Abstract

Phase retrieval is a technique for extracting quantitative phase information from X-ray propagation-based phase-contrast tomography (PPCT). In this paper, the performance of different single distance phase retrieval algorithms will be investigated. The algorithms are herein called phase-attenuation duality Born Algorithm (PAD-BA), phase-attenuation duality Rytov Algorithm (PAD-RA), phase-attenuation duality Modified Bronnikov Algorithm (PAD-MBA), phase-attenuation duality Paganin algorithm (PAD-PA) and phase-attenuation duality Wu Algorithm (PAD-WA), respectively. They are all based on phase-attenuation duality property and on weak absorption of the sample and they employ only a single distance PPCT data. In this paper, they are investigated via simulated noise-free PPCT data considering the fulfillment of PAD property and weakly absorbing conditions, and with experimental PPCT data of a mixture sample containing absorbing and weakly absorbing materials, and of a polymer sample considering different degrees of statistical and structural noise. The simulation shows all algorithms can quantitatively reconstruct the 3D refractive index of a quasi-homogeneous weakly absorbing object from noise-free PPCT data. When the weakly absorbing condition is violated, the PAD-RA and PAD-PA/WA obtain better result than PAD-BA and PAD-MBA that are shown in both simulation and mixture sample results. When considering the statistical noise, the contrast-to-noise ratio values decreases as the photon number is reduced. The structural noise study shows that the result is progressively corrupted by ring-like artifacts with the increase of structural noise (i.e. phantom thickness). The PAD-RA and PAD-PA/WA gain better density resolution than the PAD-BA and PAD-MBA in both statistical and structural noise study.

© 2013 OSA

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  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).
  2. R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
    [CrossRef] [PubMed]
  3. J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
    [CrossRef]
  4. A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys.44(9A), 6355–6367 (2005).
    [CrossRef]
  5. P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
    [CrossRef]
  6. K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
    [CrossRef] [PubMed]
  7. X. Z. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol.11(1), 33–42 (2003).
    [PubMed]
  8. T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt.43(12), 2418–2430 (2004).
    [CrossRef] [PubMed]
  9. 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(19), 2912–2914 (1999).
    [CrossRef]
  10. J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32(12), 1617–1619 (2007).
    [CrossRef] [PubMed]
  11. A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A19(3), 472–480 (2002).
    [CrossRef] [PubMed]
  12. 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(1), 33–40 (2002).
    [CrossRef] [PubMed]
  13. A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express14(18), 8103–8110 (2006).
    [CrossRef] [PubMed]
  14. X. Z. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express13(16), 6000–6014 (2005).
    [CrossRef] [PubMed]
  15. 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. Express19(11), 10359–10376 (2011).
    [CrossRef] [PubMed]
  16. L. D. Turner, B. B. Dhal, J. P. Hayes, A. P. Mancuso, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express12(13), 2960–2965 (2004).
    [CrossRef] [PubMed]
  17. M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express18(7), 6423–6436 (2010).
    [CrossRef] [PubMed]
  18. J. Moosmann, R. Hofmann, A. V. Bronnikov, and T. Baumbach, “Nonlinear phase retrieval from single-distance radiograph,” Opt. Express18(25), 25771–25785 (2010).
    [CrossRef] [PubMed]
  19. A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
    [CrossRef] [PubMed]
  20. M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
    [CrossRef] [PubMed]
  21. M. N. Boone, W. Devulder, M. Dierick, L. Brabant, E. Pauwels, and L. Van Hoorebeke, “Comparison of two single-image phase-retrieval algorithms for in-line x-ray phase-contrast imaging,” J. Opt. Soc. Am. A29(12), 2667–2672 (2012).
    [CrossRef]
  22. R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
    [CrossRef]
  23. R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
    [CrossRef] [PubMed]
  24. X. Z. Wu, H. Liu, and A. M. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett.30(4), 379–381 (2005).
    [CrossRef] [PubMed]
  25. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999).
  26. T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
    [CrossRef]
  27. B. D. Arhatari, F. De Carlo, and A. G. Peele, “Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects,” Rev. Sci. Instrum.78(5), 053701 (2007).
    [CrossRef] [PubMed]
  28. A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
    [CrossRef]
  29. R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
    [CrossRef] [PubMed]
  30. P. Thurner, F. Beckmann, and B. Muller, “An optimization procedure for spatial and density resolution in hard X-ray micro-computed tomography,” Nucl Instrum Meth B225(4), 599–603 (2004).
    [CrossRef]
  31. E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

