Abstract

We present an improved, single-distance phase retrieval algorithm applicable for holographic X-ray imaging of biological objects for an in-line germanium Bragg Magnifier Microscope (BMM). The proposed algorithm takes advantage of a modified shrink-wrap algorithm for phase objects, robust unwrapping algorithm as well as other reasonable constraints applied to the wavefield at the object and the detector plane. The performance of the algorithm is analyzed on phantom objects and the results are shown and discussed. We demonstrated the suitability of the algorithm for the phase retrieval on a more complex biological specimen Tardigrade, where we achieved successful phase retrieval from only a single hologram. The spatial resolution obtained by Fourier spectral power method for biological objects is ∼ 300 nm, the same value as obtained from the reconstructed test pattern. Our results achieved using the new algorithm confirmed the potential of BMM for in-vivo, dose-efficient single-shot imaging of biological objects.

© 2016 Optical Society of America

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References

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  1. G. Shinoda, K. Kohra, and T. Ichinokawa, Proceedings of the Sixth International Conference on X-ray Optics and Microanalysis (University of Tokyo Press, 1972).
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    [Crossref] [PubMed]
  3. R. D. Spal, “Submicrometer resolution hard x-ray holography with the asymmetric bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
    [Crossref] [PubMed]
  4. P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
    [Crossref] [PubMed]
  5. K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
    [Crossref]
  6. P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
    [Crossref]
  7. M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
    [Crossref]
  8. D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
    [Crossref]
  9. K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
    [Crossref] [PubMed]
  10. P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
    [Crossref]
  11. P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
    [Crossref]
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  13. P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
    [Crossref]
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  15. X. Huang and M. Dudley, “A universal computation method for two-beam dynamical X-ray diffraction,” Acta Crystallogr. A 59, 163–167 (2003).
    [Crossref] [PubMed]
  16. R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754–764 (2002).
    [Crossref] [PubMed]
  17. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
    [Crossref]
  18. S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” ArXiv:0911.0520 (2009).
  19. M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
    [Crossref]
  20. W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
    [Crossref] [PubMed]
  21. P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
    [Crossref]

2015 (1)

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (1)

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

2011 (1)

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

2008 (1)

2007 (2)

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

2006 (1)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

2003 (4)

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

X. Huang and M. Dudley, “A universal computation method for two-beam dynamical X-ray diffraction,” Acta Crystallogr. A 59, 163–167 (2003).
[Crossref] [PubMed]

2002 (1)

R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754–764 (2002).
[Crossref] [PubMed]

2001 (2)

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

R. D. Spal, “Submicrometer resolution hard x-ray holography with the asymmetric bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

1979 (1)

W.J. Boettinger, H. Burdette, and M. Kuriyama, “X-ray magnifier,” Rev. Sci. Instrum. 50, 26–30 (1979).
[Crossref] [PubMed]

Abela, R.

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

Authier, A.

A. Authier, Dynamical Theory of X-ray Diffraction (Oxford University, 2004).

Baumbach, T.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
[Crossref]

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Bishop, A. I.

S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” ArXiv:0911.0520 (2009).

Boettinger, W.J.

W.J. Boettinger, H. Burdette, and M. Kuriyama, “X-ray magnifier,” Rev. Sci. Instrum. 50, 26–30 (1979).
[Crossref] [PubMed]

Borchert, G.

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

Burdette, H.

W.J. Boettinger, H. Burdette, and M. Kuriyama, “X-ray magnifier,” Rev. Sci. Instrum. 50, 26–30 (1979).
[Crossref] [PubMed]

Cecilia, A.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
[Crossref]

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Chapman, H. N.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Cusack, R.

R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754–764 (2002).
[Crossref] [PubMed]

Dolbnya, I.

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Dudley, M.

X. Huang and M. Dudley, “A universal computation method for two-beam dynamical X-ray diffraction,” Acta Crystallogr. A 59, 163–167 (2003).
[Crossref] [PubMed]

Ferrari, C.

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Fiederle, M.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Fleschig, U.

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Freund, A.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Gabriel, W. N.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Gimenez, E. N.

Goldstein, B.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Gregory, T. R.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Hamann, E.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
[Crossref]

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Hanke, M.

Hänschke, D.

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Härtwig, J.

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Hau-Riege, S. P.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

He, H.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Hirano, K.

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

Howells, M. R.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Hrdý, J.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Huang, X.

X. Huang and M. Dudley, “A universal computation method for two-beam dynamical X-ray diffraction,” Acta Crystallogr. A 59, 163–167 (2003).
[Crossref] [PubMed]

Ibuki, T.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Ichinokawa, T.

G. Shinoda, K. Kohra, and T. Ichinokawa, Proceedings of the Sixth International Conference on X-ray Optics and Microanalysis (University of Tokyo Press, 1972).

Izumi, K.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Jeck, W. R.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Jones, C. D.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Kagoshima, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kimura, H.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kimura, S.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Kobayashi, K.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Koenig, T.

Köhler, R.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

Kohra, K.

