Abstract

X-ray differential phase contrast imaging methods, including projection imaging and the corresponding computed tomography (CT), have been implemented using a Talbot interferometer and either a synchrotron beam line or a low brilliance x-ray source generated by a stationary-anode x-ray tube. From small-angle scattering events which occur as an x-ray propagates through a medium, a signal intensity loss can be recorded and analyzed for an understanding of the micro-structures in an image object. This has been demonstrated using a Talbot-Lau interferometer and a stationary-anode x-ray tube. In this paper, theoretical principles and an experimental implementation of the corresponding CT imaging method are presented. First, a line integral is derived from analyzing the cross section of the small-angle scattering events. This method is referred to as small-angle scattering computed tomography (SAS-CT). Next, a Talbot-Lau interferometer and a rotating-anode x-ray tube were used to implement SAS-CT. A physical phantom and human breast tissue sample were used to demonstrate the reconstructed SAS-CT image volumes.

© 2010 OSA

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2009 (10)

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
[CrossRef] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
[CrossRef] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[CrossRef] [PubMed]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
[CrossRef] [PubMed]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z. Chen, “Quantitative grating based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

2008 (5)

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

2007 (4)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

2006 (3)

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

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(No. 6A), 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(4), 258–261 (2006).
[CrossRef]

2005 (3)

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
[CrossRef]

2002 (1)

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

2000 (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(4), 933–946 (2000).
[CrossRef] [PubMed]

1999 (1)

T. M. Sabine and W. K. Bertram, “The use of multiple-scattering data to enhance small-angle neutron scattering experiments,” Acta Crystallogr. A 55(3), 500–507 (1999).
[CrossRef]

1997 (1)

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

1996 (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

1995 (2)

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, “X-ray image contrast from a simple phase object,” Phys. Rev. Lett. 74(16), 3173–3176 (1995).
[CrossRef] [PubMed]

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 352(3), 622–628 (1995).
[CrossRef]

1984 (1)

1939 (1)

A. Guinier, “Diffraction of X-rays at Small Angles: Application to the Study of Microscopic Phenomena,” Ann. Phys. 12, 161 (1939).

Archer, A.

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

Baumann, J.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
[CrossRef] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

Bertram, W. K.

T. M. Sabine and W. K. Bertram, “The use of multiple-scattering data to enhance small-angle neutron scattering experiments,” Acta Crystallogr. A 55(3), 500–507 (1999).
[CrossRef]

Bravin, A.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

Bruder, J.

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Bunk, O.

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
[CrossRef] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (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(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

Chapman, D.

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

Chapman, L. D.

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
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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(4), 933–946 (2000).
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Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
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T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
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F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
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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. Express 13(16), 6296–6304 (2005).
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C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
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C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
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S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
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F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
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T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
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F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
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C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
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M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
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T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

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(4), 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. Express 13(16), 6296–6304 (2005).
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T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, “X-ray image contrast from a simple phase object,” Phys. Rev. Lett. 74(16), 3173–3176 (1995).
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C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
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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. Express 13(16), 6296–6304 (2005).
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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(4), 933–946 (2000).
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Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
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F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
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D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
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F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
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M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
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M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
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D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
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Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
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M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
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M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
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Gao, B.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
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C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
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M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
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F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
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A. Guinier, “Diffraction of X-rays at Small Angles: Application to the Study of Microscopic Phenomena,” Ann. Phys. 12, 161 (1939).

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S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
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T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, “X-ray image contrast from a simple phase object,” Phys. Rev. Lett. 74(16), 3173–3176 (1995).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
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Hasnah, M. O.

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
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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(No. 6A), 5254–5262 (2006).
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Henrich, B.

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

Hilger, A.

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

Hintermüller, C.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
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P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Huang, W. X.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
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Huang, Z.-F.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z. Chen, “Quantitative grating based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

Jensen, T. H.

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
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M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
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Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z. Chen, “Quantitative grating based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
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M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
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A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
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M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

Koyama, I.

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
[CrossRef]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
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Kress, J. W.

Kuwabara, H.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Le Duc, G.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

Li, J.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Liu, H.

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

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M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

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I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

Maikusa, H.

Manke, I.

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

Marone, F.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
[CrossRef] [PubMed]

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S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
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Mikuljan, G.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
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A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
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A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[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(No. 6A), 5254–5262 (2006).
[CrossRef]

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
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C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

Oltulu, O.

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

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(4), 933–946 (2000).
[CrossRef] [PubMed]

Parham, C.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
[CrossRef] [PubMed]

Pfeiffer, F.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
[CrossRef] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

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(4), 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. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Pisano, E.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

Pisano, E. D.

