Abstract

In medical X-ray imaging, phase contrast imaging is to measure refraction angles caused by the patient. The X-ray dose for a given image quality depends on the sensitivity of the setup, i.e. on the angular measurement range. Measurement ranges of existing phase contrast setups are either too high or too low for perfectly imaging a human finger in air: There is a gap in available measurement ranges, which prevents a reduction of X-ray dose. To fill the gap, this work proposes a novel variant of a Talbot-Lau interferometer. Instead of a single phase grating, it uses two phase gratings, each consisting of tiny prisms. The height of the prisms is an additional factor in the measurement range, which allows to fill the gap. The potential is a dose-reduction by a factor of 5.4 compared to Talbot-Lau setups of same post-patient length. Simulation results indicate a polychromatic visibility of up to 20%.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2017 (2)

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

2016 (4)

O. Preusche, “Lens gratings for dose optimization of medical X-ray phase contrast imaging,” Opt. Express 24(23), 26161–26174 (2016).
[Crossref] [PubMed]

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

L. B. Gromann, D. Bequé, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. I. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7(2), 381–391 (2016).
[Crossref] [PubMed]

2015 (1)

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

2014 (2)

A. Yaroshenko, M. Bech, G. Potdevin, A. Malecki, T. Biernath, J. Wolf, A. Tapfer, M. Schüttler, J. Meiser, D. Kunka, M. Amberger, J. Mohr, and F. Pfeiffer, “Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer,” Opt. Express 22(1), 547–556 (2014).
[Crossref] [PubMed]

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

2013 (3)

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

2012 (1)

D. Stutman and M. Finkenthal, “K-edge and mirror filtered x-ray grating interferometers,” AIP Conf. Proc. 1466, 229–236 (2012).
[Crossref]

2011 (3)

R. Raupach and T. G. Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

2010 (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

2009 (2)

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

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] [PubMed]

2007 (4)

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[Crossref] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (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]

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]

2005 (1)

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]

1971 (1)

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta (Lond.) 18(9), 677–682 (1971).
[Crossref]

Amberger, M.

Anderson, S. A.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

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]

Bachche, S.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Baumann, J.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Bech, M.

A. Yaroshenko, M. Bech, G. Potdevin, A. Malecki, T. Biernath, J. Wolf, A. Tapfer, M. Schüttler, J. Meiser, D. Kunka, M. Amberger, J. Mohr, and F. Pfeiffer, “Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer,” Opt. Express 22(1), 547–556 (2014).
[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] [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]

Beck, T. J.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

Bennett, E. E.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Bequé, D.

Bhandarkar, P.

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Biernath, T.

Bingham, C. O.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

Birnbacher, L.

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[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]

Bunk, O.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

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] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[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]

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]

Carrino, J. A.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

Chabior, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[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]

Chedid, N.

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Chen, L.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

Cloetens, P.

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, 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]

Coan, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

Cozzini, C.

Daerr, H.

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

David, C.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

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] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[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]

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]

De Coppi, P.

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

Diaz, A.

Diemoz, P. C.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Donath, T.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Dreossi, D.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

Endrizzi, M.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Engel, K. J.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

Feidenhans’l, 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] [PubMed]

Fernández, M.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[Crossref] [PubMed]

Finkenthal, M.

D. Stutman and M. Finkenthal, “K-edge and mirror filtered x-ray grating interferometers,” AIP Conf. Proc. 1466, 229–236 (2012).
[Crossref]

Flohr, T. G.

R. Raupach and T. G. Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

Foster, B. A.

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Geller, D.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[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]

Gomella, A. A.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Grandl, S.

Gromann, L. B.

Grünzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref] [PubMed]

Guigay, J. P.

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta (Lond.) 18(9), 677–682 (1971).
[Crossref]

Hagen, C. K.

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

Harmon, K. J.

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Hellerhoff, K.

Hempel, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Herzen, J.

Hoheisel, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Iacoviello, F.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

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]

Kageyama, M.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Kato, K.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Keyriläinen, J.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[Crossref] [PubMed]

Koehler, T.

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

Köhler, T.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

Koike, T.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref] [PubMed]

Kunka, D.

Kuribayashi, M.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

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]

Liu, C.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Loewen, 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] [PubMed]

Lynch, S. K.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Malecki, A.

