Abstract

The interference fringe visibility is a common figure of merit in designs of x-ray grating-based interferometers. Presently one has to resort to laborious computer simulations to predict fringe visibility values of interferometers with polychromatic x-ray sources. Expanding the authors’ previous work on Fourier expansion of the intensity fringe pattern, in this work the authors developed a general quantitative theory to predict the intensity fringe pattern in closed-form formulas, which incorporates the effects of partial spatial coherence, spectral average and detector pixel re-binning. These formulas can be used to predict the fringe visibility of a Talbot-Lau interferometer with any geometry configuration and any source spectrum.

© 2016 Optical Society of America

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    [Crossref] [PubMed]

2015 (4)

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

R. Miklos, M. S. Nielsen, H. Einarsdóttir, R. Feidenhans’l, and R. Lametsch, “Novel x-ray phase-contrast tomography method for quantitative studies of heat induced structural changes in meat,” Meat Sci. 100, 217–221 (2015).
[Crossref]

A. Yan, X. Wu, and H. Liu, “A general theory of interference fringes in x-ray phase grating imaging,” Med. Phys. 42(6), 3036–3047 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

2014 (2)

2013 (4)

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]

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]

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

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

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 (7)

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast CT compared with the conventional CT - Noise power spectrum NPS(k),” Med. Phys. 38, 4386–4395 (2011).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (2011).
[Crossref] [PubMed]

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray phase imaging using Lau effects,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

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).
[Crossref] [PubMed]

J. Rizzi, T. Weitkamp, N. Guerineau, M. Idir, P. Mercere, G. Druart, G. Vincent, P. Silva, and J. Primot, “Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36, 1398–1400 (2011).
[Crossref] [PubMed]

G. Sato, T. Kondoh, H. Itoh, S. Handa, K. Yamaguchi, T. Nakamura, K. Nagai, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube,” Opt. Lett. 36, 3551–3553 (2011).
[Crossref] [PubMed]

T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube,” Opt. Lett. 36, 3551–3553 (2011).
[Crossref] [PubMed]

2010 (4)

G. H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

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]

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]

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]

2009 (1)

Z. T. Wang, K. J. Kang, Z. F. Huang, and Z. Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

2008 (4)

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of x-ray scatteringâǍŤinitial results,” IEEE Trans. Med. Imaging. 27, 997–1002 (2008).
[Crossref] [PubMed]

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2D gratings,” Int. J. Biomed. Imaging 2008, 827152 (2008).
[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]

X. Wu and H. Liu, “Phase-space evolution of x-ray coherence in phase-sensitive imaging,” Appl. Opt. 47, E44–E52 (2008).
[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, 258–261 (2006).
[Crossref]

2005 (2)

2004 (1)

X. Wu and H. Liu, “A new theory of phase-contrast x-ray imaging based on Wigner distributions,” Med. Phys. 31, 2378–2384 (2004).
[Crossref] [PubMed]

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]

1965 (1)

1960 (1)

J. M. Cowley and A. F. Moodie, “Fourier images IV: The phase grating,” Proc. Phys. Soc., London 76(3), 378–384 (1960).
[Crossref]

1957 (1)

J. M. Cowley and A. F. Moodie, “Fourier images I: The point source,” Proc. Phys. Soc., London, Sect. B 70(5), 486–496 (1957).
[Crossref]

Anton, G.

A. Ritter, P. Bartl, F. Bayer, K. C. Gödel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent x-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Auweter, S.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[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.

A. Ritter, P. Bartl, F. Bayer, K. C. Gödel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent x-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Bech, M.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

Beckmann, M. W.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

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]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of x-ray scatteringâǍŤinitial results,” IEEE Trans. Med. Imaging. 27, 997–1002 (2008).
[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]

G. H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

Bravin, A.

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

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]

Carroll, S.

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of x-ray scatteringâǍŤinitial results,” IEEE Trans. Med. Imaging. 27, 997–1002 (2008).
[Crossref] [PubMed]

Chen, G. H.

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]

Chen, Z. Q.

