Abstract

Ptychographic X-ray computed tomography (PXCT) is a potential tool for visualizing three-dimensional (3D) structures of large-volume samples at high spatial resolution. Currently, both the requirement of a large number of views and the narrow depth of field limit the range of applications of PXCT. Here, we propose an improved 3D reconstruction algorithm for PXCT that is based on 3D iterative reconstruction and multislice phase retrieval calculation. Computer simulations showed that the proposed algorithm can reduce the number of required views without degrading the spatial resolution. In a synchrotron experiment, ptychographic diffraction data sets of a flat and thick processor specimen were collected under a limited-angle condition, and then high-resolution multislice images of the Cu multilevel interconnects were clearly reconstructed using the proposed algorithm. The proposed algorithm is expected to open up a new frontier of large-volume 3D nanoimaging in various fields.

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

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References

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    [Crossref] [PubMed]
  23. Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
    [Crossref] [PubMed]
  24. M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Jounal Struct. Biol. 151, 250–262 (2005).
    [Crossref]
  25. P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-tilt electron tomography,” Ultramicroscopy 60, 393–410 (1995).
    [Crossref] [PubMed]
  26. M. Randermacher, “Three-Dimensional Reconstruction of Single Particles From Random and Nonrandom Tilt Series,” Jounal Electron Microsc. Tech. 9, 359–394 (1988).
    [Crossref]
  27. I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
    [Crossref]
  28. R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing,” Acta Crystallogr. Sect. A 69, 490–497 (2013).
    [Crossref]

2018 (3)

K. Shimomura, M. Hirose, and Y. Takahashi, “Multislice imaging of integrated circuits by precession X-ray ptychography,” Acta Crystallogr. Sect. A 74, 66–70 (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]

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

2017 (2)

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] [PubMed]

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 (2017).
[Crossref]

2016 (1)

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

2015 (2)

K. Shimomura, A. Suzuki, M. Hirose, and Y. Takahashi, “Precession x-ray ptychography with multislice approach,” Phys. Rev. B 91, 214114 (2015).
[Crossref]

J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
[Crossref] [PubMed]

2014 (6)

E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59, 1–43 (2014).
[Crossref]

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (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]

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] [PubMed]

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] [PubMed]

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

2013 (1)

R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing,” Acta Crystallogr. Sect. A 69, 490–497 (2013).
[Crossref]

2012 (2)

2011 (1)

G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to X-ray microbeam and nanobeam science,” Science 334, 1234–1239 (2011).
[Crossref] [PubMed]

2010 (1)

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]

2009 (1)

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

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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]

2005 (1)

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

1995 (1)

P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-tilt electron tomography,” Ultramicroscopy 60, 393–410 (1995).
[Crossref] [PubMed]

1988 (1)

M. Randermacher, “Three-Dimensional Reconstruction of Single Particles From Random and Nonrandom Tilt Series,” Jounal Electron Microsc. Tech. 9, 359–394 (1988).
[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] [PubMed]

1970 (2)

R. A. Crowther, D. J. DeRosier, and A. Klug, “The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy,” Proc. Royal Soc. A 317, 319–340 (1970).
[Crossref]

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, 471–482 (1970).
[Crossref] [PubMed]

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] [PubMed]

Beister, M.

M. Beister, D. Kolditz, and W. A. Kalender, “Iterative reconstruction methods in X-ray CT,” Phys. Medica 28, 94–108 (2012).
[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, 471–482 (1970).
[Crossref] [PubMed]

Bergamaschi, A.

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

Billich, H.

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

Budai, J. D.

G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to X-ray microbeam and nanobeam science,” Science 334, 1234–1239 (2011).
[Crossref] [PubMed]

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] [PubMed]

J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
[Crossref] [PubMed]

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. 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]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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]

Buttle, K.

P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-tilt electron tomography,” Ultramicroscopy 60, 393–410 (1995).
[Crossref] [PubMed]

Cabana, J.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Cartier, S.

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

Celestre, R.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Chao, W.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Chen, Y.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

Chu, Y. S.

Crowther, R. A.

R. A. Crowther, D. J. DeRosier, and A. Klug, “The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy,” Proc. Royal Soc. A 317, 319–340 (1970).
[Crossref]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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]

da Silva, J. C.

J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
[Crossref] [PubMed]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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]

Deng, Y.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

DeRosier, D. J.

R. A. Crowther, D. J. DeRosier, and A. Klug, “The Reconstruction of a Three-Dimensional Structure from Projections and its Application to Electron Microscopy,” Proc. Royal Soc. A 317, 319–340 (1970).
[Crossref]

Diaz, A.