2012 (2)

M. N. Boone, W. Devulder, M. Dierick, L. Brabant, E. Pauwels, and L. Van Hoorebeke, “Comparison of two single-image phase-retrieval algorithms for in-line x-ray phase-contrast imaging,” J. Opt. Soc. Am. A29(12), 2667–2672 (2012).
[CrossRef]

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

2011 (4)

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
[CrossRef]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[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. Express19(11), 10359–10376 (2011).
[CrossRef] [PubMed]

A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
[CrossRef] [PubMed]

2010 (3)

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express18(7), 6423–6436 (2010).
[CrossRef] [PubMed]

J. Moosmann, R. Hofmann, A. V. Bronnikov, and T. Baumbach, “Nonlinear phase retrieval from single-distance radiograph,” Opt. Express18(25), 25771–25785 (2010).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

2008 (1)

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

2007 (2)

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

B. D. Arhatari, F. De Carlo, and A. G. Peele, “Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects,” Rev. Sci. Instrum.78(5), 053701 (2007).
[CrossRef] [PubMed]

2006 (3)

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express14(18), 8103–8110 (2006).
[CrossRef] [PubMed]

2005 (4)

X. Z. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express13(16), 6000–6014 (2005).
[CrossRef] [PubMed]

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys.44(9A), 6355–6367 (2005).
[CrossRef]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

X. Z. Wu, H. Liu, and A. M. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett.30(4), 379–381 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

X. Z. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol.11(1), 33–42 (2003).
[PubMed]

2002 (3)

E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A19(3), 472–480 (2002).
[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(1), 33–40 (2002).
[CrossRef] [PubMed]

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(19), 2912–2914 (1999).
[CrossRef]

1997 (1)

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

1996 (1)

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Abela, R.

Abrami, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Arfelli, F.

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Arhatari, B. D.

B. D. Arhatari, F. De Carlo, and A. G. Peele, “Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects,” Rev. Sci. Instrum.78(5), 053701 (2007).
[CrossRef] [PubMed]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Barroso, R. C.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Baruchel, J.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

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(19), 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Baumbach, T.

Beckmann, F.

P. Thurner, F. Beckmann, and B. Muller, “An optimization procedure for spatial and density resolution in hard X-ray micro-computed tomography,” Nucl Instrum Meth B225(4), 599–603 (2004).
[CrossRef]

Beltran, M. A.

Bergamaschi, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Bille, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Boistel, R.

Boone, M. N.

Brabant, L.

Bregant, P.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Brizzi, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Bronnikov, A. V.

Buffiere, J. Y.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

Buffière, J. Y.

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Burvall, A.

Casarin, K.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Castelli, E.

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Chen, R. C.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
[CrossRef]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

Chenda, V.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Cloetens, P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

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(19), 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Cookson, D. J.

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Davis, T. J.

De Carlo, F.

B. D. Arhatari, F. De Carlo, and A. G. Peele, “Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects,” Rev. Sci. Instrum.78(5), 053701 (2007).
[CrossRef] [PubMed]

De Pellegrin, A.

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

Devulder, W.

Dhal, B. B.

Di Michiel, M.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

Dierick, M.

Dreossi, D.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Fava, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Ferrie, E.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

Groso, A.

Grossberg, M. D.

E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

Guigay, J. P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32(12), 1617–1619 (2007).
[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(19), 2912–2914 (1999).
[CrossRef]

Gureyev, T. E.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt.43(12), 2418–2430 (2004).
[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(1), 33–40 (2002).
[CrossRef] [PubMed]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Hadjidemetriou, E.

E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

Hayes, J. P.

Hertz, H. M.

Hofmann, R.

Kaiser, S. R.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Kitchen, M. J.

Langer, M.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

Larsson, D. H.

Liu, H.