Z. T. Wang, K. J. Kang, Z. F. Huang, and Z. Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Cloetens, P.

Coan, P.

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

Conlon, T. M.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

Cowley, J. M.

J. M. Cowley and A. F. Moodie, “Fourier images IV: The phase grating,” Proc. Phys. Soc., London 76(3), 378–384 (1960).
[Crossref]

J. M. Cowley and A. F. Moodie, “Fourier images I: The point source,” Proc. Phys. Soc., London, Sect. B 70(5), 486–496 (1957).
[Crossref]

David, C.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (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]

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[Crossref]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast CT compared with the conventional CT - Noise power spectrum NPS(k),” Med. Phys. 38, 4386–4395 (2011).
[Crossref] [PubMed]

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]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast CT compared with the conventional CT - Noise power spectrum NPS(k),” Med. Phys. 38, 4386–4395 (2011).
[Crossref] [PubMed]

Terui, Y.

Teshima, T.

Thüring, T.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (2011).
[Crossref] [PubMed]

Trippel, M.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (2011).
[Crossref] [PubMed]

Uder, M.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Velroyen, A.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

Vincent, G.

Wachter, D. L.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Wang, G.

M. Jiang, C. Wyatt, and G. Wang, “X-ray phase-contrast imaging with three 2D gratings,” Int. J. Biomed. Imaging 2008, 827152 (2008).
[Crossref] [PubMed]

Wang, Z.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (2011).
[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]

Wang, Z. T.

Z. T. Wang, K. J. Kang, Z. F. Huang, and Z. Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Watanabe, H.

Weber, T.

A. Ritter, P. Bartl, F. Bayer, K. C. Gödel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent x-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

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]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of x-ray scatteringâǍŤinitial results,” IEEE Trans. Med. Imaging. 27, 997–1002 (2008).
[Crossref] [PubMed]

Wenkel, E.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Winthrop, J. T.

Worthington, C. R.

Wu, X.

A. Yan, X. Wu, and H. Liu, “A general theory of interference fringes in x-ray phase grating imaging,” Med. Phys. 42(6), 3036–3047 (2015).
[Crossref] [PubMed]

X. Wu and H. Liu, “Phase-space evolution of x-ray coherence in phase-sensitive imaging,” Appl. Opt. 47, E44–E52 (2008).
[Crossref] [PubMed]

X. Wu and H. Liu, “A new theory of phase-contrast x-ray imaging based on Wigner distributions,” Med. Phys. 31, 2378–2384 (2004).
[Crossref] [PubMed]

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 2008, 827152 (2008).
[Crossref] [PubMed]

Yamaguchi, K.

Yamazaki, A.

Yan, A.

A. Yan, X. Wu, and H. Liu, “A general theory of interference fringes in x-ray phase grating imaging,” Med. Phys. 42(6), 3036–3047 (2015).
[Crossref] [PubMed]

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]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast CT compared with the conventional CT - Noise power spectrum NPS(k),” Med. Phys. 38, 4386–4395 (2011).
[Crossref] [PubMed]

Yaroshenko, A.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

Yashiro, W.

Yildirim, A.

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

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]

G. H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

Zang, A.

A. Ritter, P. Bartl, F. Bayer, K. C. Gödel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent x-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

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. Opt. (1)

Appl. Phys. Express (1)

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray phase imaging using Lau effects,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

Appl. Phys. Lett. (1)

Z. T. Wang, K. J. Kang, Z. F. Huang, and Z. Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

IEEE Trans. Med. Imaging. (1)

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of x-ray scatteringâǍŤinitial results,” IEEE Trans. Med. Imaging. 27, 997–1002 (2008).
[Crossref] [PubMed]

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 2008, 827152 (2008).
[Crossref] [PubMed]

Investigative Radiology (1)

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Investigative Radiology 46(12), 801–806 (2011).
[Crossref] [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]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

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]

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

Meat Sci. (1)

R. Miklos, M. S. Nielsen, H. Einarsdóttir, R. Feidenhans’l, and R. Lametsch, “Novel x-ray phase-contrast tomography method for quantitative studies of heat induced structural changes in meat,” Meat Sci. 100, 217–221 (2015).
[Crossref]

