Abstract

Most existing differential phase-contrast computed tomography (DPC-CT) approaches are based on three kinds of scanning geometries, described by parallel-beam, fan-beam and cone-beam. Due to the potential of compact imaging systems with magnified spatial resolution, cone-beam DPC-CT has attracted significant interest. In this paper, we report a reconstruction method based on a back-projection filtration (BPF) algorithm for cone-beam DPC-CT. Due to the differential nature of phase contrast projections, the algorithm restrains from differentiation of the projection data prior to back-projection, unlike BPF algorithms commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a micro-focus x-ray tube source. Moreover, the numerical simulation and experimental results demonstrate that the proposed method can deal with several classes of truncated cone-beam datasets. We believe that this feature is of particular interest for future medical cone-beam phase-contrast CT imaging applications.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]

2011 (2)

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

2010 (2)

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

2009 (1)

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

2008 (3)

G. H. Chen and Z. Qi, “Image reconstruction for fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.53, 1015–1025 (2008).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

2007 (2)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

2006 (3)

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

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

2005 (4)

S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
[CrossRef]

X. Pan, Y. Zou, and D. Xia, “Image reconstruction in peripheral and central regions-of-interest and data redundancy,” Med. Phys.32, 673–684 (2005).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[CrossRef]

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

2004 (2)

T. G. Zhuang, S. Leng, B. E. Nett, and G. H. Chen, “Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data,” Phys. Med. Biol.49, 5489–5503 (2004).
[CrossRef]

F. Noo, R. Clackdoyle, and J. D. Pack, “A two-step Hilbert transform method for 2D image reconstruction,” Phys. Med. Biol.49, 3903–3923 (2004).
[CrossRef]

2003 (3)

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. Express11, 2289–2302 (2003).
[CrossRef]

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

2000 (2)

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today7, 23–26 (2000).
[CrossRef]

1999 (2)

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[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, 2912–2914 (1999).
[CrossRef]

1996 (1)

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

1982 (1)

Abela, R.

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

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, 2912–2914 (1999).
[CrossRef]

Bech, M.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

Beckmann, F.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Biermann, T.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Bonse, U.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Bravin, A.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Brönnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

Bruyndonckx, P.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Bunk, O.

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

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

Chapman, L. D.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Chen, G. H.

G. H. Chen and Z. Qi, “Image reconstruction for fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.53, 1015–1025 (2008).
[CrossRef]

S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
[CrossRef]

T. G. Zhuang, S. Leng, B. E. Nett, and G. H. Chen, “Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data,” Phys. Med. Biol.49, 5489–5503 (2004).
[CrossRef]

Clackdoyle, R.

F. Noo, R. Clackdoyle, and J. D. Pack, “A two-step Hilbert transform method for 2D image reconstruction,” Phys. Med. Biol.49, 3903–3923 (2004).
[CrossRef]

Cloetens, P.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[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, 2912–2914 (1999).
[CrossRef]

David, C.

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[CrossRef]

Davis, T. J.

Diaz, A.

Dilmanian, F. A.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Donath, T.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

Feidenhans’l, R.

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

Fernandez, M.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Fiedler, S.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Fitzgerald, R.

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today7, 23–26 (2000).
[CrossRef]

Fu, J.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

Groso, A.

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

Guigay, J. P.

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

Gureyev, T. E.

Hahn, D.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

Heise, K.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Ina, H.

Irving, T. H. K.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Jensen, T. H.

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

Jerjen, I.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE Press, 1987).

Karjalainen-Lindsberg, M. L.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Kaufmann, R.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Kenntner, J.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Keyrilainen, J.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Kobayashi, S.

Kohn, V.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Kolsch, B.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Kottler, C.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

Le Duc, G.

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

Leidenius, M.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Leng, S.

S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
[CrossRef]

T. G. Zhuang, S. Leng, B. E. Nett, and G. H. Chen, “Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data,” Phys. Med. Biol.49, 5489–5503 (2004).
[CrossRef]

Li, P.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

Lin, J. J. A.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Linga, S.

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

Liu, X.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Liu, X. S.

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

Liu, Y. J.

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

Ludwig, W.

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

Luethi, T.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

Marone, F.

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

Mayo, S. C.

McDonald, S. A.

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

McMahon, P. J.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

McNulty, I.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Miller, P. R.

Mohr, J.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Momose, A.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

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

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Müller, R.

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

Nemoz, C.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Nett, B. E.