A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
[CrossRef] [PubMed]

X. Z. Wu, H. Liu, and A. M. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett.30(4), 379–381 (2005).
[CrossRef] [PubMed]

X. Z. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express13(16), 6000–6014 (2005).
[CrossRef] [PubMed]

X. Z. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol.11(1), 33–42 (2003).
[PubMed]

Longo, R.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[CrossRef] [PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
[CrossRef]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Ludwig, W.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

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(19), 2912–2914 (1999).
[CrossRef]

Lundström, U.

Maire, E.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

Mancini, L.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Mancuso, A. P.

Mayo, S. C.

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt.43(12), 2418–2430 (2004).
[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(1), 33–40 (2002).
[CrossRef] [PubMed]

Menk, R.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

Menk, R. H.

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Miller, P. R.

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(1), 33–40 (2002).
[CrossRef] [PubMed]

Momose, A.

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys.44(9A), 6355–6367 (2005).
[CrossRef]

Montanari, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Moosmann, J.

Muller, B.

P. Thurner, F. Beckmann, and B. Muller, “An optimization procedure for spatial and density resolution in hard X-ray micro-computed tomography,” Nucl Instrum Meth B225(4), 599–603 (2004).
[CrossRef]

Myers, G. R.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

Nayar, S. K.

E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

Nesterets, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

Nugent, K. A.

Olivo, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Paganin, D.

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(1), 33–40 (2002).
[CrossRef] [PubMed]

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Paganin, D. M.

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express18(7), 6423–6436 (2010).
[CrossRef] [PubMed]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

Palma, L. D.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Pani, S.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Paterson, D.

Pateyron-Salomé, M.

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Pauwels, E.

Peele, A. G.

Peix, G.

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Peyrin, F.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Pillon, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Pogany, A.

Quai, E.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Rigon, L.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
[CrossRef]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Rokvic, T.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Salvo, L.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[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(19), 2912–2914 (1999).
[CrossRef]

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

Scholten, R. E.

Stampanoni, M.

Takman, P. A. C.

Thurner, P.

P. Thurner, F. Beckmann, and B. Muller, “An optimization procedure for spatial and density resolution in hard X-ray micro-computed tomography,” Nucl Instrum Meth B225(4), 599–603 (2004).
[CrossRef]

Tonutti, M.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Tran, C. Q.

Tromba, G.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Turner, L. D.

Uesugi, K.

Vallazza, E.

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

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(19), 2912–2914 (1999).
[CrossRef]

Van Hoorebeke, L.

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(19), 2912–2914 (1999).
[CrossRef]

Vaseotto, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Venanzi, C.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt.43(12), 2418–2430 (2004).
[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(1), 33–40 (2002).
[CrossRef] [PubMed]

Wu, X. Z.

A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
[CrossRef] [PubMed]

X. Z. Wu and H. Liu, “X-Ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express13(16), 6000–6014 (2005).
[CrossRef] [PubMed]

X. Z. Wu, H. Liu, and A. M. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett.30(4), 379–381 (2005).
[CrossRef] [PubMed]

X. Z. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol.11(1), 33–42 (2003).
[PubMed]

Xiao, T. Q.

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

R. C. Chen, H. L. Xie, L. Rigon, R. Longo, E. Castelli, and T. Q. Xiao, “Phase retrieval in quantitative x-ray microtomography with a single sample-to-detector distance,” Opt. Lett.36(9), 1719–1721 (2011).
[CrossRef] [PubMed]

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

Xie, H. L.

Yan, A. M.

A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
[CrossRef] [PubMed]

X. Z. Wu, H. Liu, and A. M. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett.30(4), 379–381 (2005).
[CrossRef] [PubMed]

Zanconati, F.

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Zanetti, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Zanini, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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(19), 2912–2914 (1999).
[CrossRef]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett.89(3), 034102 (2006).
[CrossRef]

Computer Vison Eccv (1)

E. Hadjidemetriou, M. D. Grossberg, and S. K. Nayar, “Resolution selection using generalized entropies of multiresolution histograms,” Computer Vison Eccv2350, 220–235 (2002).

