Abstract

Single distance X-ray propagation-based phase-contrast imaging is considered as a simple method compared to those requiring additional precise instruments and sophisticated algorithms to retrieve phase images. It requires, however, a modicum of conditions within the setup which include partial coherence and small pixel size at the sample position. While these conditions are usually satisfied at synchrotron light sources, they are not always satisfied within laboratory setups. In fact, these setups are limited by the size of the polychromatic source that directly influences the partial coherence of the beam, the propagation distance and the photon flux. A prior knowledge of the sample refractive index, namely the ratio of delta (δ) and beta (β) values, are also essential for the phase retrieval but this method is powerful in the presence of noise compared to absorption-based imaging. An investigation of the feasibility and the efficient applicability of this method in a commercially available X-ray microscope is conducted in this work.

© 2015 Optical Society of America

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Corrections

12 December 2015: A correction was made to the author affiliations.


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References

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  1. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
    [Crossref]
  2. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
    [Crossref]
  3. I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
    [Crossref] [PubMed]
  4. S. C. Mayo, A. W. Stevenson, and S. W. Wilkins, “In-line phase-contrast x-ray imaging and tomography for materials science,” Materials 5, 937–965 (2012).
    [Crossref]
  5. P. Cloetens, “Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation,” Vrije Universiteit Brussels (1999).
  6. S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
    [Crossref] [PubMed]
  7. L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
    [Crossref]
  8. A. Koch, C. Raven, P. Spanne, and A. Snigirev, “X-ray imaging with submicrometer resolution employing transparent luminescent screens,” J. Opt. Soc. Am. A 15(7), 1940–1951 (1998).
    [Crossref]
  9. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
    [Crossref]
  10. 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(11), 10359–10376 (2011).
    [Crossref] [PubMed]
  11. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
    [Crossref] [PubMed]
  12. T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
    [Crossref]
  13. J. P. Guigay, “Analyse spectrale (frequences spatiales) dúne figure de diffraction de Fresnel,” C. R. Acad. Sc. Paris 284, 193–196 (1977).
  14. B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
    [Crossref]
  15. F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
    [Crossref] [PubMed]
  16. M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
    [Crossref]
  17. Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
    [Crossref]
  18. B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
    [Crossref]
  19. P.C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three x-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
    [Crossref] [PubMed]
  20. T. E. Gureyev and S. W. Wilkins, “On x-ray phase contrast imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
    [Crossref]
  21. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
    [Crossref]
  22. T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
    [Crossref]
  23. J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
    [Crossref] [PubMed]

2014 (3)

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

2013 (1)

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

2012 (2)

2011 (2)

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(11), 10359–10376 (2011).
[Crossref] [PubMed]

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

2008 (1)

B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
[Crossref]

2007 (1)

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
[Crossref]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

2005 (1)

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

2003 (1)

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

1998 (3)

A. Koch, C. Raven, P. Spanne, and A. Snigirev, “X-ray imaging with submicrometer resolution employing transparent luminescent screens,” J. Opt. Soc. Am. A 15(7), 1940–1951 (1998).
[Crossref]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase contrast imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
[Crossref]

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

1997 (1)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[Crossref]

1996 (2)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

1993 (1)

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

1977 (1)

J. P. Guigay, “Analyse spectrale (frequences spatiales) dúne figure de diffraction de Fresnel,” C. R. Acad. Sc. Paris 284, 193–196 (1977).

Arfelli, F.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Arhatari, B.D.

B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
[Crossref]

Assante, M.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Baema, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

Balaur, E.

B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
[Crossref]

Bartels, M.

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

Bonvicini, V.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Bravin, A.

P.C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three x-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
[Crossref] [PubMed]

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

Burvall, A.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

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(11), 10359–10376 (2011).
[Crossref] [PubMed]

Cantatore, G.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Castelli, E.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Cloetens, P.

P. Cloetens, “Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation,” Vrije Universiteit Brussels (1999).

Coan, P.

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

Davis, J.C.

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Davis, T. J.

Diemoz, P.C.

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Gelb, J.

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

Guigay, J. P.

J. P. Guigay, “Analyse spectrale (frequences spatiales) dúne figure de diffraction de Fresnel,” C. R. Acad. Sc. Paris 284, 193–196 (1977).

Gullikson, E.M.

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Gureyev, T. E.

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase contrast imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Haas, D.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

Hannah, K.

B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
[Crossref]

Henke, B.L.

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

Hernandez, V. H.

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

Hertz, H. M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

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(11), 10359–10376 (2011).
[Crossref] [PubMed]

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
[Crossref]

Herzen, J.

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

Koch, A.

Krenkel, M.

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

Larsson, D. H.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

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(11), 10359–10376 (2011).
[Crossref] [PubMed]

Lavery, L. L.