S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
[CrossRef]

T. G. Zhuang, S. Leng, B. E. Nett, and G. H. Chen, “Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data,” Phys. Med. Biol.49, 5489–5503 (2004).
[CrossRef]

Noo, F.

F. Noo, R. Clackdoyle, and J. D. Pack, “A two-step Hilbert transform method for 2D image reconstruction,” Phys. Med. Biol.49, 3903–3923 (2004).
[CrossRef]

Nugent, K. A.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Orion, I.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Pack, J. D.

F. Noo, R. Clackdoyle, and J. D. Pack, “A two-step Hilbert transform method for 2D image reconstruction,” Phys. Med. Biol.49, 3903–3923 (2004).
[CrossRef]

Paganin, D.

Pan, X.

X. Pan, Y. Zou, and D. Xia, “Image reconstruction in peripheral and central regions-of-interest and data redundancy,” Med. Phys.32, 673–684 (2005).
[CrossRef]

Paterson, D.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Pauwels, B.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Peele, A. G.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
[CrossRef]

Pfeiffer, F.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
[CrossRef]

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[CrossRef]

Pogany, A.

Qi, Z.

G. H. Chen and Z. Qi, “Image reconstruction for fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.53, 1015–1025 (2008).
[CrossRef]

Rajewsky, M.

F. Beckmann, K. Heise, B. Kolsch, U. Bonse, M. Rajewsky, and T. Biermann, “Three-dimensional imaging of nerve tissue by x-ray phase-contrast microtomography,” Biophys. J.76, 98–102 (1999).
[CrossRef]

Raven, C.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Ren, B.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Revol, V.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

Sasov, A.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Schlenker, M.

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

Schneider, P.

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

Schulz, J.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Sennhauser, U.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

Sipila, P.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE Press, 1987).

Smitten, K. V.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Snigirev, A.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Snigireva, I.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Souvorov, A.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Spanne, P.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron x rays,” Appl. Phys. Lett.69, 1826–1828 (1996).
[CrossRef]

Stampanoni, M.

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, “Phase contrast tomography: an alternative approach,” Appl. Phys. Lett.88, 214104 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[CrossRef]

Stevenson, A. W.

Suortti, P.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Suzuki, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Takeda, M.

Takeda, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

Tapfer, A.

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Tenhunen, M.

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Thomlinson, W. C.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Urban, C.

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A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
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Walter, M.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
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J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
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J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
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P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
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F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys.2, 258–261 (2006).
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T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
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[CrossRef]

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X. Pan, Y. Zou, and D. Xia, “Image reconstruction in peripheral and central regions-of-interest and data redundancy,” Med. Phys.32, 673–684 (2005).
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A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
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P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
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F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
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P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
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S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
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T. G. Zhuang, S. Leng, B. E. Nett, and G. H. Chen, “Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data,” Phys. Med. Biol.49, 5489–5503 (2004).
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X. Pan, Y. Zou, and D. Xia, “Image reconstruction in peripheral and central regions-of-interest and data redundancy,” Med. Phys.32, 673–684 (2005).
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AIP Conf. Proc. (1)

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, and C. Urban, “Phase contrast cone beam tomography with an x-ray grating interferometer,” AIP Conf. Proc.1236, 227–231 (2010).
[CrossRef]

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J. Opt. Soc. Am. (1)

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A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006).
[CrossRef]

Med. Phys. (2)

X. Pan, Y. Zou, and D. Xia, “Image reconstruction in peripheral and central regions-of-interest and data redundancy,” Med. Phys.32, 673–684 (2005).
[CrossRef]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38, 5910–5915 (2011).
[CrossRef]

Nat. Phys. (1)

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

Nature Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nature Mater.7, 134 (2008).
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Opt. Commun. (1)

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative x-ray phase tomography with sub-micron resolution,” Opt. Commun.217, 53–58 (2003).
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Phys. Med. Biol. (7)

G. H. Chen and Z. Qi, “Image reconstruction for fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.53, 1015–1025 (2008).
[CrossRef]

J. Fu, P. Li, Q. Wang, S. Wang, M. Bech, A. Tapfer, D. Hahn, and F. Pfeiffer, “A reconstruction method for equidistant fan-beam differential phase contrast computed tomography,” Phys. Med. Biol.56, 4259–4238 (2011).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol.54, 2747–2753 (2009).
[CrossRef]

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[CrossRef]

F. Noo, R. Clackdoyle, and J. D. Pack, “A two-step Hilbert transform method for 2D image reconstruction,” Phys. Med. Biol.49, 3903–3923 (2004).
[CrossRef]

