Abstract

Here we present a method for the removal of multi-material artifacts which occur during the application of a single material phase retrieval procedure to X-ray tomographic data sets. For the phase retrieval we chose the most common method which is the single material filter. The correction method which we describe in the following has been designed for samples consisting of three distinct materials, hence effectively two different material interfaces. Furthermore the material phase with the strongest X-ray interaction needs to show sufficient absorption in order to allow for segmenting this phase through application of a grey value threshold. If these conditions are fulfilled the method is easy to apply through post processing as is shown for the volume images of two sample types.

© 2015 Optical Society of America

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  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]
  2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
    [Crossref]
  3. M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
    [Crossref]
  4. A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14(18), 8103–8110 (2006).
    [Crossref] [PubMed]
  5. 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]
  6. T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
    [Crossref] [PubMed]
  7. T. Weitkamp, D. Haas, D. Wegrzynek, and A. Rack, “ANKAphase: software for single-distance phase retrieval from inline X-ray phase-contrast radiographs,” J. Synchrotron Radiation 18(4), 617–629 (2011).
    [Crossref]
  8. 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,” Journal of Microscopy 206(1), 33–40 (2002).
    [Crossref] [PubMed]
  9. 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]
  10. M. A. Beltran, D. Paganin, K. Uesugi, and M.J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18(7), 6423–6436 (2010).
    [Crossref] [PubMed]
  11. M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
    [Crossref] [PubMed]
  12. M. Langer, P. Cloetens, A. Pacureanu, and F. Peyrin., ”X-ray in-line phase tomography of multimaterial objects,” Opt. Lett. 37:(11),2151–2153 (2012).
    [Crossref] [PubMed]
  13. S. Zabler, H. Riesemeier, P. Fratzl, and P. Zaslansky, “Fresnel-propagated imaging for the study of human tooth dentin by partially coherent x-ray tomography,” Opt. Express 14(19), 8584–8597 (2006).
    [Crossref] [PubMed]
  14. U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
    [Crossref]

2012 (2)

M. Langer, P. Cloetens, A. Pacureanu, and F. Peyrin., ”X-ray in-line phase tomography of multimaterial objects,” Opt. Lett. 37:(11),2151–2153 (2012).
[Crossref] [PubMed]

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

2011 (3)

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (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. 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. Synchrotron Radiation 18(4), 617–629 (2011).
[Crossref]

2010 (1)

2009 (1)

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

2007 (1)

2006 (2)

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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

2001 (1)

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[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]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

Abela, R.

Baruchel, 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]

Beltran, M. A.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. Paganin, K. Uesugi, and M.J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18(7), 6423–6436 (2010).
[Crossref] [PubMed]

Boistel, R.

Boone, M.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Burvall, A.

Choinka, G.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Cloetens, P.

Dawson, M.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

De Witte, Y.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Dierick, M.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Fouras, A.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

Fratzl, P.

Graf, W.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Groso, A.

Guigay, J.P.

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, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Gureyev, T.E.

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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

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. Synchrotron Radiation 18(4), 617–629 (2011).
[Crossref]

Herppich, W.B.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Hertz, H.M.

Hilger, A.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Hooper, S.B.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

Kitchen, M.J.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. Paganin, K. Uesugi, and M.J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18(7), 6423–6436 (2010).
[Crossref] [PubMed]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

Langer, M.

Larsson, D. H.

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Lundström, U.

Manke, I.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Matsushima, U.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Mayo, S.

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Mayo, S.C.

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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

Pacureanu, A.

Paganin, D.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. Paganin, K. Uesugi, and M.J. Kitchen, “2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18(7), 6423–6436 (2010).
[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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Peyrin., F.

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. Synchrotron Radiation 18(4), 617–629 (2011).
[Crossref]

Reser, D.H.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

Riesemeier, H.

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[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]

Siu, K.K.W.

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

Stampanoni, M.

Stevenson, A.W.

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Takman, P.A.C.

Uesugi, K.

Van den Bulcke, J.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Van Hoorebeke, L.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

Vlassenbroeck, J.

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

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. Synchrotron Radiation 18(4), 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. Synchrotron Radiation 18(4), 617–629 (2011).
[Crossref]

Wilkins, S.W.

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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Zabler, S.

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

S. Zabler, H. Riesemeier, P. Fratzl, and P. Zaslansky, “Fresnel-propagated imaging for the study of human tooth dentin by partially coherent x-ray tomography,” Opt. Express 14(19), 8584–8597 (2006).
[Crossref] [PubMed]

Zaslansky, P.