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

Longo, R.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Lundström, U.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

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(11), 10359–10376 (2011).
[Crossref] [PubMed]

Mayo, S. C.

S. C. Mayo, A. W. Stevenson, and S. W. Wilkins, “In-line phase-contrast x-ray imaging and tomography for materials science,” Materials 5, 937–965 (2012).
[Crossref]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Merkle, A. P.

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

Michiel, M. D.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Miller, P. R.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Moser, T.

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

Nesterets, Y. I.

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

Nugent, K. A.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

Olivo, A.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Otendal, M.

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
[Crossref]

Paganin, D.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

Palma, L. D.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Pani, S.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Peele, A.G.

B.D. Arhatari, K. Hannah, E. Balaur, and A.G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16(24), 199950 (2008).
[Crossref]

Pfeiffer, F.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

Pogany, A.

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Pontoni, D.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Poropat, P.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Prest, M.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Rack, A.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

Rashevsky, A.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Raven, C.

Rueckel, J.

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

Salditt, T.

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

Snigirev, A.

Spanne, P.

Steinbach, A.

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

Stevenson, A. W.

S. C. Mayo, A. W. Stevenson, and S. W. Wilkins, “In-line phase-contrast x-ray imaging and tomography for materials science,” Materials 5, 937–965 (2012).
[Crossref]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Stockmar, M.

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

Takman, P. A. C.

Thibault, P.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

Tromba, G.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Tuohimaa, T.

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
[Crossref]

Vacchi, A.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Vallazza, E.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Wegrzynek, D.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

Weitkamp, T.

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

Wilkins, S. W.

S. C. Mayo, A. W. Stevenson, and S. W. Wilkins, “In-line phase-contrast x-ray imaging and tomography for materials science,” Materials 5, 937–965 (2012).
[Crossref]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[Crossref] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

T. E. Gureyev and S. W. Wilkins, “On x-ray phase contrast imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
[Crossref]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Zanconati, F.

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Zanette, I.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

Zdora, M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

Zhou, T.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

M. Bartels, V. H. Hernandez, M. Krenkel, T. Moser, and T. Salditt, “Phase contrast tomography of the mouse cochlea at microfocus x-ray sources,” Appl. Phys. Lett. 103(8), 083703 (2013).
[Crossref]

T. Tuohimaa, M. Otendal, and H. M. Hertz, “Phase-contrast x-ray imaging with a liquid-metal-jet-anode microfocus source,” Appl. Phys. Lett. 91(7), 074104 (2007).
[Crossref]

Appl. Radiat. Isot. (1)

J. Rueckel, M. Stockmar, F. Pfeiffer, and J. Herzen, “Spatial resolution characterisation of a x-ray micro CT system,” Appl. Radiat. Isot. 94, 230–234 (2014).
[Crossref] [PubMed]

At. Data Nucl. Data Tables (1)

B.L. Henke, E.M. Gullikson, and J.C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[Crossref]

C. R. Acad. Sc. Paris (1)

J. P. Guigay, “Analyse spectrale (frequences spatiales) dúne figure de diffraction de Fresnel,” C. R. Acad. Sc. Paris 284, 193–196 (1977).

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

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

J. Synch. Rad. (1)

T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline x-ray phase-contrast radiographs,” J. Synch. Rad. 18, 617–629 (2011).
[Crossref]

Materials (1)

S. C. Mayo, A. W. Stevenson, and S. W. Wilkins, “In-line phase-contrast x-ray imaging and tomography for materials science,” Materials 5, 937–965 (2012).
[Crossref]

Micros. Today (1)

L. L. Lavery, J. Gelb, A. P. Merkle, and A. Steinbach, “X-ray microscopy for hierarchical multi-scale materials,” Micros. Today 22(03), 16–21 (2014).
[Crossref]

Nature (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Nature Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nature Phys. 2(4), 258–261 (2006).
[Crossref]

Opt. Express (4)

Phys. Med. Biol. (1)

F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, “Low-dose phase contrast x-ray medical imaging,” Phys. Med. Biol. 43(10), 2845 (1998).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-Field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref] [PubMed]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Baema, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2963–2964 (1996).
[Crossref]

Rev. Sci. Instrum. (2)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[Crossref]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for x-ray in-line phase-contrast imaging,” Rev. Sci. Instrum. 76(9), 093706 (2005).
[Crossref]

Other (1)

P. Cloetens, “Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation,” Vrije Universiteit Brussels (1999).

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Figures (7)

