Abstract

We present a rigorous forward model for phase imaging of a 3-D object illuminated by a cone-shaped x-ray beam. Our model is based on a full-wave approach valid under the first Rytov approximation, and thus can be used with large and thick objects, e.g., luggage and human patients. We unify light-matter interaction and free-space propagation into an integrated wave optics framework. Therefore, our model can accurately calculate x-ray phase images formed with sources of arbitrary shape, and it can be effectively incorporated into x-ray phase tomography as a forward model. Within the best of our knowledge, this is the first non-paraxial, full-wave model for X-ray phase imaging.

© 2013 OSA

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    [CrossRef] [PubMed]

2013 (1)

2012 (1)

Z. Zaprazny, D. Korytar, V. Ac, P. Konopka, and J. Bielecki, “Phase contrast imaging of lightweight objects using microfocus X-ray source and high resolution CCD camera,” JINST7(03), C03005 (2012).
[CrossRef]

2011 (2)

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett.36(3), 391–393 (2011).
[CrossRef] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “Refraction-contrast tomosynthesis imaging using dark-field imaging optics,” Appl. Phys. Lett.99(10), 103704 (2011).
[CrossRef]

2009 (2)

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17(1), 266–277 (2009).
[CrossRef] [PubMed]

2008 (4)

L. Poletto, M. Caldon, G. Tondello, and A. Megighian, “A system for high-resolution x-ray phase-contrast imaging and tomography of biological specimens,” Proc. SPIE7078, 70781P, 70781P-10 (2008).
[CrossRef]

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot.66(8), 1083–1090 (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 (1)

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, “X-ray phase contrast image simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B254, 307–318 (2007).

2006 (1)

D. Shimao, H. Sugiyama, T. Kunisada, and M. Ando, “Articular cartilage depicted at optimized angular position of Laue angular analyzer by X-ray dark-field imaging,” Appl. Radiat. Isot.64(8), 868–874 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

2004 (1)

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol.49(16), 3573–3583 (2004).
[CrossRef] [PubMed]

2003 (1)

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

2002 (1)

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwisawa, K. Hyodo, and C. Uyama, “Simple x-ray dark-and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys.41(Part 2, No. 9A/B), L1016–L1018 (2002).
[CrossRef]

2001 (1)

U. Bonse and F. Beckmann, “Multiple-beam X-ray interferometry for phase-contrast microtomography,” J. Synchrotron Radiat.8(1), 1–5 (2001).
[CrossRef] [PubMed]

2000 (1)

A. Momose, T. Takeda, and Y. Itai, “Blood Vessels: Depiction at Phase-Contrast X-ray Imaging without Contrast Agents in the Mouse and Rat-Feasibility Study 1,” Radiology217(2), 593–596 (2000).
[PubMed]

1999 (1)

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol.44(3), 741–749 (1999).
[CrossRef] [PubMed]

1997 (1)

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

1996 (1)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

1993 (2)

B. Henke, E. Gullikson, and J. C. Davis, “X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[CrossRef]

B. Henke, E. Gullikson, and J. C. X. Davis, “X-Ray Interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[CrossRef]

1981 (2)

R. M. Aspden and D. W. L. Hukins, “Collagen organization in articular cartilage, determined by X-ray diffraction, and its relationship to tissue function,” Proc. R. Soc. Lond. B Biol. Sci.212(1188), 299–304 (1981).
[CrossRef] [PubMed]

A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett.6(8), 374–376 (1981).
[CrossRef] [PubMed]

1976 (1)

R. E. Alvarez and A. Macovski, “Energy-selective reconstructions in x-ray computerized tomography,” Phys. Med. Biol.21(5), 733–744 (1976).
[CrossRef] [PubMed]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
[CrossRef]

1896 (1)

A. Stanton, “Wilhelm Conrad Röntgen on a new kind of rays: translation of a paper read before the Würzburg Physical and Medical Society, 1895,” Nature53, 274–276 (1896).

Ac, V.