G. Shinoda, K. Kohra, and T. Ichinokawa, Proceedings of the Sixth International Conference on X-ray Optics and Microanalysis (University of Tokyo Press, 1972).

Korytár, D.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Kubena, A.

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Kuriyama, M.

W.J. Boettinger, H. Burdette, and M. Kuriyama, “X-ray magnifier,” Rev. Sci. Instrum. 50, 26–30 (1979).
[Crossref] [PubMed]

Lafford, T. A.

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Lübbert, D.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

Marchesini, S.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Matsui, J.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

McNuff, R.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Mikulík, P.

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

Modregger, P.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

Momose, A.

Noy, A.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Oberta, P.

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Olbinado, M.

Paganin, D.

D. Paganin, Coherent X-Ray Optics (Oxford University, 2006).
[Crossref]

Paganin, D. M.

S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” ArXiv:0911.0520 (2009).

Papadakis, N.

R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754–764 (2002).
[Crossref] [PubMed]

Patel, S. K.

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

Pavlov, K. M.

Pelliccia, D.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Podorov, S. G.

S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” ArXiv:0911.0520 (2009).

Ruegsegger, P.

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

Schäfer, P.

P. Modregger, D. Lübbert, P. Schäfer, R. Köhler, T. Weitkamp, M. Hanke, and T. Baumbach, “Fresnel diffraction in the case of an inclined image plane,” Opt. Express 16, 5141–5149 (2008).
[Crossref] [PubMed]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

Shawney, K.

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Shinoda, G.

G. Shinoda, K. Kohra, and T. Ichinokawa, Proceedings of the Sixth International Conference on X-ray Optics and Microanalysis (University of Tokyo Press, 1972).

Spal, R. D.

R. D. Spal, “Submicrometer resolution hard x-ray holography with the asymmetric bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

Spence, J. C. H.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Stampanoni, M.

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

Sugiyama, H.

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

Švéda, L.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Takahashi, Y.

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

Tsusaka, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Vagovic, P.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Weierstall, U.

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Weitkamp, T.

Yamashita, Y.

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

Yang, Y.

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

Yashiro, W.

Yokoyama, Y.

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

Zápražný, Z.

P. Vagovič, L. Švéda, A. Cecilia, E. Hamann, D. Pelliccia, E. N. Gimenez, D. Korytár, K. M. Pavlov, Z. Zápražný, M. Zuber, T. Koenig, M. Olbinado, W. Yashiro, A. Momose, M. Fiederle, and T. Baumbach, “X-ray bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval,” Opt. Express 22, 21508–21520 (2014).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

Zuber, M.

Acta Crystallogr. A (1)

X. Huang and M. Dudley, “A universal computation method for two-beam dynamical X-ray diffraction,” Acta Crystallogr. A 59, 163–167 (2003).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

K. Kobayashi, K. Izumi, H. Kimura, S. Kimura, T. Ibuki, Y. Yokoyama, Y. Tsusaka, Y. Kagoshima, and J. Matsui, “X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric bragg diffractions,” Appl. Phys. Lett. 78, 132–134 (2001).
[Crossref]

M. Stampanoni, G. Borchert, R. Abela, and P. Ruegsegger, “Nanotomography based on double asymmetrical bragg diffraction,” Appl. Phys. Lett. 82, 2922–2924 (2003).
[Crossref]

Dev. Biol. (1)

W. N. Gabriel, R. McNuff, S. K. Patel, T. R. Gregory, W. R. Jeck, C. D. Jones, and B. Goldstein, “The tardigrade hypsibius dujardini, a new model for studying the evolution of development,” Dev. Biol. 312, 545–559 (2007).
[Crossref] [PubMed]

J. Instrum. (1)

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of a 2×3 timepix assembly with a 500μm thick silicon sensor,” J. Instrum. 9, C05037 (2014).
[Crossref]

J. Phys. D Appl. Phys. (1)

D. Korytár, P. Mikulík, C. Ferrari, J. Hrdý, T. Baumbach, A. Freund, and A. Kubena, “Two-dimensional x-ray magnification based on a monolithic beam conditioner,” J. Phys. D Appl. Phys. 36, A65 (2003).
[Crossref]

J. Synchrotron Radiat. (3)

K. Hirano, Y. Yamashita, Y. Takahashi, and H. Sugiyama, “Development of variable-magnification X-ray Bragg optics,” J. Synchrotron Radiat. 22, 956–960 (2015).
[Crossref] [PubMed]

P. Vagovič, D. Korytár, P. Mikulík, A. Cecilia, C. Ferrari, Y. Yang, D. Hänschke, E. Hamann, D. Pelliccia, T. A. Lafford, M. Fiederle, and T. Baumbach, “In-line Bragg magnifier based on V-shaped germanium crystals,” J. Synchrotron Radiat. 18, 753–760 (2011).
[Crossref]