Fig. 1
Fig. 1 Sketch of the procedure adopted to track the variations of the fringes at different defocusing distances, while keeping the effective pixel size constant. The distances corresponding to the positions I, II and III are summarized in Table 1.
Fig. 2
Fig. 2 Spectrum of the beam for the tungsten target measured at 40 kV tube voltage with an energy sensitive X-123SDD AMPTEK spectrometer. The beam was corrected for the 500 μm silicon path to the detector.
Fig. 3
Fig. 3 Panels (a)–(c) are single projections of a 500 μm thick Teflon phantom (C2F4) which were recorded with a exposure time of 5 s. The areas framed in (a) are used for the calculation of the signal-to-noise ratio (SNR) in each image. Panels (d)–(f) are the intensity profiles of the phantom, recorded at the given distances in Table 1, respectively, showing an increase of the edge enhancement. Panels (g)–(i) depict the thicknesses of the phantom calculated for different energies using Eq. (11). The orange broken lines show the correct thickness of the phantom. The edges of the phantom (in the rectangle box in (g)–(i)) are magnified to j, k and l, respectively. These serve for qualitative interpretation of the image.
Fig. 4
Fig. 4 Panels (a)–(c) are projections of a 250 μm thick Teflon phantom, recorded an exposure time of 5 s at a source-to-sample distance R1 = 10 mm and various sample-to-detector distances R2=20, 30 and 60 mm. Panels (d)–(f) are the respective intensity profiles of (a)–(c). A correction for the magnification was applied to make the plots comparable. The calculated thicknesses according to Eq. (11) are plotted for various energies in (g)–(i). The broken orange line correspond to the correct thickness of the phantom. The course of the plots surrounded by the boxes in (g)–(i) is magnified in (j)–(l), respectively.
Fig. 5
Fig. 5 Variation of the effective propagation distance Zeff with the sample-to-detector distance R2, for a constant (blue) and variable (dark) magnification. Solid lines indicated the values resumed in Table 1 and Table 2. Dashed lines show the real course of the functions Z eff experimentI and Z eff experimentII .
Fig. 6
Fig. 6 Images of an ant head projections (a)–(c) were taken with 5 s exposure time at the three variable distances in Fig. 1. Panels (d)– (f) are their respective phases. The selected square regions in each phase image provide a proof that the contrast differs with the effective propagation distance.
Fig. 7
Fig. 7 Panels (a)–(c) Tomograms of the ant recorded with 5 s exposure time at the three variable distances in Fig 1. Panels (d)–(f) are the corresponding slices from the reconstructed phases. Profiles along the green solid lines in (d)–(f) are plotted in (g)–(i), respectively. The contrast is obviously accurate in (d) as shown by the plot, but also the arrows in (d)–(f) indicate some contrast variabilities in these images, along the tape (made of plastic and glue) used to fix the sample.

Tables (2)

Tables Icon

Table 1 Propagation distances and calculated parameters used to evaluate the quality of the images. The magnification is constant and implies a unique ps eff = 0.964 μm

Tables Icon

Table 2 Propagation distances and calculated parameters used to evaluate the quality of the images for variable magnifications.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

f ( x ; Z ) = ( i λ Z ) 1 / 2 exp ( i k Z ) q ( X ) × exp ( k ( x X ) 2 2 Z ) d X .
F ( u ; Z ) = exp ( i k Z ) Q ( u ) exp ( i π λ Z u 2 ) ,
f s ( x ; R 1 , R 2 ) = ( i λ R 2 ) 1 / 2 exp ( i k R 2 ) exp ( i k X 2 2 R 1 ) × q ( X ) exp ( i k ( x X ) 2 2 R 2 ) d X .
f s ( x ; R 1 , R 2 ) f p ( R 1 x / R 2 ; R 1 ) .
n = 1 δ + i β .
β = λ μ 4 π .
Z a 2 λ ,
Z eff = R 1 × R 2 R 1 + R 2 .
M geom = R 1 + R 2 R 1 ,
Z eff = R 2 M geom .
t ( x , y ) = 1 μ log ( F 1 { F [ I ( x , y ) I 0 ( x , y ) ] 1 + Z eff δ μ 1 ( u 2 + v 2 ) } ) ,
φ ( x , y ) = 2 π δ λ t ( x , y ) .
σ sys 2 = ( M geom 1 ) 2 M geom 2 σ src 2 + M geom 2 σ det 2 ,
ps eff = ps M geom × M opt ,
visibility = I max I min I max + I min ,
d = λ R 1 γ = 0.52 μ m ,
E av = E ϕ ( E ) d E ϕ ( E ) d E .
SNR area = A ( I obj I back ) std 2 ( I obj ) + std 2 ( I back ) A ( I obj I back ) ( I obj + I back ) ,
Z eff experimentI = R 2 M geom ,
Z eff experimentII = 1 1 R 1 + 1 R 2 = 1 const + 1 R 2 ,

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