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[Crossref]

J. Synchrotron Radiation (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. Synchrotron Radiation 18(4), 617–629 (2011).
[Crossref]

Journal of Microscopy (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,” Journal of Microscopy 206(1), 33–40 (2002).
[Crossref] [PubMed]

Nucl. Instr. Meth. Phys. Res. (1)

M. Boone, Y. De Witte, M. Dierick, J. Van den Bulcke, J. Vlassenbroeck, and L. Van Hoorebeke, “Practical use of the modified Bronnikov algorithm in micro-CT,” Nucl. Instr. Meth. Phys. Res. 267(7), 1182–1186 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Med. Biol. (1)

M. A. Beltran, D. Paganin, K.K.W. Siu, A. Fouras, S.B. Hooper, D.H. Reser, and M.J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56(23), 7353 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

T. E. Gureyev, S. Mayo, S.W. Wilkins, D. Paganin, and A.W. Stevenson, “Quantitative in-line phase-contrast imaging with multienergy x rays,” Phys. Rev. Lett. 86(25), 5827 (2001).
[Crossref] [PubMed]

Postharvest Biol. Tec. (1)

U. Matsushima, A. Hilger, W. Graf, S. Zabler, I. Manke, M. Dawson, G. Choinka, and W.B. Herppich, “Calcium oxalate crystal distribution in rose peduncles: Noninvasive analysis by synchrotron X-ray micro-tomography,” Postharvest Biol. Tec. 72, 27–34 (2012).
[Crossref]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12) 5486–5492 (1995).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Axial CT-slices of a dry rose stem. (a) Overview over the upper right quadrant (1.6 mm wide), (b, c) close up onto the structure showing typical multi material artifacts, examples for artifacts indicated by arrows. If the phase retrieval is applied to the softer tissue (cells), it causes a blurring around the harder calcium oxalate (CaOx, black) crystals, some of which lie above or below the displayed slice (b). If it is applied to the CaOx, phase contrast artifacts (fringe contrast) will remain for the softer material (gray) (c).

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Fig. 2
Fig. 2 The filter steps (of the backward correction) shown for the rose stem sample from Fig. 1. The gray value ranges are (0, 5.5) for (c), (−1.5, 0.5) for (d) and (0, 2.2) for the rest. The first step consists of separating the single material phase retrieved image (a) into the masked area (c) and the rest (b). Next, the correction filter KA→B(u) is applied to (b), resulting in (d). The final result (e) is achieved by summing (b) and (d). The blurring artefacts can be seen in (c) and (d) with opposite sign.

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Fig. 3
Fig. 3 Axial CT-slices from the holo-tomographies of the rose stem sample. Without (top) and with (bottom) multi material correction applied. The visible gray scale range is [0.0, 2.4] for (a), (c) and (d) and [−1.5, 3.9] for (b), the gray value for the CaOx (black) is ouside of the visible gray value range. Both materials have varying densities. The image area shown is 0.72 mm wide and 0.54 mm high.

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Fig. 4
Fig. 4 Volume histograms (top) and line plots (bottom) for the rose stem sample. The position of the line plot in the sample is indicated in Fig. 3(b). Single material holotomographies (dashed lines) for wood-air and CaOx-wood/air, results of the multi material corrections (solid lines).

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Fig. 5
Fig. 5 Axial CT-slices from the holo-tomographies of the metal alloy sample. Single material phase retrieved ((a), (b) and (c)), forward corrected result (d), based on (a). In addition to the blurring artifacts, there are horizontal streaks in (b), which appear only if the phase retrieval is applied on projections. These straks originate from the rotational centre of the CT, which is to the left of the image area. They are not visible in (c), where the phase retrieval is applied as a volume filter starting from the weak projection-based phase retrieval (a). Identical gray scales, Cu (black) is outside of the visible gray value range. The image area shown is 0.29 mm wide and 0.22 mm high.

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Equations (8)

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∫ μ ( r → ) d l = − ln ( ℱ 2 D − 1 { 1 1 + p 2 u 2 ℱ 2 D { I ( x , y ) I 0 ( x , y ) } } ) ,
K p ( u ) = 1 1 + p 2 u 2
k p ( r ) = ℱ − 1 { K p ( u ) } ∝ π p exp ( − 2 π | r | p )
K A → B ( u ) = K B ( u ) K A ( u ) = 1 + p A 2 u 2 1 + p B 2 u 2
k A → B ( r ) ∝ p A 2 p B 2 δ ( r ) − p A 2 − p B 2 p B 2 π p B exp ( − 2 π | r | p B )
M A ( r → ) = { 1 for     V ( r → ) ≥ t 0 for     V ( r → ) < t
V AB ( r → ) = V A ( r → ) M A ( r → ) + ℱ 3 D − 1 { K A → B ℱ 3 D { V A ( r → ) M B ( r → ) } } ( r → )
V BA ( r → ) = V B ( r → ) M B ( r → ) + ℱ 3 D − 1 { K B → A ℱ 3 D { V B ( r → ) M A ( r → ) } } ( r → )

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