Abstract

The beam hardening is one of the two causes of the fringe shift distortion in polychromatic X-ray grating interferometry. Based on the assumption of the uniform energy dependence, we developed a novel analytic approach to accurately retrieve the monochromatic attenuation function and fringe phase shift from the polychromatic measurement. This approach provides a useful tool for precise measurement of sample electron density distribution in X-ray grating interferometry.

© 2017 Optical Society of America

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References

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    [Crossref]

2017 (2)

A. Yan, X. Wu, and H. Liu, “Polychromatic x-ray effects on fringe phase shifts in grating interferometry,” Opt. Express 25, 6053–6068 (2017).
[Crossref] [PubMed]

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

2016 (2)

A. Yan, X. Wu, and H. Liu, “Predicting visibility of interference fringes in x-ray grating interometry,” Opt. Express 24, 15927–15939 (2016).
[Crossref] [PubMed]

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

2015 (2)

2014 (5)

2013 (3)

P. Munro and A. Olivo, “X-ray phase-contrast imaging with polychromatic sources and the concept of effective energy,” Phys. Rev. A 87, 053838 (2013).
[Crossref]

J. Rizzi, P. Mercere, M. Idir, P. D. Silva, G. Vincent, and J. Primot, “X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer,” Opt. Express 21, 17340–17351 (2013).
[Crossref] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Physics in Medicine and Biology 58, R1–R35 (2013).
[Crossref]

2012 (2)

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
[Crossref] [PubMed]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast ct compared with the conventional ct: Spectrum of noise equivalent quanta neq(k),” Med. Phys. 39, 4367–4382 (2012).
[Crossref]

2011 (5)

2010 (3)

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
[Crossref] [PubMed]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[Crossref] [PubMed]

E. Bennett, R. Kopace, A. Stein, and H. Wen, “A grating-based single shot x-ray phase contrast and diffraction method for in vivo imaging,” Med. Phys. 37, 6047–6054 (2010).
[Crossref] [PubMed]

2008 (2)

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2d gratings,” Int. J. Biomed. Imaging 2008827152 (2008).
[PubMed]

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

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, 258–261 (2006).
[Crossref]

2005 (2)

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
[Crossref]

1981 (1)

D. F. Jackson and D. Hawkes, “X-ray attenuation coefficients of elements and mixtures,” Phys. Rep. 70, 169–233 (1981).
[Crossref]

1979 (1)

G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
[Crossref] [PubMed]

Abis, M.

T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

Achterhold, K.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
[Crossref]

An-ton, G.

Auweter, S.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
[Crossref]

Baehr, A.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Bartl, P.

Baumann, J.

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

Bayer, F.

Bennett, E.

E. Bennett, R. Kopace, A. Stein, and H. Wen, “A grating-based single shot x-ray phase contrast and diffraction method for in vivo imaging,” Med. Phys. 37, 6047–6054 (2010).
[Crossref] [PubMed]

Bevins, N.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
[Crossref] [PubMed]

Birnbacher, L.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Physics in Medicine and Biology 58, R1–R35 (2013).
[Crossref]

Bun, O.

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

Bunk, O.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microscopy 232, 145–157 (2008).
[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, 258–261 (2006).
[Crossref]

Chabior, M.

A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

Chen, G.-H.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
[Crossref] [PubMed]

Cloetens, P.

Coan, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Physics in Medicine and Biology 58, R1–R35 (2013).
[Crossref]

David, C.

T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microscopy 232, 145–157 (2008).
[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, 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, 6296–6304 (2005).
[Crossref] [PubMed]

Den, T.

Diaz, A.

Dmochewitz, M.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Donath, T.

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

Druart, G.

Engelhardt, M.

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

Fingerle, A. A.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Finkenthal, M.

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University), 2nd ed.

Fujino, S.

Gleich, B.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Gödel, K. C.

Goodman, J.

J. Goodman, Statistical Optics (John Wiley and Sons, Inc., 1985).

Gromann, L. B.

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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
[Crossref]

Kunka, D.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

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G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
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N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
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Liu, X.

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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
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L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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Masterson, M. E.

G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
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McDonald, S.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
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Meiser, J.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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Meyer, P.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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Miller, D. W.

G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
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Muenzel, D.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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Pfeiffer, F.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
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M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microscopy 232, 145–157 (2008).
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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, 258–261 (2006).
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Pralow, T.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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Proksa, R.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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Qi, Z.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
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Reiser, M.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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Rieger, J.

Rindt, K.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Ritter, A.

Rizzi, J.

Rummeny, E. J.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Sarapata, A.

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

Sato, G.

Scherer, K.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Schroer, C.