Martens, G.

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

Meiser, J.

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]

Miao, H.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Mohr, J.

A. Yaroshenko, M. Bech, G. Potdevin, A. Malecki, T. Biernath, J. Wolf, A. Tapfer, M. Schüttler, J. Meiser, D. Kunka, M. Amberger, J. Mohr, and F. Pfeiffer, “Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer,” Opt. Express 22(1), 547–556 (2014).
[Crossref] [PubMed]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Momose, A.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Morgan, N. Y.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Nonoguchi, M.

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

Olivo, A.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Panna, A.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Patel, A.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Pešic, Z. D.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Pfeiffer, F.

L. B. Gromann, D. Bequé, K. Scherer, K. Willer, L. Birnbacher, M. Willner, J. Herzen, S. Grandl, K. Hellerhoff, J. I. Sperl, F. Pfeiffer, and C. Cozzini, “Low-dose, phase-contrast mammography with high signal-to-noise ratio,” Biomed. Opt. Express 7(2), 381–391 (2016).
[Crossref] [PubMed]

A. Yaroshenko, M. Bech, G. Potdevin, A. Malecki, T. Biernath, J. Wolf, A. Tapfer, M. Schüttler, J. Meiser, D. Kunka, M. Amberger, J. Mohr, and F. Pfeiffer, “Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer,” Opt. Express 22(1), 547–556 (2014).
[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] [PubMed]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[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. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (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]

Popescu, S.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Potdevin, G.

Preusche, O.

Rau, C.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Raupach, R.

R. Raupach and T. G. Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Reznikova, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

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] [PubMed]

Rigon, L.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

Robinson, I. K.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Roessl, E.

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

Rössl, E.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[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] [PubMed]

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]

Scherer, K.

Schusser, S.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

Schuster, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

Schüttler, M.

Shearing, P. R.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

Speller, R.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Sperl, J. I.

Stampanoni, M.

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Stutman, D.

D. Stutman and M. Finkenthal, “K-edge and mirror filtered x-ray grating interferometers,” AIP Conf. Proc. 1466, 229–236 (2012).
[Crossref]

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

Suhonen, H.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[Crossref] [PubMed]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[Crossref] [PubMed]

Tapfer, A.

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, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Urbani, L.

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

van Stevendaal, U.

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

Vittoria, F. A.

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

Vogtmeier, G.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

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. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Willer, K.

Willner, M.

Wolf, J.

Wolfe, D. E.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Xiao, X.

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Yaroshenko, A.

Zamir, A.

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

Zapata, C. E.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[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]

Ziegler, E.

Znati, S.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

AIP Conf. Proc. (1)

D. Stutman and M. Finkenthal, “K-edge and mirror filtered x-ray grating interferometers,” AIP Conf. Proc. 1466, 229–236 (2012).
[Crossref]

Appl. Phys. Lett. (1)

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Biomed. Opt. Express (1)

J. Appl. Phys. (1)

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[Crossref]

J. Synchrotron Radiat. (2)

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[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] [PubMed]

Nat. Commun. (1)

H. Wen, A. A. Gomella, A. Patel, S. K. Lynch, N. Y. Morgan, S. A. Anderson, E. E. Bennett, X. Xiao, C. Liu, and D. E. Wolfe, “Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings,” Nat. Commun. 4, 2659 (2013).
[Crossref] [PubMed]

Nat. Phys. (2)

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]

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in x-ray phase-contrast imaging,” Nat. Phys. 12(9), 830–834 (2016).
[Crossref] [PubMed]

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

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Methods Phys. Res. A 648, S202–S207 (2011).
[Crossref]

Opt. Acta (Lond.) (1)

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta (Lond.) 18(9), 677–682 (1971).
[Crossref]

Opt. Express (3)

Philos Trans A Math Phys Eng Sci (1)

E. Roessl, H. Daerr, T. Koehler, G. Martens, and U. van Stevendaal, “Clinical boundary conditions for grating-based differential phase-contrast mammography,” Philos Trans A Math Phys Eng Sci 372(2010), 20130033 (2014).
[Crossref] [PubMed]

Phys. Med. Biol. (5)

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56(17), 5697–5720 (2011).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref] [PubMed]

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]

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]