Dierolf, M.

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]

Dinapoli, R.

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] [PubMed]

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]

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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]

Dong, Z.

Frank, J.

P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-tilt electron tomography,” Ultramicroscopy 60, 393–410 (1995).
[Crossref] [PubMed]

Furutaku, S.

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] [PubMed]

Ge, M.

Gilbert, P.

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

Godden, T. M.

Gordon, 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, 471–482 (1970).
[Crossref] [PubMed]

Greiffenberg, D.

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
[Crossref]

Guizar-Sicairos, M.

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 (2017).
[Crossref]

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] [PubMed]

J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
[Crossref] [PubMed]

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]

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Öztürk, H.

Padmore, H. A.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
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G. E. Ice, J. D. Budai, and J. W. L. Pang, “The race to X-ray microbeam and nanobeam science,” Science 334, 1234–1239 (2011).
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P. Penczek, M. Marko, K. Buttle, and J. Frank, “Double-tilt electron tomography,” Ultramicroscopy 60, 393–410 (1995).
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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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J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. 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).
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Raabe, J.

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).
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J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
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M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” Jounal Struct. Biol. 151, 250–262 (2005).
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I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
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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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D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
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Shi, X.

I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
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K. Shimomura, M. Hirose, and Y. Takahashi, “Multislice imaging of integrated circuits by precession X-ray ptychography,” Acta Crystallogr. Sect. A 74, 66–70 (2018).
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K. Shimomura, A. Suzuki, M. Hirose, and Y. Takahashi, “Precession x-ray ptychography with multislice approach,” Phys. Rev. B 91, 214114 (2015).
[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).
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A. C. Kak and M. Slaney, “Principles of computerized tomographic imaging,” (IEEE Press, 1988).

Stadler, H.-C.

Suman, R.

Sun, F.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
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K. Shimomura, A. Suzuki, M. Hirose, and Y. Takahashi, “Precession x-ray ptychography with multislice approach,” Phys. Rev. B 91, 214114 (2015).
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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).
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Takahashi, Y.

K. Shimomura, M. Hirose, and Y. Takahashi, “Multislice imaging of integrated circuits by precession X-ray ptychography,” Acta Crystallogr. Sect. A 74, 66–70 (2018).
[Crossref]

K. Shimomura, A. Suzuki, M. Hirose, and Y. Takahashi, “Precession x-ray ptychography with multislice approach,” Phys. Rev. B 91, 214114 (2015).
[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).
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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).
[Crossref] [PubMed]

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I. Johnson, A. Bergamaschi, H. Billich, S. Cartier, R. Dinapoli, D. Greiffenberg, M. Guizar-Sicairos, B. Henrich, J. Jungmann, D. Mezza, A. Mozzanica, B. Schmitt, X. Shi, and G. Tinti, “Eiger: a single-photon counting x-ray detector,” J. Instrumentation 9, C05032 (2014).
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J. C. da Silva, P. Trtik, A. Diaz, M. Holler, M. Guizar-Sicairos, J. Raabe, O. Bunk, and A. Menzel, “Mass Density and Water Content of Saturated Never-Dried Calcium Silicate Hydrates,” Langmuir 31, 3779–3783 (2015).
[Crossref] [PubMed]

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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] [PubMed]

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 (2017).
[Crossref]

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D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
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van Heel, M.

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

Vassholz, M.

R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing,” Acta Crystallogr. Sect. A 69, 490–497 (2013).
[Crossref]

Wang, S.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

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D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Wepf, R.

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]

Wilke, R. N.

R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing,” Acta Crystallogr. Sect. A 69, 490–497 (2013).
[Crossref]

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E. Maire and P. J. Withers, “Quantitative X-ray tomography,” Int. Mater. Rev. 59, 1–43 (2014).
[Crossref]

Yamauchi, K.

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).
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Yan, H.

Yang, L. L.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
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Yu, Y.-S.

D. A. Shapiro, Y.-S. Yu, T. Tyliszczak, J. Cabana, R. Celestre, W. Chao, K. Kaznatcheev, A. L. D. Kilcoyne, F. Maia, S. Marchesini, Y. S. Meng, T. Warwick, L. L. Yang, and H. A. Padmore, “Chemical composition mapping with nanometre resolution by soft X-ray microscopy,” Nat. Photonics 8, 765–769 (2014).
[Crossref]

Zhang, F.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

Zhang, K.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

Zhang, Y.