Z. Zaprazny, D. Korytar, V. Ac, P. Konopka, and J. Bielecki, “Phase contrast imaging of lightweight objects using microfocus X-ray source and high resolution CCD camera,” JINST7(03), C03005 (2012).
[CrossRef]

Alvarez, R. E.

R. E. Alvarez and A. Macovski, “Energy-selective reconstructions in x-ray computerized tomography,” Phys. Med. Biol.21(5), 733–744 (1976).
[CrossRef] [PubMed]

An, L.

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

Ando, M.

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “Refraction-contrast tomosynthesis imaging using dark-field imaging optics,” Appl. Phys. Lett.99(10), 103704 (2011).
[CrossRef]

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett.36(3), 391–393 (2011).
[CrossRef] [PubMed]

D. Shimao, H. Sugiyama, T. Kunisada, and M. Ando, “Articular cartilage depicted at optimized angular position of Laue angular analyzer by X-ray dark-field imaging,” Appl. Radiat. Isot.64(8), 868–874 (2006).
[CrossRef] [PubMed]

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwisawa, K. Hyodo, and C. Uyama, “Simple x-ray dark-and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys.41(Part 2, No. 9A/B), L1016–L1018 (2002).
[CrossRef]

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Aspden, R. M.

R. M. Aspden and D. W. L. Hukins, “Collagen organization in articular cartilage, determined by X-ray diffraction, and its relationship to tissue function,” Proc. R. Soc. Lond. B Biol. Sci.212(1188), 299–304 (1981).
[CrossRef] [PubMed]

Babot, D.

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, “X-ray phase contrast image simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B254, 307–318 (2007).

Badizadegan, K.

Barbastathis, G.

Bech, M.

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]

Beckmann, F.

U. Bonse and F. Beckmann, “Multiple-beam X-ray interferometry for phase-contrast microtomography,” J. Synchrotron Radiat.8(1), 1–5 (2001).
[CrossRef] [PubMed]

Berthier, J.

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, “X-ray phase contrast image simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B254, 307–318 (2007).

Bielecki, J.

Z. Zaprazny, D. Korytar, V. Ac, P. Konopka, and J. Bielecki, “Phase contrast imaging of lightweight objects using microfocus X-ray source and high resolution CCD camera,” JINST7(03), C03005 (2012).
[CrossRef]

Bonse, U.

U. Bonse and F. Beckmann, “Multiple-beam X-ray interferometry for phase-contrast microtomography,” J. Synchrotron Radiat.8(1), 1–5 (2001).
[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]

Bunk, O.

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]

Calderón-Colon, X.

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

Caldon, M.

L. Poletto, M. Caldon, G. Tondello, and A. Megighian, “A system for high-resolution x-ray phase-contrast imaging and tomography of biological specimens,” Proc. SPIE7078, 70781P, 70781P-10 (2008).
[CrossRef]

Cao, G.

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

Choi, W.

Cloetens, P.

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]

Dasari, R. R.

David, C.

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]

Davis, J. C.

B. Henke, E. Gullikson, and J. C. Davis, “X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[CrossRef]

Davis, J. C. X.

B. Henke, E. Gullikson, and J. C. X. Davis, “X-Ray Interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[CrossRef]

Devaney, A. J.

Do, S.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Duvauchelle, P.

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, “X-ray phase contrast image simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B254, 307–318 (2007).

Eikenberry, E. F.

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]

Fang-Yen, C.

Feld, M. S.

Ferrero, C.

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, “X-ray phase contrast image simulation,” Nucl. Instrum. Methods Phys. Res., Sect. B254, 307–318 (2007).

Furukawa, A.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Gao, D.

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N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “Refraction-contrast tomosynthesis imaging using dark-field imaging optics,” Appl. Phys. Lett.99(10), 103704 (2011).
[CrossRef]

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Sung, Y.