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

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

Schroeter, T. J.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Schröter, T.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

Schuster, M.

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

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

Setomoto, Y.

Shimura, T.

Siewerdsen, J. H.

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

Silva, P.

Silva, P. D.

Stampanoni, M.

T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[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, 6296–6304 (2005).
[Crossref] [PubMed]

Stayman, J. W.

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

Stein, A.

E. Bennett, R. Kopace, A. Stein, and H. Wen, “A grating-based single shot x-ray phase contrast and diffraction method for in vivo imaging,” Med. Phys. 37, 6047–6054 (2010).
[Crossref] [PubMed]

Stutman, D.

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Physics in Medicine and Biology 58, R1–R35 (2013).
[Crossref]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
[Crossref]

Takai, H.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
[Crossref]

Tang, S.

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast ct compared with the conventional ct: Spectrum of noise equivalent quanta neq(k),” Med. Phys. 39, 4367–4382 (2012).
[Crossref]

Tang, X.

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast ct compared with the conventional ct: Spectrum of noise equivalent quanta neq(k),” Med. Phys. 39, 4367–4382 (2012).
[Crossref]

Terui, Y.

Teshima, T.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University), 2nd ed.

Thüring, T.

T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

van der Heijden, H.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Velroyen, A.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University), 2nd ed.

Vincent, G.

Wang, G.

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2d gratings,” Int. J. Biomed. Imaging 2008827152 (2008).
[PubMed]

Wang, Z.

T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[Crossref] [PubMed]

Watanabe, H.

Weber, T.

Weitkamp, T.

Wen, H.

E. Bennett, R. Kopace, A. Stein, and H. Wen, “A grating-based single shot x-ray phase contrast and diffraction method for in vivo imaging,” Med. Phys. 37, 6047–6054 (2010).
[Crossref] [PubMed]

White, D. R.

G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
[Crossref] [PubMed]

Wieberneit, N.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Willer, K.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Willner, M.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref]

A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
[Crossref]

Woodard, H. Q.

G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, and J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979).
[Crossref] [PubMed]

Wu, X.

Wu, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[Crossref] [PubMed]

Wyatt, C.

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2d gratings,” Int. J. Biomed. Imaging 2008827152 (2008).
[PubMed]

Yamaguchi, K.

Yamazaki, A.

Yan, A.

Yang, Y.

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast ct compared with the conventional ct: Spectrum of noise equivalent quanta neq(k),” Med. Phys. 39, 4367–4382 (2012).
[Crossref]

Yaroshenko, A.

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
[Crossref] [PubMed]

Yashiro, W.

Zambelli, J.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
[Crossref] [PubMed]

Zang, A.

Zhang, K.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[Crossref] [PubMed]

Zhu, P.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
[Crossref] [PubMed]

Ziegler, E.

Appl. Phys. Express (1)

A. Momose, “X-ray phase imaging using lau effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

Int. J. Biomed. Imaging (1)

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2d gratings,” Int. J. Biomed. Imaging 2008827152 (2008).
[PubMed]

J. Microscopy (1)

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

Jpn. J. Appl. Phys. (2)

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42, 866 (2003).
[Crossref]

Med. Phys. (6)

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G.-H. Chen, “Multicontrast x-ray computed tomography imaging using talbot-lau interferometry without phase stepping,” Med. Phys. 39, 424–428 (2012).
[Crossref] [PubMed]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast ct compared with the conventional ct: Spectrum of noise equivalent quanta neq(k),” Med. Phys. 39, 4367–4382 (2012).
[Crossref]

E. Bennett, R. Kopace, A. Stein, and H. Wen, “A grating-based single shot x-ray phase contrast and diffraction method for in vivo imaging,” Med. Phys. 37, 6047–6054 (2010).
[Crossref] [PubMed]

A. Yan, X. Wu, and H. Liu, “A general theory of interference fringes in x-ray phase grating imaging,” Med. Phys. 42, 3036–3047 (2015).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, O. Bun, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, “High energy x-ray phase contrast ct using glancing-angle grating interferometers,” Med. Phys. 41, 021904 (2014).
[Crossref] [PubMed]

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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, 258–261 (2006).
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W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
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T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X–ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

A. Yan, X. Wu, and H. Liu, “Predicting visibility of interference fringes in x-ray grating interometry,” Opt. Express 24, 15927–15939 (2016).
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H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based x-ray phase-contrast imaging using fourier transform phase retrieval,” Opt. Express 19, 3339–3346 (2011).
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J. Rizzi, P. Mercere, M. Idir, P. D. Silva, G. Vincent, and J. Primot, “X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer,” Opt. Express 21, 17340–17351 (2013).
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N. Morimoto, S. Fujino, A. Yamazaki, Y. Ito, T. Hosoi, H. Watanabe, and T. Shimura, “Two dimensional x-ray phase imaging using single grating interferometer with embedded x-ray targets,” Opt. Express 23, 16582–16588 (2015).
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A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic x-ray sources,” Opt. Express 22, 30394–30409 (2014).
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Physics in Medicine and Biology (1)