P. Vagovič, D. Korytár, A. Cecilia, E. Hamann, L. Švéda, D. Pelliccia, J. Härtwig, Z. Zápražný, P. Oberta, I. Dolbnya, K. Shawney, U. Fleschig, M. Fiederle, and T. Baumbach, “High-resolution high-efficiency X-ray imaging system based on the in-line Bragg magnifier and the Medipix detector,” J. Synchrotron Radiat. 20, 153–159 (2013).
[Crossref]

NeuroImage (1)

R. Cusack and N. Papadakis, “New robust 3-d phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” NeuroImage 16, 754–764 (2002).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Rev. B (2)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Magnified x-ray phase imaging using asymmetric bragg reflection: Experiment and theory,” Phys. Rev. B 74, 054107 (2006).
[Crossref]

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

Phys. Rev. Lett. (1)

R. D. Spal, “Submicrometer resolution hard x-ray holography with the asymmetric bragg diffraction microscope,” Phys. Rev. Lett. 86, 3044–3047 (2001).
[Crossref] [PubMed]

Phys. Status Solidi A (1)

P. Modregger, D. Lübbert, P. Schäfer, and R. Köhler, “Spatial resolution in bragg-magnified x-ray images as determined by fourier analysis,” Phys. Status Solidi A 204, 2746–2752 (2007).
[Crossref]

Rev. Sci. Instrum. (1)

W.J. Boettinger, H. Burdette, and M. Kuriyama, “X-ray magnifier,” Rev. Sci. Instrum. 50, 26–30 (1979).
[Crossref] [PubMed]

Other (4)

G. Shinoda, K. Kohra, and T. Ichinokawa, Proceedings of the Sixth International Conference on X-ray Optics and Microanalysis (University of Tokyo Press, 1972).

D. Paganin, Coherent X-Ray Optics (Oxford University, 2006).
[Crossref]

S. G. Podorov, A. I. Bishop, D. M. Paganin, and K. M. Pavlov, “Re-sampling of inline holographic images for improved reconstruction resolution,” ArXiv:0911.0520 (2009).

A. Authier, Dynamical Theory of X-ray Diffraction (Oxford University, 2004).

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Figures (4)

Fig. 1
Fig. 1

X-ray imaging using Bragg Magnifier Microscope. The source of the radiation is producing X-rays (their direction is marked by red arrows), which hit the sample and further propagate through the set of four crystals increasing the width of the beam. Finally, the hologram is formed at the detector plane.

Fig. 2
Fig. 2

Recorded hologram of the PS spheres (upper left), the reconstructed phase map using the described new algorithm (upper right), the reconstructed phase map using the old algorithm [13] (lower left) and the phase profile (for both, old and new algorithm) along the horizontal axis compared with the theoretical phase profile (lower right), where we have also plotted an errorbar of the theoretical curve at the middle point based on the manufactoring errors of the sphere.

Fig. 3
Fig. 3

Recorded hologram of the X-radia 50-30-2 (upper left), the reconstructed phase map using the described algorithm (upper right) and the zoom of the blue rectangular area using no up-sampling (lower left) and up-sampling of order 2 (lower right). Three arrows show the positions (same color - same position), where the improvement of the reconstruction is clearly visible.

Fig. 4
Fig. 4

Recorded hologram of the Tardigrade (upper left) with the reconstructed phase map using the described algorithm (upper right). The lower left image presents an alternative visualization of the phase map by showing the phase gradients in horizontal direction. Finally, the lower right plot shows the spectral power along the blue line marked in phase map. Black and red horizontal lines represent the noise level and the resolution threshold, respectively. Dashed vertical lines indicate the position of the smallest and the highest frequencies fulfilling the resolution criterion. Solid vertical line marks their average, giving the resolution in Fourier space (3.1 ± 1.0)μm−1 and making the resolution in real space (0.3 ± 0.1)μm.

Equations (10)

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Ψ D ( x , y ) = 1 [ [ Ψ O ( x , y ) ] P BMM ( k x , k y ) ] ,
Ψ O ( x , y ) = 1 [ [ Ψ D ( x , y ) ] P BMM ( k x , k y ) ] ,
P BMM = P S 1 E 1 P 12 E 2 P 23 E 3 P 34 E 4 P 4 D ,
Ψ O ( x , y ) = Ψ S ( x , y ) T ( x , y ) ,
φ 0 ( i = 1 ) : = { 0 ( x , y ) S , min { φ 0 ( i 1 ) ; 0 } ( x , y ) S .
| Ψ O ( i 1 ) | : = { 1 ( x , y ) S , min { | Ψ O ( i 1 ) | ; 1 } ( x , y ) S .
Ψ D ( i ) : = I D Ψ D ( i ) | Ψ D ( i ) . |
S = { 1 ( x , y ) : φ s ( i 1 ) < t φ min ( i 1 ) , 0 otherwise ,
I m M ( p , q ) = I M ( ( p 1 ) \ m + 1 , ( q 1 ) \ m + 1 ) ,
e i = 1 M [ m , n = 1 M ( Ψ O ( i ) ( x m , y n ) Ψ O ( i 1 ) ( x m , y n ) ) 2 ] 1 / 2 .

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