Abstract

We present the theoretical description of the image formation with the in-line germanium Bragg Magnifier Microscope (BMM) and the first successful phase retrieval of X-ray holograms recorded with this imaging system. The conditions under which the BMM acts as a linear shift invariant system are theoretically explained and supported by the experiment. Such an approach simplifies the mathematical treatment of the image formation and reconstruction as complicated propagation of the wavefront onto inclined planes can be avoided. Quantitative phase retrieval is demonstrated using a test sample and a proof of concept phase imaging of a spider leg is also presented.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref]
  4. G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
    [Crossref]
  5. P. Schäfer and R. Köhler, “Asymmetric Bragg reflection as X-ray magnifier,” J. Phys. D: Appl. Phys. 36, A113–A117 (2003).
    [Crossref]
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    [Crossref]
  7. R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).
  8. K. Hirano, Y. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
    [Crossref]
  9. 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).
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    [Crossref]
  16. A. Burvall, U. Lundström, P. A. C. Takman, D. H. Larsson, and H. M. Hertz, “Phase retrieval in X-ray phase-contrast imaging suitable for tomography,” Opt. Express 19, 10359 (2011).
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  17. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
    [Crossref]
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    [Crossref] [PubMed]
  19. D. Paganin, Coherent X-Ray Optics (Oxford University, 2006).
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    [Crossref]
  22. K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
    [Crossref]
  23. P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
    [Crossref] [PubMed]
  24. D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
    [Crossref]
  25. T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
    [Crossref] [PubMed]
  26. M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of 2×3 timepix assembly with a 500 um thick silicon sensor,” J. Instrum. 9, C05037 (2014).
    [Crossref]
  27. J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis, The Multiscale Approach (Cambridge University, 1998).
    [Crossref]

2014 (2)

K. Hirano, Y. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
[Crossref]

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

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 (2)

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]

A. Burvall, U. Lundström, P. A. C. Takman, D. H. Larsson, and H. M. Hertz, “Phase retrieval in X-ray phase-contrast imaging suitable for tomography,” Opt. Express 19, 10359 (2011).
[Crossref] [PubMed]

2008 (1)

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref] [PubMed]

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]

2005 (2)

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

2004 (1)

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

2003 (2)

P. Schäfer and R. Köhler, “Asymmetric Bragg reflection as X-ray magnifier,” J. Phys. D: Appl. Phys. 36, A113–A117 (2003).
[Crossref]

G. Taylor, “The phase problem,” Acta Crystallogr. Sect. D 59, 1881–1890 (2003).
[Crossref]

2002 (1)

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

1996 (1)

1990 (1)

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

1987 (1)

1982 (1)

1979 (1)

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

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Abela, R.

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

Asadchikov, V. E.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

Authier, A.

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

Baruchel, J.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Baumbach, T.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of 2×3 timepix assembly with a 500 um 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]

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]

Bijaoui, A.

J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis, The Multiscale Approach (Cambridge University, 1998).
[Crossref]

Black, D.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

Boetinger, W. J.

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

Borchert, R.

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

Bravin, A.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

Burdette, H. E.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

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

Burvall, A.

Buzmakov, A. V.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

Cecilia, A.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of 2×3 timepix assembly with a 500 um 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]

Cloetens, P.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Coan, P.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

Dobbyn, R. C.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

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]

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]

Fiederle, M.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of 2×3 timepix assembly with a 500 um 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]

Fiedler, S.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

Fienup, J. R.

Fink, H.-W.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref] [PubMed]

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]

Geranin, A. S.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Gillam, J.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Gureyev, T.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Gureyev, T. E.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13, 1670–1682 (1996).
[Crossref]

Hamann, E.

M. Zuber, T. Koenig, E. Hamann, A. Cecilia, M. Fiederle, and T. Baumbach, “Characterization of 2×3 timepix assembly with a 500 um 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]

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]

Hertz, H. M.

Hirano, K.

K. Hirano, Y. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
[Crossref]

Kitchen, M.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Koenig, T.

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

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, “Magnified X-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B. 74, 054107 (2006).
[Crossref]

P. Schäfer and R. Köhler, “Asymmetric Bragg reflection as X-ray magnifier,” J. Phys. D: Appl. Phys. 36, A113–A117 (2003).
[Crossref]

Konovko, A. V.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

Korytár, D.