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
[CrossRef] [PubMed]

Pogany, A.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (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(4), 933–946 (2000).
[CrossRef] [PubMed]

Rifkin, J.

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Ruth, R.

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

Sabine, T. M.

T. M. Sabine and W. K. Bertram, “The use of multiple-scattering data to enhance small-angle neutron scattering experiments,” Acta Crystallogr. A 55(3), 500–507 (1999).
[CrossRef]

Sayers, D.

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Schuster, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

Shu, H.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Stampanoni, M.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
[CrossRef] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Stevenson, A. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, “X-ray image contrast from a simple phase object,” Phys. Rev. Lett. 74(16), 3173–3176 (1995).
[CrossRef] [PubMed]

Strobl, M.

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

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(No. 6A), 5254–5262 (2006).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
[CrossRef]

Takai, H.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
[CrossRef]

Takeda, T.

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

Takeda, Y.

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[CrossRef] [PubMed]

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(No. 6A), 5254–5262 (2006).
[CrossRef]

Thomlinson, W.

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

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(4), 933–946 (2000).
[CrossRef] [PubMed]

Wang, J. Y.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Wang, Z.-T.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z. Chen, “Quantitative grating based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

Weitkamp, T.

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

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(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, C. David, C. Kottler, O. Bunk, and F. Pfeiffer, “Tomography with grating interferometers at low-brilliance source,” Proc. SPIE 6318, 631828 (2006).

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Wilkins, S. W.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

T. J. Davis, T. E. Gureyev, D. Gao, A. W. Stevenson, and S. W. Wilkins, “X-ray image contrast from a simple phase object,” Phys. Rev. Lett. 74(16), 3173–3176 (1995).
[CrossRef] [PubMed]

Wu, J.

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

Wu, X.

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

Wu, X. Y.

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(4), 933–946 (2000).
[CrossRef] [PubMed]

Wu, Z. Y.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Yashiro, W.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[CrossRef] [PubMed]

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(No. 6A), 5254–5262 (2006).
[CrossRef]

Yuan, Q. X.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Zhang, D.

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

Zhang, L.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Zhong, Z.

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
[CrossRef] [PubMed]

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

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(4), 933–946 (2000).
[CrossRef] [PubMed]

Zhu, P. P.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Ziegler, E.

Acad. Radiol. (2)

C. Muehleman, J. Li, D. Connor, C. Parham, E. Pisano, and Z. Zhong, “Diffraction-enhanced imaging of musculoskeletal tissues using a conventional x-ray tube,” Acad. Radiol. 16(8), 918–923 (2009).
[CrossRef] [PubMed]

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, “Design and implementation of a compact low-dose diffraction enhanced medical imaging system,” Acad. Radiol. 16(8), 911–917 (2009).
[CrossRef] [PubMed]

Acta Crystallogr. A (1)

T. M. Sabine and W. K. Bertram, “The use of multiple-scattering data to enhance small-angle neutron scattering experiments,” Acta Crystallogr. A 55(3), 500–507 (1999).
[CrossRef]

Ann. Phys. (1)

A. Guinier, “Diffraction of X-rays at Small Angles: Application to the Study of Microscopic Phenomena,” Ann. Phys. 12, 161 (1939).

Appl. Phys. Lett. (3)

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[CrossRef]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z. Chen, “Quantitative grating based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High resolution differential phase contrast imaging using a magnifying projection geometry with micro-focus x-ray source,” Appl. Phys. Lett. 90(22), 224101 (2007).
[CrossRef]

Eur. J. Radiol. (1)

T. Weitkamp, C. David, O. Bunk, J. Bruder, P. Cloetens, and F. Pfeiffer, “X-ray phase radiography and tomography of soft tissue using grating interferometry,” Eur. J. Radiol. 68(3Suppl), S13–S17 (2008).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (1)

D. Zhang, M. Donovan, L. L. Fajardo, A. Archer, X. Wu, and H. Liu, “Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype,” IEEE Trans. Biomed. Eng. 55(9), 2249–2257 (2008).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

F. Pfeiffer, M. Bech, O. Bunk, T. Donath, B. Henrich, P. Kraft, and C. David, “X-ray dark-field and phase-contrast imaging using a grating interferometer,” J. Appl. Phys. 105(10), 102006 (2009).
[CrossRef]

J. Microsc. (1)

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Synchrotron Radiat. (2)

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16(4), 562–572 (2009).
[CrossRef] [PubMed]

M. Bech, O. Bunk, C. David, R. Ruth, J. Rifkin, R. Loewen, R. Feidenhans’l, and F. Pfeiffer, “Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays,” J. Synchrotron Radiat. 16(1), 43–47 (2009).
[CrossRef]