J. Appl. Phys. (1)

P. Cloetens, M. Pateyron-Salomé, J. Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys.81(9), 5878–5886 (1997).
[CrossRef]

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(1), 33–40 (2002).
[CrossRef] [PubMed]

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

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

R. C. Chen, L. Rigon, and R. Longo, “Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data,” J. Phys. D Appl. Phys.44(49), 495401 (2011).
[CrossRef]

J. Synchrotron Radiat. (1)

R. C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T. Q. Xiao, and R. Longo, “PITRE: software for phase-sensitive X-ray image processing and tomography reconstruction,” J. Synchrotron Radiat.19(5), 836–845 (2012).
[CrossRef] [PubMed]

J. XRay Sci. Technol. (1)

X. Z. Wu and H. Liu, “A general theoretical formalism for X-ray phase contrast imaging,” J. XRay Sci. Technol.11(1), 33–42 (2003).
[PubMed]

Jpn. J. Appl. Phys. (1)

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys.44(9A), 6355–6367 (2005).
[CrossRef]

Med. Phys. (2)

A. M. Yan, X. Z. Wu, and H. Liu, “Robustness of phase retrieval methods in x-ray phase contrast imaging: A comparison,” Med. Phys.38(9), 5073–5080 (2011).
[CrossRef] [PubMed]

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35(10), 4556–4566 (2008).
[CrossRef] [PubMed]

Nucl Instrum Meth A (1)

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. D. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl Instrum Meth A548(1-2), 221–227 (2005).
[CrossRef]

Nucl Instrum Meth B (1)

P. Thurner, F. Beckmann, and B. Muller, “An optimization procedure for spatial and density resolution in hard X-ray micro-computed tomography,” Nucl Instrum Meth B225(4), 599–603 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Phys. Med. Biol. (1)

R. C. Chen, R. Longo, L. Rigon, F. Zanconati, A. De Pellegrin, F. Arfelli, D. Dreossi, R. H. Menk, E. Vallazza, T. Q. Xiao, and E. Castelli, “Measurement of the linear attenuation coefficients of breast tissues by synchrotron radiation computed tomography,” Phys. Med. Biol.55(17), 4993–5005 (2010).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

K. A. Nugent, T. E. Gureyev, D. J. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett.77(14), 2961–2964 (1996).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

B. D. Arhatari, F. De Carlo, and A. G. Peele, “Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects,” Rev. Sci. Instrum.78(5), 053701 (2007).
[CrossRef] [PubMed]

Scr. Mater. (1)

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, “Advances in synchrotron radiation microtomography,” Scr. Mater.55(1), 41–46 (2006).
[CrossRef]

Other (2)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society of Industrial and Applied Mathematics, 2001).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, New York, 1999).

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Figures (12)

Fig. 1
Fig. 1

Schematic of PPCT scanning geometry.

Fig. 2
Fig. 2

Simulation phantom: (a) 3D phantom, (b)-(d) phantom slices according to the line positions in (a).

Fig. 3
Fig. 3

Photo of structural noise phantom showing five different thicknesses of Polyamide powder.

Fig. 4
Fig. 4

Noise-free weakly absorbing ratio phantom simulation results: (a)-(d) are phase retrieval results, same slice as Fig. 2(c), of PAD-BA, PAD-MBA, PAD-RA and PAD-PA/WA (ε = 1000) respectively, (f) profile of (a)-(d) and of the phantom itself, i.e. Figure 2(c), at line position shown in Fig. 4(a).

Fig. 5
Fig. 5

(a) Profile of weakly absorbing no-ratio phantom simulation results, same slice as Fig. 2(c), after implementing PAD-BA, PAD-MBA, PAD-RA and PAD-PA/WA (with ε = 1000) and phantom itself, i.e. Fig. 2(c), at same line position shown in Fig. 4(a), (b) Profile of absorbing ratio phantom simulation results, same slice as Fig. 2(c), after implementing PAD-BA, PAD-MBA, PAD-RA and PAD-PA/WA (with ε = 100) and phantom itself, i.e. Fig. 2(c), at same line position shown in Fig. 4(a).

Fig. 6
Fig. 6

Profile of absorbing ratio phantom simulation results, same slice as Fig. 2(c), after implementing PAD-MBA and Log-PAD-MBA (with ε = 100) and phantom itself, i.e. Figure 2(c), at same line position shown in Fig. 4(a).