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Physics in Medicine and Biology 58, R1–R35 (2013).
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P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc Natl. Acad. Sci. USA 107, 13576–13581 (2010).
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[Crossref] [PubMed]

Sci. Rep. (3)

L. B. Gromann, F. D. Marco, K. Willer, P. B. Noël, K. Scherer, B. Renger, B. Gleich, K. Achterhold, A. A. Fingerle, D. Muenzel, S. Auweter, K. Hellbach, M. Reiser, A. Baehr, M. Dmochewitz, T. J. Schroeter, F. J. Koch, P. Meyer, D. Kunka, J. Mohr, A. Yaroshenko, H.-I. Maack, T. Pralow, H. van der Heijden, R. Proksa, T. Koehler, N. Wieberneit, K. Rindt, E. J. Rummeny, F. Pfeiffer, and J. Herzen, “In-vivo x-ray dark-field chest radiography of a pig,” Sci. Rep. 7, 4807 (2017).
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T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, “X-ray phase-contrast imaging at 100 kev on a conventional source,” Sci. Rep. 4, 5198 (2014).
[Crossref]

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental realization of high-sensitivity laboratory x-ray grating-based phase-contrast computed tomography,” Sci. Rep. 6, 24022 (2016).
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Figures (8)

Fig. 1
Fig. 1 Schematic of an x-ray phase grating interferometer with an X-ray source and source grating.
Fig. 2
Fig. 2 3D manifest of the phantom employed in the simulations.
Fig. 3
Fig. 3 26 kVp x-ray effective spectrum employed in the simulations.
Fig. 4
Fig. 4 Plots of the ray-sums: The design energy is set to ED = 17 keV for π/2-grating interferometer with 26 kVp x-ray effective spectrum shown in Fig. 3. In this simulation, the phantom is made of homogeneous glandular tissue with the shape as shown in Fig. 2 except it has only one layer (layer I). The total height of the phantom is 40.5 mm. In the plot, the solid blue line, p D Theo, represents the theoretical ray-sum at design energy ED. The dash-dot green line, pPoly(x), is the polychromatic ray-sum directly computed from A Poly 2 ( x ) ( p Poly ( x ) = log ( A Poly 2 ( x ) ), which is derived from the zero-th diffracted order of the fringe pattern. The dashed red line, p D Iter ( x ), is the retrieved ray-sum at design energy ED using Algorithm 1. After 11 iterations, the relative error falls in 0.03%.
Fig. 5
Fig. 5 Plots of the fringe shifts: The solid blue line ϕ 1 , D Theo ( x ) represents the true theoretical values which are set to ±45° degrees at the two bumps. The dash-dot green line, ϕ1,Poly, is the polychromatic fringe phase shifts retrieved from the simulated fringe pattern by using the Fourier analysis method. The dashed red line, ϕ 1 , D Iter ( x ), is the iterative solution using Eq. (13). After 29 iteration steps, the relative error falls in 0.11%.
Fig. 6
Fig. 6 Plots of the fringe shifts with different f (E) approximation: In this simulation, the phantom is reset to have multiple layers of different tissues with the shape shown in Fig. 2. There are total of 4 layers. The layers I, II, III, and IV represent 100% glandular tissue, 75% glandular and 25% adipose tissues, 50% glandular and 50% adipose tissues, and 25% glandular and 75% adipose tissues respectively. The total height of the phantom still 40.5 mm. The solid blue line ϕ 1 , D Theo ( x ) represents the true theoretical values which are set to ±45° degrees at the two bumps. The dash-dot green line, ϕ1,Poly, is the polychromatic fringe phase shifts retrieved from the simulated fringe pattern by using the Fourier analysis method. The retrieved iterative solution using Eq. (13) with different position-dependent effective spectrums Θ(E; x) corresponding to f (E) = En, with n = 2, 2.5, 3, and 3.5 are shown in different colors in the figure.
Fig. 7
Fig. 7 Plots of the fringe shifts with different f (E) approximation: In this simulation, a part layer IV of the previous phantom is replaced with a 3.5 mm layer of aluminum. All other setups are the same. The solid blue line ϕ 1 , D Theo ( x ) represents the true theoretical values which are set to ±45° degrees at the two bumps. The dash-dot green line, ϕ1,Poly, is the polychromatic fringe phase shifts retrieved from the simulated fringe pattern by using the Fourier analysis method. The retrieved iterative solution using Eq. (13) with different position-dependent effective spectrums Θ(E; x) corresponding to f (E) = En, with n = 2, 2.5, 3, and 3.5 are shown in different colors in the figure.
Fig. 8
Fig. 8 Performance of the iterative Eq. (13) with noisy data. The setup and phantom is the same as Fig. 6. We add some Gaussian white noise (5%) to fringe intensity image I and the reference grating only image. The solid blue line ϕ 1 , D Theo ( x ) represents the true theoretical values which are set to ±45° degrees. The dash-dot green line, ϕ1,Poly, is the noisy polychromatic fringe phase shifts retrieved from the simulated fringe pattern by using the Fourier analysis method. The dashed red line, ϕ 1 , D Iter ( x ), is the iterative solution using Eq. (13) with f (E) = E−2.5. The SNRs of ϕ1,Poly(x) and ϕ 1 , D Iter ( x ) at the left bump are 32.8 and 52.7 respectively.