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]

Kuriyama, M.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

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

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]

Larsson, D. H.

Latychevskaia, T.

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref] [PubMed]

Lewis, R.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Lewis, R. A.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[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, “Magnified X-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B. 74, 054107 (2006).
[Crossref]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Lundström, U.

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]

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, “Magnified X-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B. 74, 054107 (2006).
[Crossref]

Morgan, M.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Morgan, M. J.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

Murtagh, F.

J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis, The Multiscale Approach (Cambridge University, 1998).
[Crossref]

Nesterets, Y.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Nesterets, Y. I.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

Nugent, K. A.

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]

Paganin, D.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

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

Pagot, E.

P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

Pauli, W.

W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik (Handb. Phys., 1933).

Pavlov, K.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Pavlov, K. M.

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

Pelliccia, D.

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]

Rüegsegger, P.

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

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, “Magnified X-ray phase imaging using asymmetric Bragg reflection: Experiment and theory,” Phys. Rev. B. 74, 054107 (2006).
[Crossref]

P. Schäfer and R. Köhler, “Asymmetric Bragg reflection as X-ray magnifier,” J. Phys. D: Appl. Phys. 36, A113–A117 (2003).
[Crossref]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Senin, R. A.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

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]

Siu, K.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Smirnov, I. S.

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

Spal, R. D.

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

Stampanoni, G.

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

Starck, J. L.

J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis, The Multiscale Approach (Cambridge University, 1998).
[Crossref]

Sugiyama, H.

K. Hirano, Y. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
[Crossref]

Švéda, L.

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. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
[Crossref]

Takman, P. A. C.

Taylor, G.

G. Taylor, “The phase problem,” Acta Crystallogr. Sect. D 59, 1881–1890 (2003).
[Crossref]

Uesugi, K.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

Vagovic, 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]

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]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Weitkamp, T.

Yagi, N.

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

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]

Zápražný, Z.

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.

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

Acta Crystallogr. Sect. D (1)

G. Taylor, “The phase problem,” Acta Crystallogr. Sect. D 59, 1881–1890 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

J. Appl. Phys. (1)

G. Stampanoni, R. Borchert, R. Abela, and P. Rüegsegger, “Bragg magnifier: A detector for submicrometer X-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[Crossref]

J. Instrum. (1)

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

J. Opt. Soc. Am. A (2)

J. Phys. D: Appl. Phys. (2)

P. Schäfer and R. Köhler, “Asymmetric Bragg reflection as X-ray magnifier,” J. Phys. D: Appl. Phys. 36, A113–A117 (2003).
[Crossref]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37, 2746 (2004).
[Crossref]

J. Res. Natl. Inst. Stand. Technol. (1)

M. Kuriyama, R. C. Dobbyn, R. D. Spal, H. E. Burdette, and D. Black, “Hard x-ray microscope with submicrometer spatial resolution,” J. Res. Natl. Inst. Stand. Technol. 95, 559 (1990).
[Crossref]

J. Synchrotron Radiat. (3)

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. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat. 12, 241–245 (2005).
[Crossref] [PubMed]

Nucl. Instr. Meth. Phys. Res. A (2)

K. Pavlov, T. Gureyev, D. Paganin, Y. Nesterets, M. Kitchen, K. Siu, J. Gillam, K. Uesugi, N. Yagi, M. Morgan, and R. Lewis, “Unification of analyser-based and propagation-based X-ray phase-contrast imaging,” Nucl. Instr. Meth. Phys. Res. A 548, 163–168 (2005).
[Crossref]

K. Hirano, Y. Takahashi, and H. Sugiyama, “Development and application of variable-magnification X-ray Bragg magnifiers,” Nucl. Instr. Meth. Phys. Res. A 741, 78– 83 (2014).
[Crossref]

Opt. Express (2)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Phys. Rev. B. (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]

Phys. Rev. Lett. (2)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901 (2007).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

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

Other (5)

R. A. Senin, A. V. Buzmakov, A. V. Konovko, I. S. Smirnov, A. S. Geranin, and V. E. Asadchikov, “Gain in spatial resolution of X-ray laboratory microtomographs with enlarging X-ray optical elements,” JPCS186(2009).

W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik (Handb. Phys., 1933).