R. Raupach and T. G. Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

M. Endrizzi, F. A. Vittoria, L. Rigon, D. Dreossi, F. Iacoviello, P. R. Shearing, and A. Olivo, “X-ray phase-contrast radiography and tomography with a multiaperture analyzer,” Phys. Rev. Lett. 118(24), 243902 (2017).
[Crossref] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett. 110(13), 138105 (2013).
[Crossref] [PubMed]

Rev. Sci. Instrum. (2)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard X-ray phase contrast imaging,” Rev. Sci. Instrum. 78(4), 043710 (2007).
[Crossref] [PubMed]

Sci. Rep. (3)

S. Bachche, M. Nonoguchi, K. Kato, M. Kageyama, T. Koike, M. Kuribayashi, and A. Momose, “Laboratory-based X-ray phase-imaging scanner using Talbot-Lau interferometer for non-destructive testing,” Sci. Rep. 7(1), 6711 (2017).
[Crossref] [PubMed]

A. Zamir, M. Endrizzi, C. K. Hagen, F. A. Vittoria, L. Urbani, P. De Coppi, and A. Olivo, “Robust phase retrieval for high resolution edge illumination x-ray phase-contrast computed tomography in non-ideal environments,” Sci. Rep. 6(1), 31197 (2016).
[Crossref] [PubMed]

H. Miao, A. A. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5(1), 13581 (2015).
[Crossref] [PubMed]

Other (2)

O. Preusche, patent US 9,763,634 B2 (2017).

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-ray form factor, attenuation and scattering tables,” (version 2.1, 2005) http://physics.nist.gov/ffast .

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Figures (14)

Fig. 1
Fig. 1 Measurement ranges αR of several differential phase contrast imaging techniques. Smaller ranges save dose D since D~ α R 2 . The aim of this paper is a combination of a low dose and a short post-patient distance d, see the encircled area. Gray numbers indicate the year of the corresponding literature, see the text below.
Fig. 2
Fig. 2 A Talbot-Lau interferometer (a) compared to the proposed setup “fringe-formation” (b). Fringe formation compares phases of wavefront sections which originally are separated by a lateral shear L. This is done be rearranging wavefront sections of height sA ( = one strip): Refraction in GA gets compensated in GB, resulting in an rearranged wavefront. A following Talbot-Lau section translates phase differences into detectable intensity contrast. Gray numbers at the bottom indicate corresponding sections in this paper.
Fig. 3
Fig. 3 (a) The basic idea is that x-shifts rearrange the wavefront ①, creating a rectangular phase of shift ΔΦ(α), which translates into contrast (②, Talbot effect). (b) Simplified setup to explain why wavefront sections reach matching prisms in GB. (c) Quantitative situation for an x-shift by S = 2 strips. Parallel-beam geometry is used for simplicity.
Fig. 4
Fig. 4 Simulated consequences at the detector of varying the wavefront angle α within measurement range αR in monochromatic example setup G (point source; design energy 30 keV): (a) shows the average intensity I1 within the slits of G2, (b) the contrast C=( I 1 I 2 )/( I 1 + I 2 ) (where I2 is the average intensity in front of the bars of G2). All graphs look sine-like, the contrast graphs are exactly point-symmetric to the origin. Based on the average I ¯ and on the amplitude V, a synthetic sine was defined for each graph and the resulting small differences “sine − graph” are shown as dotted lines using the scale on the right hand side of each diagram. For | α/ α R |<50% the graphs closely match the sines.
Fig. 5
Fig. 5 Monochromatic simulation results for (a) a phase step and (b) a wedge for an x-shift in GA by S = 16 strips. The scales at the top illustrate that the phases separated by L = 16 periods were being compared. ① shows that the phase behind GB had the added rectangular phase shift ΔΦ, ② shows the strip-averaged intensity I and ③ the contrast C in front of G2.
Fig. 6
Fig. 6 Hierarchical source grating G0 for an x-shift of S=N m A =31 prisms; the geometry is the same as in Fig. 2(a). Source grating period P0 and width Q0/4 depend on distances and periods, the finest period p0 additionally depends on the prism height. Groups of p0-periodic slits (up to a width of Q 0 /4) can be opened within each P0-period in monochromatic setups.
Fig. 7
Fig. 7 Simplified intensity transfer (a) at design energy and (b) at a lower photon energy for monochromatic setups (“even mA”). Parallelized wavefronts contribute to visibility. (c) Point-source visibilities (simulated) for the setups G (monochromatic) and H (polychromatic).
Fig. 8
Fig. 8 Setup H (poly 30 keV; mA = 1; point source) had a flat phase behind GB for (a) a narrow and (b) a wide spectrum. GB consisted of a single large prism and in GA, all non-matching prisms blocked all light.
Fig. 9
Fig. 9 (a) Contrasts of different polychromatic setups are quite similar near the design energy; the overall visibility indicated by the arrows is about 30% in each case. (b) The visibility depended on the slit-count in G0: Increasing the number of p0-periodic slits within a P0-group increased the x-ray flux but reduced the resulting visibilities shown next to the arrows.
Fig. 10
Fig. 10 (a) Stepping G0 without sample and (b) a changing sample refraction with a fixed G0. Setup H (polychromatic; 30 keV) was simulated using imperfect absorption gratings, however a “blocker” G0 of larger opening width and larger absorber height was assumed. All graphs are sine-like near the origin x = 0 p0. The difference to the sine and the energy dependency are larger for the varied sample gradient in (b) due to energy-dependent refraction in the sample.
Fig. 11
Fig. 11 Sheared production: (a) x-shear, (b) y-shear layout mask and (c) resulting 3D-prism.
Fig. 12
Fig. 12 Sensitivity depending on compactness of the setups proposed in Table 1.
Fig. 13
Fig. 13 (a) The three contributions to sensitivity along with all variables used within the text.
Fig. 14
Fig. 14 (a) Milled PMMA grating. Images taken in G2-plane (the phase sensitive x-axis is the horizontal axis): (b) Monochromatic setup M (651 nm), (c) Polychromatic setup P (651 nm), (d) P (532 nm), (e) P (420 nm).

