Abstract

We demonstrate a single shot two-dimensional grating-based X-ray phase-contrast imaging using a synchrotron radiation source. A checkerboard designed phase grating for π phase modulation at 17 keV and 35 keV, and a lattice-shaped amplitude grating with a high aspect ratio to shield X-rays up to 35 keV were fabricated. A Fourier analysis of Moiré fringe generated by the gratings was introduced to obtain the two-dimensional differential phase-contrast image with a single exposure. The results show that soft tissues and cartilages of a chicken wing sample are clearly seen with differential phase variation in two-dimensional directions. Using this method not only the whole of an object but also only an inner part of the object can be imaged.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2010

2009

2008

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

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

2003

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

1997

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

1996

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

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

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

1982

1965

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[CrossRef]

1836

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

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]

Beliaevskaya, E. A.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Bennett, E. E.

Bonse, U.

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[CrossRef]

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]

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]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15(3), 1175–1181 (2007).
[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]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Cloetens, P.

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]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15(3), 1175–1181 (2007).
[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, 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]

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Diaz, A.

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]

Gao, D.

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, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Grünzweig, 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]

Gureyev, T. E.

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, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Hart, M.

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[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(No. 6A), 5254–5262 (2006).
[CrossRef]

Ina, H.

Ingal, V. N.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Kobayashi, S.

Kohn, V.

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

Kopace, R.

Kottler, C.

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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Kraft, P.

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]

Kuznetsov, S.

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

Maikusa, H.

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Momose, A.

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]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Pai, V.

Pfeiffer, 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]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15(3), 1175–1181 (2007).
[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, 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.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Pogany, A.

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]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Schelokov, I.

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

Snigirev, A.

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

Snigireva, I.

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

Stampanoni, M.

Stein, A. F.

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, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[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(No. 6A), 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(Part 2, No. 7B), 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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Takeda, M.

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]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Weitkamp, T.

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]

Wen, H. H.

Wilkins, S. 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, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Yashiro, W.

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]

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Ziegler, E.

Appl. Phys. Lett.

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. D Appl. Phys.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Jpn. J. Appl. Phys.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (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]

Nat. Mater.

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.

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

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, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Mag.

H. F. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401–407 (1836).

Phys. Med. Biol.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

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

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of two-dimensional grating-based (Talbot) interferometer. Z denotes the Talbot length which is expressed by the pitch of phase grating (p) and X-ray wavelength (λ). An amplitude grating is positioned close to X-ray detector to generate Moiré fringe.

Fig. 2
Fig. 2

Fourier analysis of Moiré fringe. A simple sphere phantom is used in this simulation. The differential phase image is calculated via the inverse Fourier transform of the first Fourier spectrum of Moiré fringe.

Fig. 3
Fig. 3

SEM image of the cross-section of the checkerboard designed phase grating (a) with π modulation at 35 keV with the pitch of 11.4 μm and the depth 46 μm. The phase grating was fabricated by deep etching into silicon substrate. SEM image of the cross-section (b) and the expanded image of the region surrounded by the white line (c) of lattice-shaped amplitude grating with the pitch of 8.24 μm and the depth 100 μm. The amplitude grating was fabricated from silicon-based structure with gold electroplating. The amplitude grating is expected to shield about 97% of X-rays at 35 keV.

Fig. 4
Fig. 4

Comparison of differential phase-contrast image in x-direction of a Teflon rod (left) and a polyamide rod (right) with the absorption image taken at 17.5 keV. A double layered structure of the polyamide rod can be identified in the differential phase-contrast image (b), whereas the absorption image has a very low contrast (a). The dashed line in (b) represents the edge of the inner part of the double layered structure of the Teflon rod. The line profile of the differential phase of the polyamide rod (c) is obtained following the solid line in (b). The differential phase resolution about 0.05 rad/μm at the boundary of a double layered structure can be resolved by the present imaging system.

Fig. 5
Fig. 5

Comparison of differential phase-contrast image in x-direction of a joint part of a chicken wing (a) with the contact image (b) taken at 17.5 keV.

Fig. 6
Fig. 6

Differential phase-contrast image in x-direction of a joint part of a chicken wing taken at 17.5 keV (a) and 35 keV (b). The inset figures represent the cartilage around the edge of the bone.

Fig. 7
Fig. 7

Full image of a chicken wing stitched from 99 images in size of 15mm by 15mm taken at 35 keV. Differential phase-contrast image in x-direction (a) and the square-root of sum of squares of the differential phase-contrast image in x- and y-directions (b).

Equations (11)

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I Self ( x , y , z ) | n x , n y ψ n x n y exp [ i 2 π λ z ] exp [ i π z λ ( n x 2 + n y 2 ) p G1 2 ] exp [ i 2 π ( n x x + n y y ) p G1 ] × exp [ i Φ ( x z λ n x p G1 , y z λ n y p G1 ) ] | 2 .
I Moire ( x , y , z ) = I Self ( x , y , z ) × T Amp ( x , y ) ,
a ( x , y ) + m x , m y b m x , m y ( x , y ) { exp ( i 2 π m x x p Moire φ x m x ( x , y , z ) ) × exp ( i 2 π m y y p Moire φ y m y ( x , y , z ) ) ,
φ x m x ( x , y , z ) = z λ m x p G1 Φ ( x , y ) x ,
φ y m y ( x , y , z ) = z λ m y p G1 Φ ( x , y ) y ,
F [ I Moire ( x , y , z ) ] = A ˜ ( k x , k y ) + m x , m y { B ˜ m x m y ( k x , k y ) δ ( k x 2 π m x p Moire ) δ ( k y 2 π m y p Moire ) } ,
= A ˜ ( k x , k y ) + m x , m y { B ˜ m x , m y ( k x 2 π m x p Moire , k y 2 π m y p Moire ) } ,
A ˜ ( k x , k y ) = F [ a ( x , y ) ] ,
B ˜ m x , m y ( k x , k y ) = F [ b m x , m y ( x , y ) exp [ i φ x m x ( x , y , z ) i φ y m y ( x , y , z ) ] ] ,
Φ ( x , y ) x = p G1 z λ arg [ F 1 [ B ˜ 1 , 0 ( k x , k y ) ] ] ,
Φ ( x , y ) y = p G1 z λ arg [ F 1 [ B ˜ 0 , 1 ( k x , k y ) ] ] ,

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