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

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

J. L. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis, The Multiscale Approach (Cambridge University, 1998).
[Crossref]

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Figures (7)

Figure 1
Figure 1

Schematic drawing of the variation of the propagation distance for the points at the sample plane along the x-direction in the case of asymmetric diffraction.

Figure 2
Figure 2

The images of the Kapton edge at the opposite sides of the field of view at propagation distance 131 mm (a)–(b) and at the propagation distance 668 mm (c)–(d). The corresponding 1D profiles (e)–(f).

Figure 3
Figure 3

The measured hologram of PMMA spheres at B16 of Diamond light source (a) and the forward image simulation of the single PMMA sphere (b).

Figure 4
Figure 4

The illustration of spatial frequency transformation by the asymmetric crystal by the transforming the angular input/output widths (left) and the resulting scaling of the propagation distance behind the asymmetric diffraction (right).

Figure 5
Figure 5

An example of the numerical simulation and its reconstruction by iterative method described in the text. Images represent the phase of the synthetic object (a), detected propagated intensity image after BMM at the detector plane (b), phase map reconstructed without wavelet filtering (c), and the phase map reconstructed with the wavelet filtering (d). Used photon energy was 10.65 keV, propagation distance to the first magnifying crystal was 200 mm, the phase of the squares was set to 0.2 rad., 0.3 rad. and 0.4 rad. Objects were slightly absorbing.

Figure 6
Figure 6

The measured in-line hologram at Diamond Light Source I13 beamline of 10 μm diameter PS spheres (a), retrieved phase map (b), line profiles through the spheres where t,b means top,bottom sphere, h,v means horizontal,vertical profile and PS is the theoretical phase profile through the PS 10 μm diameter sphere. In Fig. (c) for the phase retrieval we used crystal functions (CF) and in Fig. (d) they have not been used. The used photon energy was 10.7 keV and the magnification achieved at this energy was ∼170-fold.

Figure 7
Figure 7

Measured hologram of a spider leg as a result of stitching the number of detected images during a synchrotron experiment (a), retrieved phase map (b) and zoomed areas of the hologram (c) and phase map (d).

Equations (15)

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U ( x , y ) = U 0 ( x , y ) T ( x , y ) ,
U ˜ 1 ( f x , f y ) = U ˜ ( f x , f y ) H 1 ( f x , f y ) z 1 ,
H 1 ( f x , f y ) z 1 = exp [ 2 π i z 1 ( f 2 f x 2 f z 2 ) ]
U ˜ 1 c ( f x , f y ) = U ˜ 1 ( f x , f y ) E H 1 ( f x , f y ) ,
U ˜ 2 ( f x M 1 , f y ) = U ˜ 1 c ( f x M 1 , f y ) H 1 , 2 ( f x M 1 , f y )
U ˜ 2 c ( f x M 1 , f y ) = U ˜ 2 ( f x M 1 , f y ) E H 2 ( f x M 1 , f y ) ,
U ˜ 3 ( f x M 1 M 2 , f y ) = U ˜ 2 c ( f x M 1 , M 2 , f y ) H 2 , 3 ( f x M 1 M 2 , f y ) ,
U ˜ 3 c ( f x M 1 M 2 , f y ) = U ˜ 3 ( f x M 1 M 2 , f y ) E H 3 ( f x M 1 M 2 , f y ) ,
U ˜ 4 ( f x M 1 M 2 , f y M 3 ) = U ˜ 3 c ( f x M 1 M 2 , f y M 3 ) H 3 , 4 ( f x M 1 M 2 , f y M 3 ) .
U ˜ 4 c ( f x M 1 M 2 , f y M 3 ) = U ˜ 4 ( f x M 1 M 2 , f y M 3 ) E H 4 ( f x M 1 M 2 , f y M 3 ) ,
U ˜ D ( f x M 1 M 2 , f y M 3 M 4 ) = U ˜ 4 c ( f x M 1 M 2 , f y M 3 M 4 ) H 4 , D ( f x M 1 M 2 , f y M 3 M 4 ) ,
U ˜ D = U ˜ H 1 E H 1 H 1 , 2 E H 2 H 2 , 3 E H 3 H 3 , 4 E H 4 H 4 , D
I D ( x D , y D ) = | U D ( x D , y D ) | 2 * PSF ,
Δ θ in Δ θ out = M .
z = z tan ( Δ θ in / 2 ) tan ( Δ θ in / ( 2 M ) ) .

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