Y. Sung and G. Barbastathis, “Rytov approximation for x-ray phase imaging,” Opt. Express21(3), 2674–2682 (2013).
[CrossRef] [PubMed]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17(1), 266–277 (2009).
[CrossRef] [PubMed]

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Takahashi, M.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Takeda, T.

A. Momose, T. Takeda, and Y. Itai, “Blood Vessels: Depiction at Phase-Contrast X-ray Imaging without Contrast Agents in the Mouse and Rat-Feasibility Study 1,” Radiology217(2), 593–596 (2000).
[PubMed]

Tanaka, T.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Tokumori, K.

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

Tondello, G.

L. Poletto, M. Caldon, G. Tondello, and A. Megighian, “A system for high-resolution x-ray phase-contrast imaging and tomography of biological specimens,” Proc. SPIE7078, 70781P, 70781P-10 (2008).
[CrossRef]

Toyofuku, F.

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

Tsuchiya, K.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Tsuneyoshi, M.

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

Ueno, E.

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

Uyama, C.

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwisawa, K. Hyodo, and C. Uyama, “Simple x-ray dark-and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys.41(Part 2, No. 9A/B), L1016–L1018 (2002).
[CrossRef]

Wang, P.

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

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]

Wilkins, S. W.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun.1(4), 153–156 (1969).
[CrossRef]

Wu, X.

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

Wu, Y.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Yadav, P. S.

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot.66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

Yamada, A.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Yamasaki, K.

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[CrossRef]

Yamasaki, M.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

Yuasa, T.

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett.36(3), 391–393 (2011).
[CrossRef] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “Refraction-contrast tomosynthesis imaging using dark-field imaging optics,” Appl. Phys. Lett.99(10), 103704 (2011).
[CrossRef]

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

Zaprazny, Z.

Z. Zaprazny, D. Korytar, V. Ac, P. Konopka, and J. Bielecki, “Phase contrast imaging of lightweight objects using microfocus X-ray source and high resolution CCD camera,” JINST7(03), C03005 (2012).
[CrossRef]

Zhou, O.

G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “Refraction-contrast tomosynthesis imaging using dark-field imaging optics,” Appl. Phys. Lett.99(10), 103704 (2011).
[CrossRef]

Appl. Radiat. Isot. (2)

Y. S. Kashyap, P. S. Yadav, T. Roy, P. S. Sarkar, M. Shukla, and A. Sinha, “Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications,” Appl. Radiat. Isot.66(8), 1083–1090 (2008).
[CrossRef] [PubMed]

D. Shimao, H. Sugiyama, T. Kunisada, and M. Ando, “Articular cartilage depicted at optimized angular position of Laue angular analyzer by X-ray dark-field imaging,” Appl. Radiat. Isot.64(8), 868–874 (2006).
[CrossRef] [PubMed]

At. Data Nucl. Data Tables (2)

B. Henke, E. Gullikson, and J. C. Davis, “X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[CrossRef]

B. Henke, E. Gullikson, and J. C. X. Davis, “X-Ray Interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables54(2), 181–342 (1993).
[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]

Invest. Radiol. (2)

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal Analyser-based X-ray Phase Contrast Imaging in the Dark Field: Implementation and Evaluation using Excised Tissue Specimens,” Invest. Radiol.under review.

T. Tanaka, C. Honda, S. Matsuo, K. Noma, H. Oohara, N. Nitta, S. Ota, K. Tsuchiya, Y. Sakashita, A. Yamada, M. Yamasaki, A. Furukawa, M. Takahashi, and K. Murata, “The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube,” Invest. Radiol.40(7), 385–396 (2005).
[CrossRef] [PubMed]

J. Synchrotron Radiat. (1)

U. Bonse and F. Beckmann, “Multiple-beam X-ray interferometry for phase-contrast microtomography,” J. Synchrotron Radiat.8(1), 1–5 (2001).
[CrossRef] [PubMed]

J. XRay Sci. Technol. (1)

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

JINST (1)

Z. Zaprazny, D. Korytar, V. Ac, P. Konopka, and J. Bielecki, “Phase contrast imaging of lightweight objects using microfocus X-ray source and high resolution CCD camera,” JINST7(03), C03005 (2012).
[CrossRef]

Jpn. J. Appl. Phys. (2)

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwisawa, K. Hyodo, and C. Uyama, “Simple x-ray dark-and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys.41(Part 2, No. 9A/B), L1016–L1018 (2002).
[CrossRef]

M. Ando, K. Yamasaki, F. Toyofuku, H. Sugiyama, C. Ohbayashi, G. Li, L. Pan, X. Jiang, W. Pattanasiriwisawa, D. Shimao, E. Hashimoto, T. Kimura, M. Tsuneyoshi, E. Ueno, K. Tokumori, A. Maksimenko, Y. Higashida, and M. Hirano, “Attempt at visualizing breast cancer with x-ray dark field imaging,” Jpn. J. Appl. Phys.44(17), L528–L531 (2005).
[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]

Nature (2)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

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[CrossRef]

Opt. Express (2)

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G. Cao, Y. Z. Lee, R. Peng, Z. Liu, R. Rajaram, X. Calderón-Colon, L. An, P. Wang, T. Phan, S. Sultana, D. S. Lalush, J. P. Lu, and O. Zhou, “A dynamic micro-CT scanner based on a carbon nanotube field emission x-ray source,” Phys. Med. Biol.54(8), 2323–2340 (2009).
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Proc. SPIE (1)

L. Poletto, M. Caldon, G. Tondello, and A. Megighian, “A system for high-resolution x-ray phase-contrast imaging and tomography of biological specimens,” Proc. SPIE7078, 70781P, 70781P-10 (2008).
[CrossRef]

Radiology (1)

A. Momose, T. Takeda, and Y. Itai, “Blood Vessels: Depiction at Phase-Contrast X-ray Imaging without Contrast Agents in the Mouse and Rat-Feasibility Study 1,” Radiology217(2), 593–596 (2000).
[PubMed]

Rev. Sci. Instrum. (1)

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

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the imaging geometry.

Fig. 2
Fig. 2

Near-field x-ray diffraction patterns of homogeneous, spherical water beads of different radii: (a) 10 μm, (b) 100 μm, and (c) 1 mm. The images were numerically generated assuming a cone-beam x-ray set-up with an infinitesimally small focal spot and 30keV monochromatic x-ray beam. The source-to-object distance R1 and the object-to-detector distance R2 are each 1 m.

Fig. 3
Fig. 3

Near-field x-ray diffraction patterns of homogeneous water beads of different radii. (a) Intensity profile across the center of bead for the bead radii: 10, 20, 50, and 100 μm; (b) near-edge portion of the intensity profile for two bead radii (30keV monochromatic x-ray beam): 500 μm and 1 mm. The detector coordinate (horizontal axis) was scaled so that the edges of the bead are located at ± 1.

Fig. 4
Fig. 4

Simulation with a modified 3-D Shepp-Logan phantom: (a) real (δ) and imaginary (β) parts of a horizontal cross-section of the refractive index phantom shown in 3-D in the image below the cross-sectional image. (The 3-D image was obtained by modifying the code from https://sites.google.com/site/hispeedpackets/Home/shepplogan.) (b, d) simulated x-ray images without (b) and with (d) applying Gaussian smoothing to the phantom. The FWHM of the applied Gaussian kernel is about 200 μm along each axis. (c) and (e) are the zoom-in views of (b) and (d), respectively.

Fig. 5
Fig. 5

Refractive index map of an iliac artery sample acquired with crystal analyzer-based CT: (a) 3-D rendered image of the data cube; (b) Sample cross-sections of the complex refractive index map: (i) absorption (β), and (ii) phase (δ) part. a: plastic tube; b: plastic rod (inserted for comparison); c: three-layer artery wall; and d: tissue shrinkage.