S. Leng, T. G. Zhuang, B. E. Nett, and G. H. Chen, “Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector,” Phys. Med. Biol.50, 1805–1820 (2005).
[CrossRef]

A. Bravin, J. Keyrilainen, M. Fernandez, S. Fiedler, C. Nemoz, M. L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. V. Smitten, P. Sipila, and P. Suortti, “High-resolution ct by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol.52, 2197–2211 (2007).
[CrossRef]

Phys. Med.Biol. (1)

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med.Biol.45, 933–946 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 108105 (2007).
[CrossRef]

Phys. Rev.Lett. (1)

F. Pfeiffer, C. David, O. Bunk, T. Donath, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “Region-of-interest tomography for grating-based differential phase-contrast imaging,” Phys. Rev.Lett.101, 168101 (2008).
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[CrossRef]

Proc. Natl Acad. Sci. USA (1)

P. P. Zhu, K. Zhang, Z. L. Wang, Y. J. Liu, X. S. Liu, Z. Y. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl Acad. Sci. USA107, 13576–13581 (2010).
[CrossRef]

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A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE Press, 1987).

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Figures (5)

Fig. 1
Fig. 1

Schematic geometry of x-ray refraction in a medium for cone-beam DPC-CT. (x′, z′) represents the index of detector channel. OAC is the central plane. D is the distance from the source to the rotation center O. γ represents the view angle under which the data was taken. l is any incident ray in the three dimensional space under γ. P is the line integral of δ along l.

Fig. 2
Fig. 2

Schematic representation of the cone-beam DPC-CT BPF algorithm. The sample slice in question is illustrated by green solid straight lines that are parallel to each other. L(γ) is the distance from the reconstructed point (x, y, z) to the x-ray source focus at view angle γ. γ 1 γ 2 ¯ is the horizontal straight line through the reference point (x, y, 0). OtAtCt is the tilted plane through the reconstructed point (x, y, z). Dt is the distance from the x-ray source focus to the rotation center Ot in the tilted plane. The reconstruction of the point (x, y, z) only needs the data taken in the angular range [γ1  γ2] marked by the yellow curve. ϑ is the full cone-beam angle.

Fig. 3
Fig. 3

Four cases of truncated data resolved by the cone-beam DPC-CT BPF algorithm. The blue regions are the areas that can be reconstructed. (a) illustrates that the entire field of view can be reconstructed if the scanning angular range is larger than π + ϑ. (b) illustrates that a local region of interest (ROI) can be reconstructed if the scanning angular range is smaller than π + ϑ. (c) illustrates that a local ROI can be reconstructed if the projections are truncated to a smaller view angle. (d) illustrates that the imaging field of view can be enlarged if the detector is asymmetrically placed.

Fig. 4
Fig. 4

Numerical simulation results for the cases in Fig. 3. (a), (c), (e) and (g) are the truncated DPC datasets with sizes 256 × 256 × 191, 256 × 256 × 185, 200 × 200 × 360 and 138 × 256 × 360 pixels respectively. (b), (d), (f) and (h) are the 3D visualization of the corresponding DPC-CT images reconstructed with the BPF algorithm that is expressed by Eq. (1). We cut some part of the sample, which is indicated by the red curves in (b), to show the internal structure.

Fig. 5
Fig. 5

Experimental results. Sub-panels I, II, III and IV are corresponding to the cases in Figs. 3(a)–3(d) respectively. First columns in sub-panels are the truncated DPC datasets with sizes 560 × 1110 × 315, 560 × 1110 × 307, 200 × 1110 × 600 and 290 × 1110 × 600 pixels respectively. Second columns display the typical axial and sagittal slices reconstructed by Eq. (1). Third and forth columns show the orthogonal view slices and 3D rendering of the DPC-CT images respectively. We cut some part of the sample, which is indicated by the red curves, to show the internal structure.

Equations (5)

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

δ ( x , y , z ) = ( 1 / ( 2 π ) ) B ( x , y , z ) / ( x x ) d x .
B ( x , y , z ) = γ 1 γ 2 1 L ( γ ) D z 2 + D 2 x 2 + z 2 + D 2 α ( x , z , γ ) d γ
d γ t = D / D 2 + z 2 d γ .
δ ( x , y , z ) = ( 1 / ( 2 π ) ) B ( x , y , z ) / ( x x ) d x
B ( x , y , z ) = γ 1 γ 2 1 L ( γ t ) D t 2 x 2 + D t 2 α ( x , z , γ ) d γ t .

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