Med. Phys. (6)

A. Yan, X. Wu, and H. Liu, “A general theory of interference fringes in x-ray phase grating imaging,” Med. Phys. 42(6), 3036–3047 (2015).
[Crossref] [PubMed]

X. Wu and H. Liu, “A new theory of phase-contrast x-ray imaging based on Wigner distributions,” Med. Phys. 31, 2378–2384 (2004).
[Crossref] [PubMed]

X. Tang, Y. Yang, and S. Tang, “Characterization of imaging performance in differential phase contrast CT compared with the conventional CT - Noise power spectrum NPS(k),” Med. Phys. 38, 4386–4395 (2011).
[Crossref] [PubMed]

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]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

Opt. Express (7)

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]

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]

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).
[Crossref] [PubMed]

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]

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).
[Crossref] [PubMed]

G. H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

A. Ritter, P. Bartl, F. Bayer, K. C. Gödel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent x-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014).
[Crossref] [PubMed]

Opt. Lett. (4)

Phys. Med. Biol. (2)

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

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Durst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Phys. Rev. A (1)

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]

Proc. Natl. Acad. Sci. USA (1)

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]

Proc. Phys. Soc., London (1)

J. M. Cowley and A. F. Moodie, “Fourier images IV: The phase grating,” Proc. Phys. Soc., London 76(3), 378–384 (1960).
[Crossref]

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[Crossref]

Sci. Rep. (1)

A. Yaroshenko, K. Hellbach, A. Yildirim, T. M. Conlon, I. E. Fernandez, M. Bech, A. Velroyen, F. G. Meinel, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “Improved In vivo Assessment of Pulmonary Fibrosis in Mice using X-Ray Dark-Field Radiography,” Sci. Rep. 5, 17492 (2015).
[Crossref] [PubMed]

Other (1)

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Figures (4)

Fig. 1
Fig. 1 Schematic of an x-ray phase grating interferometer with a microfocus source
Fig. 2
Fig. 2 Value of μ in ( λ R 2 m / M g p 1 ) with different m with the constructive interference condition Eq. (14), where p0 is the period of the micro-source array, and a is the radius of the individual micro-source.
Fig. 3
Fig. 3 Utilized x-ray spectrum
Fig. 4
Fig. 4 (a). The fringe image from the computer simulation. In the simulation, R1 = 8.4cm, R2 = 117.6cm, the phase grating period p1 = 5μm. The source is a 25 × 25 array of micro-tungsten-targets. The source array has a bidirectional period p0 = 5.36μm, and each micro-target has a diameter 2a = 2μm. The source array operate at 35 kV and with a 50μm rhodium filter. The maximum, minimum and thereby the visibility of the fringes are 1.5746, 0.5673 and 0.4703 respectively. (b). The fringe image obtained from Eq. (19).

Equations (26)