Fig. 6
Fig. 6

X-ray phase imaging simulation using the complex refractive index map in Fig. 5: (i) Simple projection of the phase map δ; (ii)-(iv): x-ray phase images simulated with the proposed model for various focal spot size of the source (20 μm, 100 μm, and 500 μm). A cone-shaped x-ray beam illuminates the sample from the side of the data cube shown in Fig. 5. The source-to-object and object-to-detector distance were fixed at 0.2 m.

Equations (19)

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

n=1δ+iβ.
U (i) ( x,y; x 0 , y 0 )= exp[ ik( p 1 x 0 + q 1 y 0 ) ] u (i) ( x,y; p 1 , q 1 )d p 1 d q 1 .
u (i) ( x,y; p 1 , q 1 )=( i/ λ m 1 )exp{ ik[ p 1 x+ q 1 y+ m 1 ( R 2 + R 1 ) ] },
U( x,y; x 0 , y 0 )= exp[ ik( p 1 x 0 + q 1 y 0 ) ]u( x,y; p 1 , q 1 )d p 1 d q 1 ,
u ¯ (s) ( x,y; p 1 , q 1 )= [ i4π( W+ m 1 /λ ) ] 1 f ˜ ( U,V,W )exp[ i2π( Ux+Vy+W R 2 ) ]dUdV ,
I( x,y )= I 0 ( x 0 , y 0 ) | U( x,y; x 0 , y 0 ) | 2 d x 0 d y 0 .
I( x,y )= I ˜ 0 ( λ 1 ( p 1 p ¯ 1 ), λ 1 ( q 1 q ¯ 1 ) )u( x,y; p 1 , q 1 ) u * ( x,y; p ¯ 1 , q ¯ 1 )d p 1 d q 1 d p ¯ 1 d q ¯ 1 .
I ˜ 0 ( u,v )= S 0 .
I( x,y )= S 0 | u( x,y; p 1 , q 1 )d p 1 d q 1 | 2 .
u( x,y; p 1 , q 1 )d p 1 d q 1 ~( 1/r )exp( ikr ) u ¯ ( x,y;x/r ,y/r ),
First Born approximation:       I( x,y )=( I 0 / r 2 ) | 1+ u ¯ (s) ( x,y;x/r ,y/r ) | 2 ,
First Rytov approximation:  I( x,y )=( I 0 / r 2 )exp[ 2Re{ u ¯ (s) ( x,y;x/r ,y/r ) } ].
λ 1 ( p 1 p ¯ 1 )=P, λ 1 ( q 1 q ¯ 1 )=Q, λ 1 ( m 1 m ¯ 1 )=M.
I( x,y )= I ˜ 0 ( P,Q )exp{ i2π[ Px+Qy+M( R 2 + R 1 ) ] } × m 1 1 ( m 1 λM ) 1 u ¯ ( x,y; p 1 , q 1 ) u ¯ * ( x,y; p 1 λP, q 1 λQ )d p 1 d q 1 dPdQ.
( m 1 λM ) 1 m 1 1 , u ¯ ( x,y; p 1 λP, q 1 λQ ) u ¯ ( x,y; p 1 , q 1 ), M= λ 1 ( m 1 m ¯ 1 )( p 1 / m 1 )P( q 1 / m 1 )Q+ϑ( λ P 2 / m 1 ).
I( x,y )= I 0 ( x x p ,y y p )( 1/ m 1 2 ) | u ¯ ( x,y; p 1 , q 1 ) | 2 d p 1 d q 1 ,
I( x,y )= ( 1/ r p 2 ) I 0 ( x x p ,y y p ) | 1+ u ¯ (s) ( x,y; x p / r p , y p / r p ) | 2 d x p d y p ,
I( x,y )= ( 1/ r p 2 ) I 0 ( x x p ,y y p )exp[ 2Re{ u ¯ (s) ( x,y; x p / r p , y p / r p ) } ]d x p d y p ,
h( x,y,z )= ( 2π σ 2 ) 3/2 exp[ ( x 2 + y 2 + z 2 ) / 2 σ 2 ],

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