Abstract

X-ray phase-contrast imaging based on grating interferometry has become a common method due to its superior contrast in biological soft tissue imaging. The high sensitivity relies on the high-aspect ratio structures of the planar gratings, which prohibit the large field of view applications with a diverging X-ray source. Curved gratings allow a high X-ray flux for a wider angular range, but the interference fringes are only visible within ~10° range due to the geometrical mismatch with the commonly used flat array detectors. In this paper, we propose a design using a curved quasi-periodic grating for large field of view imaging with a flat detector array. Our scheme is numerically verified in the X-ray regime and experimentally verified in the visible optical regime. The interference fringe pattern is observed over 25°, with less than 10% of decrease in visibility in our experiments.

© 2015 Optical Society of America

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References

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  1. 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]
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    [Crossref] [PubMed]
  4. 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]
  5. 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).
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    [Crossref]
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2014 (1)

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

2013 (1)

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

2011 (1)

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

2007 (2)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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]

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

2006 (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]

2003 (1)

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), L866–L868 (2003).
[Crossref]

1997 (1)

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 (3)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[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]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

1995 (1)

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]

1983 (1)

1967 (1)

1950 (1)

S. Silver and W. K. Saunders, “The external field produced by a slot in an infinite circular cylinder,” J. Appl. Phys. 21(2), 153–158 (1950).
[Crossref]

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]

Berry, M. V.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Bravin, A.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Bruder, J.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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, 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]

Cardot, F.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[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]

Cohen-Sabban, Y.

David, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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, 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]

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.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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]

Endo, T.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Fernández, M.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Fiedler, S.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[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.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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]

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), L866–L868 (2003).
[Crossref]

Hattori, T.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Hirano, K.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Honda, C.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Hoshino, Y.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Itai, Y.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Ito, T.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Jerjen, I.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[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]

Joyeux, D.

Karjalainen-Lindsberg, M.-L.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2), L866–L868 (2003).
[Crossref]

Keyriläinen, J.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Kido, K.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Kiyohara, J.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Klein, S.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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]

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), L866–L868 (2003).
[Crossref]

Leidenius, M.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Lüthi, T.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Makifuchi, C.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

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, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

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), L866–L868 (2003).
[Crossref]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Montgomery, W. D.

Nagashima, M.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Nagatsuka, S.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Nemoz, C.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Niedermann, P.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Nishino, S.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Noda, D.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Pfeiffer, F.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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, 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]

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]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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]

Saunders, W. K.

S. Silver and W. K. Saunders, “The external field produced by a slot in an infinite circular cylinder,” J. Appl. Phys. 21(2), 153–158 (1950).
[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]

Sennhauser, U.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Silver, S.

S. Silver and W. K. Saunders, “The external field produced by a slot in an infinite circular cylinder,” J. Appl. Phys. 21(2), 153–158 (1950).
[Crossref]

Sipilä, P.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Smitten, K.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[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, 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]

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Suortti, P.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Suzuki, 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), 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), L866–L868 (2003).
[Crossref]

Takeda, T.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Tanaka, J.

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Tenhunen, M.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

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]

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Virkkunen, P.

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[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]

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, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

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]

J. Appl. Phys. (1)

S. Silver and W. K. Saunders, “The external field produced by a slot in an infinite circular cylinder,” J. Appl. Phys. 21(2), 153–158 (1950).
[Crossref]

J. Mod. Opt. (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

J. Opt. Soc. Am. (2)

Jpn. J. Appl. Phys. (1)

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), L866–L868 (2003).
[Crossref]

Microelectron. Eng. (1)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, 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. Med. (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[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 (2)

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]

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., Sect. A (1)

V. Revol, C. Kottler, R. Kaufmann, I. Jerjen, T. Lüthi, F. Cardot, P. Niedermann, U. Straumann, U. Sennhauser, and C. Urban, “X-ray interferometer with bent gratings: Towards larger fields of view,” Nucl. Instrum. Methods Phys. Res., Sect. A 648, S302–S305 (2011).
[Crossref]

Philos. Trans. R. Soc., A (1)

A. Momose, W. Yashiro, K. Kido, J. Kiyohara, C. Makifuchi, T. Ito, S. Nagatsuka, C. Honda, D. Noda, T. Hattori, T. Endo, M. Nagashima, and J. Tanaka, “X-ray phase imaging: from synchrotron to hospital,” Philos. Trans. R. Soc., A 372(2010), 20130023 (2014).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

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]

A. Bravin, J. Keyriläinen, M. Fernández, S. Fiedler, C. Nemoz, M.-L. Karjalainen-Lindsberg, M. Tenhunen, P. Virkkunen, M. Leidenius, K. Smitten, P. Sipilä, and P. Suortti, “High-resolution CT by diffraction-enhanced x-ray imaging: mapping of breast tissue samples and comparison with their histo-pathology,” Phys. Med. Biol. 52(8), 2197–2211 (2007).
[Crossref] [PubMed]

Z. Med. Phys. (1)

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23(3), 222–227 (2013).
[Crossref] [PubMed]

Other (3)

T. Thüring, “Compact X-ray grating interferometry for phase and dark-field computed tomography in the diagnostic energy range,” Diss. Diss., ETH Zürich, Nr. 21321, (2013).

M. Abramowitz, I. A. Stegun, and D. Miller, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (Courier Corporation, 1965).

J. A. Stratton, Electromagnetic Theory (John Wiley & Sons, 2007).

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Figures (6)

Fig. 1
Fig. 1

Setups of grating-based PCI systems. (a) Two flat gratings G1 and G2. (b) A curved phase grating G1 and a flat analyzer grating G2.

Fig. 2
Fig. 2

The simulations in X-ray regime. (a) The visibilities of stepping curves of both G1 and G1’. (b) The intensity profiles at the first fractional Talbot distance of both G1 and G1’ at 0° and 16°. (c) The period of the quasi-periodic phase grating G1’ as a function of θ.

Fig. 3
Fig. 3

Simulations in visible optical regime. The wavelength of the source is 0.67 μm. The radius of the grating is 75 mm. The white line, indicating the self-imaging plane, is located at Y = 111.9 mm. (a) The Talbot carpet of the periodic grating G1. The period of the grating is 91 μm. (b) The Talbot carpet of the quasi-periodic grating G1’. The Insert is the line profile of the fields at 0° and 12.6°. (c) The period of the quasi-periodic grating G1’ as a function of θ, calculated from Eq. (9).

Fig. 4
Fig. 4

(a) Experimental setup schematic: S is the point source λ = 0.67 μm, A periodic grating G1 or quasi-periodic grading G1’ is fixed on a cylindrical surface. P denotes the observation plane. Obj is the microscope objectives; L is the tube lens; and D is the CMOS detector. (b-d) The images of interference fringes of the observation angles at 0° (b), 7.4° (c), and 12.2°(d) on the observation plane.

Fig. 5
Fig. 5

Experimental data of the visibility with the periodic grating G1 and quasi-periodic grating G1’ on the observation plane.

Fig. 6
Fig. 6

(a) The simulated visibility profile along the radius direction of the periodic grating, the origin is set at the observation plane. (b) Experimental images of interference fringes at −2 mm, 0 mm, 2 mm from observation plane. (c) Profiles of the interference fringes. Red curves denote simulated profiles. Blue curves denote the gray-scale value profiles of the blue lines marked in 6(b).

Equations (18)

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

u(θ,r)= m= c m H m (2) (kr) e imθ ,
| H m (2) (kr) |= 2 πkr +Ο( 1 (kr) 2 ) ,
arg H m (2) (kr)=kr+( 1 2 m+ 1 4 )π 4 m 2 1 8kr +Ο( 1 (kr) 3 ).
u(θ, r 0 )= m A m e imθ ,
u(θ,r)= r 0 r e i(k r 0 kr+ 1 8kr 1 8k r 0 ) m= { e i( m 2 2k ( 1 r 0 1 r )) } A m e imθ .
1 r D = 1 r 0 l 2 p 2 λ r 0 2 ,l=1,2,3,
g(θ, r 0 )= i rect( 2 r 0 p i θ)δ(θ θ i ) ,
θ i = 1 r 0 ( p 0 + p i 2 + j=1 | i1 | p j ),i=1,2,3...,
2 p i 2 λ r 0 2 + 1 r 0 =( 2 p 0 2 λ r 0 2 + 1 r 0 )cos( θ i ),
E z = m a m H m (2) (kr) e imθ ,
E θ = i η 0 k m b m r H m (2) (kr) e imθ ,
E r = η 0 m kr m b m H m (2) (kr) e imθ ,
| H m (2) (kr) |= 2 πkr + 4 m 2 1 2 (2kr) 2 + ,
arg H m (2) (kr)=kr+( 1 2 m+ 1 4 )π 4 m 2 1 8kr + (4 m 2 1)(4 m 2 9) 6 (4kr) 3 +,
E z = m a m H m (2) (kr) e imθ ,
E θ = η 0 mZ b m H m (2) (kr) e imθ ,
E r = m kr η 0 mZ b m H m (2) (kr) e imθ ,
u(θ,r)= m c m 1 kr e kr+ m 2 4 m 2 1 8kr e imθ ,

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