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V = I max I min I max + I min .
Z T 2 D = n p 1 2 8 λ ,
G 1 ( r ) = exp ( i Δ ϕ h ( r / p 1 r / p 1 1 / 2 ) ) , h ( s ) = { 1 , if s [ 1 / 2 , 0 ) 2 [ 0 , 1 / 2 ) 2 , 0 , otherwise ,
I ˜ λ ( u M g ; R 1 + R 2 ) = I in , λ μ in ( λ R 2 u M g ) G 1 ( s + λ R 2 u 2 M g ) G 1 ( s λ R 2 u 2 M g ) exp ( i 2 π s u ) d s ,
I ˜ λ ( u M g ; R 1 + R 2 ) = I in , λ m 2 μ in ( λ R 2 m M g p 1 ) C ( m ; λ ) δ ( u m p 1 ) ,
C ( m ; λ ) { 1 , if m = n = 0 , 0 , if m + n = odd , 2 ( 1 cos Δ ϕ ) f ( k ) f ( l ) , if m = 2 k , n = 2 l , sin Δ ϕ sin [ ( 4 π λ R 2 / M g p 1 2 ) ( ( k + 1 / 2 ) 2 + ( l + 1 / 2 ) 2 ) ] π 2 ( k + 1 / 2 ) ( l + 1 / 2 ) , if m = 2 k + 1 , n = 2 l + 1 ,
f ( k ) = ( 1 ) 4 k λ R 2 / M g p 1 2 { 1 2 , if k = 0 , sin ( 4 k 2 π λ R 2 / M g p 1 2 ) k π , otherwise .
μ in ( λ R 2 u M g ) = I source ( s ) exp ( i 2 π R 2 u s / M g R 1 ) d s I source ( s ) d s .
I λ ( r ; R 1 + R 2 ) = I in , λ M g 2 m 2 μ in ( λ R 2 m M g p 1 ) C ( m ; λ ) exp ( i 2 π m r M g p 1 ) .
I source ( s ) = I s 0 k = N x N x l = N y N y Circ ( | s k p 0 e x l p 0 e y | a ) ,
Circ ( r ) = { 1 , if | r | 1 , 0 , otherwise ,
μ in ( λ R 2 u / M g ) = 2 J 1 ( 2 π a ( M g 1 ) | u | / M g ) 2 π a ( M g 1 ) | u | / M g W ( λ R 2 u / M g ) ,
W ( λ R 2 u / M g ) = sin ( ( 2 N x + 1 ) π ( M g 1 ) p 0 u x M g ) sin ( ( 2 N y + 1 ) π ( M g 1 ) p 0 u y M g ) ( 2 N x + 1 ) ( 2 N y + 1 ) sin ( π ( M g 1 ) p 0 u x M g ) sin ( π ( M g 1 ) p 0 u y M g ) .
p 0 = R 1 R 2 M g p 1 .
μ in ( λ R 2 m M g p 1 ) = 2 J 1 ( 2 π m 2 + n 2 a / p 0 ) 2 π m 2 + n 2 a / p 0 ,
I ( r ; R 1 + R 2 ) = I in M g 2 m 2 V ( m ) exp ( i 2 π m r M g p 1 ) , V ( m ) S ( λ ) μ in ( λ R 2 m / M g p 1 ) C ( m ; λ ) d λ ,
I ( r ) = I in M g 2 { 1 + 2 ( m > 0 , n 0 ) V ( m ) cos ( 2 π m x + n y M g p 1 ) + + 2 ( m > 0 , n = 0 ) V ( m ) [ cos ( 2 π m x M g p 1 ) + cos ( 2 π m y M g p 1 ) ] } .
I ( r ) = I in M g 2 { 1 + 2 ( m > 0 , n 0 ) V ( m ) sinc ( m p d M g p 1 ) sinc ( n p d M g p 1 ) cos ( 2 π m x + n y M g p 1 ) + + 2 ( m > 0 , n = 0 ) V ( m ) sinc ( m p d M g p 1 ) [ cos ( 2 π m x M g p 1 ) + cos ( 2 π m y M g p 1 ) ] } .
I ( r ; R 1 + R 2 ) = I in M g 2 { 1 + 2 × 0.168 × [ cos ( 2 π x + y M g p 1 ) + cos ( 2 π x y M g p 1 ) ] 2 × 0.3333 × [ cos ( 2 π 2 x M g p 1 ) + cos ( 2 π 2 y M g p 1 ) ] } .
I ( r ; R 1 + R 2 ) = I in M g 2 { 1 + 2 × 0.133 × [ cos ( 2 π x + y M g p 1 ) + cos ( 2 π x y M g p 1 ) ] 2 × 0.0182 × [ cos ( 2 π 2 x M g p 1 ) + cos ( 2 π 2 y M g p 1 ) ] } .
I source ( s ) = Q 2 π σ 2 k = N x N x l = N y N y exp [ ( s k p 0 e x l p 0 e y ) 2 2 σ 2 ] ,
μ in ( λ R 2 m M g p 1 ) = exp ( 2 π 2 ( m 2 + n 2 ) σ 2 p 0 2 ) .
C ( m ; λ ) = { 1 , if m = 0 , ( 1 cos Δ ