2008 (1)

2004 (2)

C. Badea and R. Gordon, “Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography,” Phys. Med. Biol. 49, 1455 (2004).
[Crossref]

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20, 73–97 (2004).
[Crossref]

2003 (1)

M. Jiang and G. Wang, “Convergence of the simultaneous algebraic reconstruction technique (SART),” IEEE Trans. Image Process. 12, 957–961 (2003).
[Crossref]

1984 (1)

A. Andersen and A. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[Crossref]

1972 (1)

P. Gilbert, “Iterative methods for the three-dimensional reconstruction of an object from projections,” J. Theor. Biol. 36, 105–117 (1972).
[Crossref]

1970 (1)

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[Crossref]

Aeppli, G.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

Agapov, I.

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

Ahmed, S.

Al-Dmour, E.

P. F. Tavares, E. Al-Dmour, Å. Andersson, F. Cullinan, B. N. Jensen, D. Olsson, D. K. Olsson, M. Sjöström, H. Tarawneh, S. Thorin, and A. Vorozhtsov, “Commissioning and first-year operational results of the MAX IV 3 GeV ring,” J. Synchrotron Rad. 25, 1291–1316 (2018).
[Crossref]

Allner, S.

Andersen, A.

A. Andersen and A. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[Crossref]

Andersen, M. S.

T. Ramos, B. E. Grønager, M. S. Andersen, and J. W. Andreasen, “Direct three-dimensional tomographic reconstruction and phase retrieval of far-field coherent diffraction patterns,” Phys. Rev. A 99, 023801 (2019).
[Crossref]

Andersen, T. R.

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

Andersson, Å.

P. F. Tavares, E. Al-Dmour, Å. Andersson, F. Cullinan, B. N. Jensen, D. Olsson, D. K. Olsson, M. Sjöström, H. Tarawneh, S. Thorin, and A. Vorozhtsov, “Commissioning and first-year operational results of the MAX IV 3 GeV ring,” J. Synchrotron Rad. 25, 1291–1316 (2018).
[Crossref]

Andreasen, J. W.

T. Ramos, B. E. Grønager, M. S. Andersen, and J. W. Andreasen, “Direct three-dimensional tomographic reconstruction and phase retrieval of far-field coherent diffraction patterns,” Phys. Rev. A 99, 023801 (2019).
[Crossref]

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

Apeleo Zubiri, B.

T. Weissenberger, R. Leonhardt, B. Apeleo Zubiri, M. Pitínová-Štekrová, T. L. Sheppard, B. Reiprich, J. Bauer, R. Dotzel, M. Kahnt, A. Schropp, C. G. Schroer, J.-D. Grunwaldt, J. Casci, J. Čejka, E. Spiecker, and W. Schwieger, “Synthesis and characterisation of hierarchically structured titanium silicalite‐1 zeolites with large intracrystalline macropores,” Chemistry 25, 03287 (2019).
[Crossref]

Arnold, B.

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, “Full spatial characterization of a nanofocused x-ray free-electron laser beam by ptychographic imaging,” Sci. Rep. 3, 1633 (2013).
[Crossref]

Aslan, S.

Badea, C.

C. Badea and R. Gordon, “Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography,” Phys. Med. Biol. 49, 1455 (2004).
[Crossref]

Baier, S.

J. Reinhardt, R. Hoppe, G. Hofmann, C. D. Damsgaard, J. Patommel, C. Baumbach, S. Baier, A. Rochet, J.-D. Grunwaldt, G. Falkenberg, and C. G. Schroer, “Beamstop-based low-background ptychography to image weakly scattering objects,” Ultramicroscopy 173, 52–57 (2017).
[Crossref]

Batey, D.

D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Ródriguez-Pérez, and C. Rau, “Coherence branch at I13, DLS: the multiscale, multimodal, ptycho-tomographic end station,” Microsc. Microanal. 24, 40–41 (2018).
[Crossref]

Batey, D. J.

Bauer, J.

T. Weissenberger, R. Leonhardt, B. Apeleo Zubiri, M. Pitínová-Štekrová, T. L. Sheppard, B. Reiprich, J. Bauer, R. Dotzel, M. Kahnt, A. Schropp, C. G. Schroer, J.-D. Grunwaldt, J. Casci, J. Čejka, E. Spiecker, and W. Schwieger, “Synthesis and characterisation of hierarchically structured titanium silicalite‐1 zeolites with large intracrystalline macropores,” Chemistry 25, 03287 (2019).
[Crossref]

Baumbach, C.

J. Reinhardt, R. Hoppe, G. Hofmann, C. D. Damsgaard, J. Patommel, C. Baumbach, S. Baier, A. Rochet, J.-D. Grunwaldt, G. Falkenberg, and C. G. Schroer, “Beamstop-based low-background ptychography to image weakly scattering objects,” Ultramicroscopy 173, 52–57 (2017).
[Crossref]

Bean, R.

Beltrán, A. M.

A. G. Machoke, A. M. Beltrán, A. Inayat, B. Winter, T. Weissenberger, N. Kruse, R. Güttel, E. Spiecker, and W. Schwieger, “Micro/macroporous system: Mfi-type zeolite crystals with embedded macropores,” Adv. Mater. 27, 1066–1070 (2015).
[Crossref]

Bender, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[Crossref]

Berenguer, F.

Bicer, T.

Bloch, L.

J. C. da Silva, J. Haubrich, G. Requena, M. Hubert, A. Pacureanu, L. Bloch, Y. Yang, and P. Cloetens, “High energy near- and far-field ptychographic tomography at the ESRF,” Proc. SPIE 10391, 1039106 (2017).
[Crossref]

Botta, S.

C. G. Schroer, M. Seyrich, M. Kahnt, S. Botta, R. Döhrmann, G. Falkenberg, J. Garrevoet, M. Lyubomirskiy, M. Scholz, A. Schropp, and F. Wittwer, “PtyNAMi: ptychographic nano-analytical microscope at PETRA III—interferometrically tracking positions for 3D x-ray scanning microscopy using a ball-lens retroreflector,” Proc. SPIE 10389, 103890E (2017).
[Crossref]

Brefeld, W.

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

Brinkmann, R.

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

Bundgaard, E.

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

Bunk, O.

M. Holler, M. Guizar-Sicairos, E. H. R. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543, 402–406 (2017).
[Crossref]

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 16 nm 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]

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]

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

Cabana, J.

Y.-S. Yu, M. Farmand, C. Kim, Y. Liu, C. P. Grey, F. C. Strobridge, T. Tyliszczak, R. Celestre, P. Denes, J. Joseph, H. Krishnan, F. R. N. C. Maia, A. L. D. Kilcoyne, S. Marchesini, T. P. C. Leite, T. Warwick, H. Padmore, J. Cabana, and D. A. Shapiro, “Three-dimensional localization of nanoscale battery reactions using soft x-ray tomography,” Nat. Commun. 9, 921 (2018).
[Crossref]

Carlé, J. E.

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

Casci, J.

T. Weissenberger, R. Leonhardt, B. Apeleo Zubiri, M. Pitínová-Štekrová, T. L. Sheppard, B. Reiprich, J. Bauer, R. Dotzel, M. Kahnt, A. Schropp, C. G. Schroer, J.-D. Grunwaldt, J. Casci, J. Čejka, E. Spiecker, and W. Schwieger, “Synthesis and characterisation of hierarchically structured titanium silicalite‐1 zeolites with large intracrystalline macropores,” Chemistry 25, 03287 (2019).
[Crossref]

Cejka, J.

T. Weissenberger, R. Leonhardt, B. Apeleo Zubiri, M. Pitínová-Štekrová, T. L. Sheppard, B. Reiprich, J. Bauer, R. Dotzel, M. Kahnt, A. Schropp, C. G. Schroer, J.-D. Grunwaldt, J. Casci, J. Čejka, E. Spiecker, and W. Schwieger, “Synthesis and characterisation of hierarchically structured titanium silicalite‐1 zeolites with large intracrystalline macropores,” Chemistry 25, 03287 (2019).
[Crossref]

Celestre, R.

Y.-S. Yu, M. Farmand, C. Kim, Y. Liu, C. P. Grey, F. C. Strobridge, T. Tyliszczak, R. Celestre, P. Denes, J. Joseph, H. Krishnan, F. R. N. C. Maia, A. L. D. Kilcoyne, S. Marchesini, T. P. C. Leite, T. Warwick, H. Padmore, J. Cabana, and D. A. Shapiro, “Three-dimensional localization of nanoscale battery reactions using soft x-ray tomography,” Nat. Commun. 9, 921 (2018).
[Crossref]

Chae, Y.-C.

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vis. 20, 73–97 (2004).
[Crossref]

Chao, H.-C.

C. G. Schroer, I. Agapov, W. Brefeld, R. Brinkmann, Y.-C. Chae, H.-C. Chao, M. Eriksson, J. Keil, X. N. Gavaldà, R. Röhlsberger, O. H. Seeck, M. Sprung, M. Tischer, R. Wanzenberg, and E. Weckert, “PETRA IV: the ultra-low emittance source project at DESY,” J. Synchrotran Rad. 25, 1277–1290 (2018).
[Crossref]

Chen, B.

Chen, S.

Ching, D. J.

Chu, Y. S.

X. Huang, H. Yan, Y. He, M. Ge, H. Öztürk, Y.-L. L. Fang, S. Ha, M. Lin, M. Lu, E. Nazaretski, I. K. Robinson, and Y. S. Chu, “Resolving 500 nm axial separation by multi-slice X-ray ptychography,” Acta Crystallogr. A 75, 336–341 (2019).
[Crossref]

H. Öztürk, H. Yan, Y. He, M. Ge, Z. Dong, M. Lin, E. Nazaretski, I. K. Robinson, Y. S. Chu, and X. Huang, “Multi-slice ptychography with large numerical aperture multilayer Laue lenses,” Optica 5, 601–607 (2018).
[Crossref]

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

Cimavilla, P.

D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Ródriguez-Pérez, and C. Rau, “Coherence branch at I13, DLS: the multiscale, multimodal, ptycho-tomographic end station,” Microsc. Microanal. 24, 40–41 (2018).
[Crossref]

Cipiccia, S.

D. Batey, S. Cipiccia, X. Shi, S. Williams, K. Wanelik, A. Wilson, S. Pérez-Tamarit, P. Cimavilla, M. A. Ródriguez-Pérez, and C. Rau, “Coherence branch at I13, DLS: the multiscale, multimodal, ptycho-tomographic end station,” Microsc. Microanal. 24, 40–41 (2018).
[Crossref]

Clare, R.

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. Rep. 5, 9074 (2015).
[Crossref]

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref]

Cloetens, P.

J. C. da Silva, J. Haubrich, G. Requena, M. Hubert, A. Pacureanu, L. Bloch, Y. Yang, and P. Cloetens, “High energy near- and far-field ptychographic tomography at the ESRF,” Proc. SPIE 10391, 1039106 (2017).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref]

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104, 171104 (2014).
[Crossref]

Cullinan, F.

P. F. Tavares, E. Al-Dmour, Å. Andersson, F. Cullinan, B. N. Jensen, D. Olsson, D. K. Olsson, M. Sjöström, H. Tarawneh, S. Thorin, and A. Vorozhtsov, “Commissioning and first-year operational results of the MAX IV 3 GeV ring,” J. Synchrotron Rad. 25, 1291–1316 (2018).
[Crossref]

da Silva, J. C.

J. C. da Silva, J. Haubrich, G. Requena, M. Hubert, A. Pacureanu, L. Bloch, Y. Yang, and P. Cloetens, “High energy near- and far-field ptychographic tomography at the ESRF,” Proc. SPIE 10391, 1039106 (2017).
[Crossref]

Dam, H. F.

H. F. Dam, T. R. Andersen, E. B. L. Pedersen, K. T. S. Thydén, M. Helgesen, J. E. Carlé, P. S. Jørgensen, J. Reinhardt, R. R. Søndergaard, M. Jørgensen, E. Bundgaard, F. C. Krebs, and J. W. Andreasen, “Enabling flexible polymer tandem solar cells by 3D ptychographic imaging,” Adv. Energy Mater. 5, 1400736 (2015).
[Crossref]

Damsgaard, C. D.

J. Reinhardt, R. Hoppe, G. Hofmann, C. D. Damsgaard, J. Patommel, C. Baumbach, S. Baier, A. Rochet, J.-D. Grunwaldt, G. Falkenberg, and C. G. Schroer, “Beamstop-based low-background ptychography to image weakly scattering objects,” Ultramicroscopy 173, 52–57 (2017).
[Crossref]

R. Hoppe, J. Reinhardt, G. Hofmann, J. Patommel, J.-D. Grunwaldt, C. D. Damsgaard, G. Wellenreuther, G. Falkenberg, and C. G. Schroer, “High-resolution chemical imaging of gold nanoparticles using hard x-ray ptychography,” Appl. Phys. Lett. 102, 203104 (2013).
[Crossref]

Daurer, B. J.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Crystallogr. 49, 1245–1252 (2016).
[Crossref]

Denes, P.

Y.-S. Yu, M. Farmand, C. Kim, Y. Liu, C. P. Grey, F. C. Strobridge, T. Tyliszczak, R. Celestre, P. Denes, J. Joseph, H. Krishnan, F. R. N. C. Maia, A. L. D. Kilcoyne, S. Marchesini, T. P. C. Leite, T. Warwick, H. Padmore, J. Cabana, and D. A. Shapiro, “Three-dimensional localization of nanoscale battery reactions using soft x-ray tomography,” Nat. Commun. 9, 921 (2018).
[Crossref]

Deng, J.

Diaz, A.

Dierolf, M.

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref]

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104, 171104 (2014).
[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]

Dinapoli, R.

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Supplementary Material (1)

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» Supplement 1       Supplemental Document

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Figures (5)

Fig. 1.
Fig. 1. Geometry for ptychographic tomography. To record a projection, the sample is scanned perpendicularly to the probing beam (red) along ρx and ρy, recording a far-field diffraction pattern at each position of the scan. A tomographic data set is recorded by acquiring a series of projections rotating the sample around the ρy axis to multiple angles Θ. The sample is described in the coordinate system r=(rx,ry,rz) fixed to the frame of the sample. It is rotated by Θ relative to the laboratory coordinate system ρ=(ρx,ρy,ρz).
Fig. 2.
Fig. 2. (a) SEM image of the macroporous zeolite particle, mounted freestanding on top of a platinum pedestal at the tip of an Al pin; (b) phase image of a ptychographically reconstructed projection OΘ(ρx,ρy) with phase wrap at the bottom of the reconstructed field of view and corresponding reconstructed complex probing wave field PΘ(ρx,ρy); (c) 3D isophase surface rendering of the reconstructed volume n(r) with a cutout to reveal the inner pore structure of the sample.
Fig. 3.
Fig. 3. Comparison of the phase reconstructions Φ(r) using (a), (b) the standard PXCT framework; (c), (d) the CPT framework using Algorithm 1 and an individual probe for each projection angle; and (e), (f) the CPT framework with one shared probe for all projection angles. All reconstructions were done on a volume of 6603 voxels, N=50 3D iterations, M=1 ePIE iteration, and the update strengths α=1.0 for the object, β=1.0 for the probing wave fields, and γ=1.0 for the volume.
Fig. 4.
Fig. 4. Resolution estimation for the volumes reconstructed using the PXCT algorithm and the CPT algorithm. (a) Estimation using Fourier shell correlation; (b) estimation using the spatial signal-to-noise ratio.
Fig. 5.
Fig. 5. Reconstructions of the data set when only every nth diffraction pattern in the horizontal direction (n=1,,5) is used, effectively increasing the horizontal step size from 400 to 2000 nm. (a)–(e) show the reconstructed projections using 100 iterations of the ePIE algorithm (left) against the projection of the volume reconstructed using N=100 iterations of Algorithm 1. The color scale is chosen such that the reconstruction artifacts are highlighted. (f)–(j) show a slice through the reconstructed volume using the PXCT algorithm (left) and the CPT algorithm (right). (k)–(o) show the overlap of the probing beam intensities of two neighboring horizontal positions for each case.

Tables (1)

Tables Icon

Algorithm 1. Coupled ptychography and tomography reconstruction of a PXCT data set. This algorithm equals the framework of [9] with M iterations of the ePIE algorithm [15] used as data constraint and the SART algorithm for the object constraint. A detailed description can be found in Supplement 1.

Equations (5)

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n(r)=1δ(r)iβ(r),
r=(rxryrz)=(ρxcosΘρzsinΘρyρxsinΘ+ρzcosΘ)=RΘ·ρ.
ΨΘ,j(ρx,ρy)=P(ρx,ρy)OΘ(ρxϱx,j,ρyϱy,j),
OΘ(ρx,ρy)=exp(ik·[1+n(ρ)dρz])=exp(i·[k·δ(ρ)dρz]=ϕ(ρx,ρy))exp([k·β(ρ)dρz]=a(ρx,ρy))
IΘ,j(qx,qy)=|F[ΨΘ,j(ρx,ρy)]|2.