Tables (1)

Tables Icon

Table 1 Example configurations corresponding to Fig. 12 (which visualizes columns αR and dA + dB)

Equations (24)

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

tanα=(λ/2π)(ΔΦ/Δx)
SNR~V(Δα/ α R )DT/ DT .
D~ α R 2 /( V 2 T).
u H (η)= i λ d G e ik d G x u G (x) e (ik δ G µ G ) h G (x) e ik (ηx) 2 /2 d G dx,
ΔΦ= 2π λ Ltanα 2π λ S p A α
α R =λ/L=λ/(S p A ).
ΔΦ/2π=α(L/λ)=α/ α R
I 1 = I ¯ (1+ Vsin(ΔΦ)) C = Vsin(ΔΦ)
λ p A = m A 2 p A D A = m A 2 p B d A
(λ/2)/ s A =( m A s B )/ d A .
S=N m A
α R = λ S p A = λ N m A p A = p B 2N d A .
P 0 /( d 0 + d A )= p 2 / d B
Q 0 /( d 0 + d A )=( p 2 / d B )/ m A
α R = p 0 / d 0 ,
p 0 /( d 0 + d A )=( p 2 / d B )/(2S).
p 0 = Q 0 /2N= P 0 /2S
ΔΦ=Lα(2π/λ)=2γdα(2π/λ)=2Δ l 1 (2π/λ)
2Δ l 1 =2αγd.
2Δ l 2 [ (α+γ) 2 (αγ) 2 ] d 2 /2d=2αγd.
2Δ l 3 =2(αd)(h/s)δ=2αγd.
ΔΦ~1/ α R ~Δ l 1 /λ~λ~1/E
Q 0 d 0 := p B d A = p A D A = p A M A 2 D B m A = p B D B M A m A = p 2 d B M A m A (def) (SC) p B = M A p A (LE) d A = M A D A M A =( d 0 + d A )/ d 0 D B / D A = p B 2 /( m A p A 2 ) = M A 2 / m A (SC) M B p B = p 2 (LE) M B D B = d B M B =1+ d B /( d 0 + d A )
p 0 d 0 + d A = λ pB /S = p B 2 D B /S = p 2 d B /2S [Eq.(6)] D B = p B 2 /2λ λ/ p B = p B /2 D B (SC) M B p B = p 2 (LE) M B D B = d B

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