Jpn. J. Appl. Phys. (4)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), 866–868 (2003).
[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(No. 6A), 5254–5262 (2006).
[CrossRef]

I. Koyama, A. Momose, J. Wu, T. T. Lwin, and T. Takeda, “Biological imaging by X-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys. 44(11), 8219–8221 (2005).
[CrossRef]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48(7), 076512 (2009).
[CrossRef]

Med. Phys. (1)

M. O. Hasnah, Z. Zhong, O. Oltulu, E. Pisano, R. E. Johnston, D. Sayers, W. Thomlinson, and D. Chapman, “Diffraction enhanced imaging contrast mechanisms in breast cancer specimens,” Med. Phys. 29(10), 2216–2221 (2002).
[CrossRef] [PubMed]

Microelectron. Eng. (1)

C. David, J. Bruder, T. Rohbeck, C. Grunzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard x-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[CrossRef]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[CrossRef] [PubMed]

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(4), 258–261 (2006).
[CrossRef]

Nature (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 352(3), 622–628 (1995).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (3)

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography,” Phys. Med. Biol. 52(23), 6923–6930 (2007).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an x-ray tube source,” Phys. Med. Biol. 54(9), 2747–2753 (2009).
[CrossRef] [PubMed]

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(4), 933–946 (2000).
[CrossRef] [PubMed]

Phys. Rev. A (1)

Z.-F. Huang, K.-J. Kang, L. Zhang, Z. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron dark-field tomography,” Phys. Rev. Lett. 101(12), 123902 (2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Proc. SPIE (1)

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Rev. Sci. Instrum. (1)

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Illustration of geometry used in deriving the basic equations in SAS-CT.

Fig. 2
Fig. 2

Photographs of the grating interferometer x-ray system. Subfigure (a) shows the x-ray tube and the G0 grating, while (b) shows the detector, G1, and G2 gratings.

Fig. 3
Fig. 3

Calcification phantom made by filling a PMMA tube with gelatin and placing various sizes of calcifications (indicated on the right) in different layers. A cross section of the phantom is shown on the left, with the approximate arrangement of the calcifications within each layer.

Fig. 4
Fig. 4

SAS-CT (a) and absorption contrast CT (b) reconstructions of the calcification phantom. The images shown are both maximal intensity projections (MIP) over the same image volume, with a pixel size of (80 μm)2 and a thickness of 1.12 mm. A MIP was used in order to visualize all calcifications within one size layer.

Fig. 5
Fig. 5

SAS-CT (a) and absorption contrast CT (b) reconstructions of human breast tissue. Each image shows the same slice from the same data set. An oil cyst is clearly visible in both of the images, with additional contrast from background structure present in the attenuation contrast reconstruction.

Equations (21)

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I ( x , y ) I 0 + I 1 cos [ 2 π p 2 x g + φ ( x , y ) ]   ,
k ' = q + k   .
q = 2 k sin θ 2 k θ   .
d Ω q d q d ϕ k 2 = λ 2 4 π 2 q d q d ϕ   .
P n ( q ) = d Ω 1 P n 1 ( q 1 ) P 1 ( q q 1 )   .
S n ( r ) = d Ω P n ( q ) e i q r   ,
S n ( r ) = S n 1 ( r ) S 1 ( r )   .
S n ( r ) = [ S 1 ( r ) ] n   .
P 1 ( q ) = ( 2 π λ ) 2 R 2 π e q 2 R 2   ,
S 1 ( r ) = e ( r 2 R ) 2   .
d z SAS   ,
SAS = 1 σ SAS ρ SAS ( x , y , z ) ,
U ( r ) = exp [ r 2 4 d z σ SAS ρ SAS R 2 ( z ) ]   .
U ( r ) = exp [ r 2 4 R eff 2 ]   , and
1 R eff 2 = d z σ SAS ρ SAS R 2 ( z )   .
V obj ( m , n ) I 1 obj ( m , n ) I 0 obj ( m , n )   ,
V SAS ( m , n ) V obj ( m , n ) V bkgd ( m , n ) = I 1 obj ( m , n ) I 0 obj ( m , n ) I 0 bkgd ( m , n ) I 1 bkgd ( m , n )   .
V SAS = U ( r ) = exp [ r 2 4 d z σ SAS ρ SAS R 2 ( z ) ] .
ln V SAS = r 2 4 d z σ SAS ρ SAS R 2 ( z ) = d z σ SAS ρ SAS R ˜ 2 ( z ) ,
R ˜ ( z ) = 2 R ( z ) r .
I ( x , y ) I 0 { 1 + V cos [ 2 π p 2 x g + φ ( x , y ) ] } ,

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