Equations (14)

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I ( M g x , M g y ; E ) = I in M g 2 × m C m ( E ) γ ( m ) × A 2 ( x , y ; E ) × exp [ i ( 2 π m x p 1 + ϕ m ( x , y ; E ) ) ] ,
ϕ m ( x , y ; E ) = m × r e ( R 2 / M g ) p 1 × c 2 h 2 E 2 × ρ e , p ( x , y ) x ,
I ( M g x , M g y ) = I in M g 2 m D ( E ) C m ( E ) A 2 ( x , y ; E ) exp [ i π E D 2 E 2 ϕ m , D ( x , y ) ] dE × × γ ( m ) × exp [ i 2 π m x p 1 ] ,
A Poly 2 ( x , y ) = D ( E ) × exp [ p D ( x , y ) × f ( E ) f ( E D ) ] dE .
H ( p ( x , y ) = E D ( E ) × exp [ f ( E ) f ( E D ) p ( x , y ) ] dE ,
H ( p ( x , y ) ) = E D ( E ) × f ( E ) f ( E D ) × exp [ f ( E ) f ( E D ) p ( x , y ) ] dE .
δ ( x , y ) = Δ ( x , y ) H ( p k ( x , y ) ) = A Poly 2 ( x , y ) H ( p k ( x , y ) ) H ( p k ( x , y ) ) .
Θ ( E ; x , y ) = D ( E ) A 2 ( x , y ; E ) D ( E ) A 2 ( x , y ; E ) dE = D ( E ) A 2 ( x , y ; E ) A Poly 2 ( x , y ) .
I ( M g x , M g y ) = I in M g 2 A Poly 2 ( x , y ) m Θ ( E ; x , y ) C m ( E ) exp [ i E D 2 E 2 ϕ m , D ( x , y ) ] dE × × γ ( m ) × exp [ π 2 π m x p 1 ] .
ϕ m , Poly ( x , y ) = Arg { Θ ( E ; x , y ) C m ( E ) × exp [ i E D 2 E 2 ϕ m , D ( x , y ) ] dE Θ ( E ; x , y ) C m ( E ) dE } ,
C ( m ; λ ) = { 1 , if m = 0 , ( 1 cos Δ ϕ ( E ) ) × ( 1 ) 4 k λ R 2 / M g p 1 2 sin [ 4 k 2 λ R 2 / M g p 1 2 ] k π , if m = 2 k , k 0 , i sin Δ ϕ ( E ) × sin [ ( 4 π λ R 2 / M g p 1 2 ) × ( ( k + 1 / 2 ) 2 ] ) π ( k + 1 / 2 ) , if m = 2 k + 1 .
Q m ( n ; x , y ) Θ ( E ; x , y ) C m ( E ) E D 2 n E 2 n dE , n = 1 , 2 , 3 , .
ϕ m , D ( q + 1 ) ( x , y ) = tan [ ϕ m , Poly ( x , y ) ] × [ k = 0 q ( 1 ) k ( 2 k ) ! × Q m ( 2 k ) Q m ( 1 ) × ( ϕ m , D ( q ) ( x , y ) ) 2 k ] k = 1 q ( 1 ) k ( 2 k + 1 ) ! × Q m ( 2 k + 1 ) Q m ( 1 ) × ( ϕ m , D ( q ) ( x , y ) ) 2 k + 1 .
Q 1 ( n ; x , y ) i 2 π Θ ( E ; x , y ) × sin 2 ( π E D 2 E ) × E D 2 n E 2 n dE , n = 1 , 2 , 3 , .

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