Fig. 7
Fig. 7

Mixture sample reconstructed slices: (a)-(d) are using PAD-BA, PAD-MBA, PAD-RA and PAD-PA/WA (ε = 1663) phase retrieval algorithm respectively.

Fig. 8
Fig. 8

Histogram of reconstructed slices of PAD-BA, PAD-RA, PAD-MBA and PAD-PA/WA (ε = 1663) in Fig. 7.

Fig. 9
Fig. 9

Polymer sample reconstructed slices: (a)-(c) are phase contrast slices of statistical noise PPCT data index 1, 5 and 8 respectively (see Table 1); (d)-(f) are phase retrieval slices with PAD-BA algorithm and ε = 1739 of the same PPCT data as in (a)-(c)

Fig. 10
Fig. 10

Histogram of reconstructed slices of PPCT data index 8 in Table 1 with different phase retrieval algorithm: (a)-(d) are of PAD-BA, PAD-RA, PAD-MBA and PAD-PA/WA (ε = 1739) respectively. Each histogram identifies all densities on the image in the form of a graph: in this case, X-axis is related to δ value, while Y-axis displays the number of pixels for each δ value.

Fig. 11
Fig. 11

Polymer sample reconstructed slices: (a)-(c) are phase contrast slices of structural noise PPCT data index 3, 7 and 11 respectively (see Table 2); (d)-(f) are phase retrieval slices with PAD-BA (ε = 1739) algorithm of the same data as in (a)-(c).

Fig. 12
Fig. 12

Histogram of reconstructed slices of PPCT data index 11 in Table 2 with different phase retrieval algorithm: (a)-(d) are of PAD-BA, PAD-RA, PAD-MBA and PAD-PA/WA (ε = 1739) respectively.

Tables (4)

Tables Icon

Table 1 Fluence (photons/pixel) in the background for the eight PPCT data sets collected for the statistical noise study.

Tables Icon

Table 2 The parameters of collected PPCT data sets for structural noise study.

Tables Icon

Table 3 CNR values for PMMA, nylon or polystyrene of reconstructed slices of polymer sample in the statistical noise study.

Tables Icon

Table 4 CNR values for PMMA, nylon or polystyrene of structural noise reconstructed slices of polymer sample.

Equations (16)

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

T θ (x,y)=exp[ γ θ (x,y)i ϕ θ (x,y) ]
ϕ θ (x,y)=k Lθ δ(x,y,z)dz γ θ (x,y)=k Lθ β(x,y,z)dz
δ(x,y,z)=εβ(x,y,z)
F[( I θ,z / I θ,0 1)/2]( ξ,η )= γ ^ θ cosχ+ ϕ ^ θ sinχ
ϕ θ (x,y)= F 1 { F[( I z,θ 1)/2] ε 1 cosχ+sinχ }
δ(x,y,z)= k 1 0 π ϕ θ (x,y)νdθ
F[ln( I θ,z / I θ,0 )/2]( ξ,η )= γ ^ θ cosχ+ ϕ ^ θ sinχ
ϕ θ (x,y)= F 1 { F[ln( I z,θ )/2] ε 1 cosχ+sinχ }
δ(x,y,z)= 1 4 π 2 z 0 π [ q(x,y) g θ (x,y) ]dθ
Q(ξ,η)= | ξ | ξ 2 + η 2 +α
α= 1 πελz
t(x,y)= 1 μ ln[ F 1 (μ F( I z,θ / I θ,0 ) 4 π 2 zδ( ξ 2 + η 2 )+μ ) ]
ϕ θ (x,y)= 1 2 εln{ F 1 [ F( I z,θ ) 1+πελz( ξ 2 + η 2 ) ] }
ϕ θ (x,y)= λ r e σ KN ln{ F 1 [ F( I z,θ ) / { I in μ ˜ in (λz)OT F det [ 1+ 2π λ 2 z r e σ KN ( ξ 2 + η 2 ) ] } ] }
ϕ θ (x,y)= 1 2 εln{ F 1 [ F( I z,θ ) 1+πελz( ξ 2 + η 2 ) ] }
CNR= | S a S b | σ a 2 + σ b 2

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