Y. Chen, Y. Zhang, K. Zhang, Y. Deng, S. Wang, F. Zhang, and F. Sun, “FIRT: Filtered iterative reconstruction technique with information restoration,” J. Struct. Biol. 195, 49–61 (2016).
[Crossref] [PubMed]

Acta Crystallogr. Sect. A (2)

K. Shimomura, M. Hirose, and Y. Takahashi, “Multislice imaging of integrated circuits by precession X-ray ptychography,” Acta Crystallogr. Sect. A 74, 66–70 (2018).
[Crossref]

R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing,” Acta Crystallogr. Sect. A 69, 490–497 (2013).
[Crossref]

Int. Mater. Rev. (1)

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Supplementary Material (1)

NameDescription
» Visualization 1       Multislice images of Cu multilevel interconnects reconstructed by PXCT. All slices can be seen in Visualization 1.

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Figures (6)

Fig. 1
Fig. 1 Procedure of the proposed 3D reconstruction algorithm. This algorithm alternately repeats 3D iterative reconstruction and multislice phase retrieval calculation. Multiple complex transmission functions are reconstructed by multislice phase retrieval and then are directly used in the 3D iterative reconstruction.
Fig. 2
Fig. 2 (a) Three-dimensional model used in the computer simulation of PXCT. The ptychographic diffraction patterns were calculated at 150 angles between −90° and 90° with 1.2° spacing. (b–f) xz cross-sectional phase images corresponding to the plane surrounded by the red square in (a). (b) Model. (c–f) Combinations of (c) FBP and 3PIE, (d) ART and 3PIE, (e) IR and ePIE, and (f) IR and 3PIE. (g) Fourier ring correlation (FRC) between the model image and reconstructed images.
Fig. 3
Fig. 3 (a) First and ninth layers of the plate model. (b–e) Reconstructed images at the 1st and 9th layers. (b) Combination of FBP and 3PIE. (c) Combination of ART and 3PIE. (d) Combination of IR and ePIE. (e) Combination of IR and 3PIE. (f) Fourier ring correlation (FRC) between the model image and reconstructed images.
Fig. 4
Fig. 4 Experimental setup of multislice X-ray ptychography under the limited-angle condition. A 6.5 keV X-ray was two-dimensionally focused to a ∼500 nm spot size by K–B mirrors. The sample was an Intel processor whose bottom layer was thinned to ∼30 μm by dry etching. The focused X-ray was illuminated at 11 × 11 raster-grid positions with a step size of 300 nm. The diffraction patterns were collected by an EIGER 1M pixel array detector at two positions on the detector to complement the missing area between the modules. An 800 × 800 μm2 Si attenuator was placed approximately 830 mm upstream from the detector to increase the effective dynamic range of the diffraction patterns. Ptychographic measurements were performed at 21 angles, (φ, ω)=(0°,0°), (1°,0°), (2°,0°), (3°,0°), (4°,0°), (5°,0°), (−1°,0°), (−2°,0°), (−3°,0°), (−4°,0°), (−5°,0°), (0°,1°), (0°,2°), (0°,3°), (0°,4°), (0°,5°), (0°, −1°), (0°, −2°), (0°, −3°), (0°, −4°), and (0°, −5°), by using rotation and swivel stages.
Fig. 5
Fig. 5 (a, b) Projected phase images of Cu multilevel interconnects reconstructed by ePIE and 3PIE from diffraction patterns measured at (φ, ω)=(0°,0°). (a) ePIE. (b) 3PIE. The projection was produced by superimposing four reconstructions. (c) Profiles through the red lines in (a) and (b).
Fig. 6
Fig. 6 Images of the 10th, 16th, 18th, 21st, and 25th layers selected from the 3D reconstruction of Cu multilevel interconnects. The number of layers is 31. Each slice is a projection of 240 nm thickness. All slices can be seen in Visualization 1.

Equations (5)

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O i , Θ ( k ) ( x , y , z ) = Θ ^ O i ( k ) ( x , y , z ) ,
M i , Θ ( k ) ( x , y , z ) = ( S i , l ( x , y ) S i , l ( k ) ( x , y ) ) 1 / N l z l th layer .
M i ( k ) ( x , y , z ) = Θ ^ 1 M i , Θ ( k ) ( x , y , z ) .
O i + 1 ( k ) ( x , y , z ) = O i ( k ) ( x , y , z ) × M i ( k ) ( x , y , z ) .
d z = d x , y α + cos α sin α α cos α sin α ,

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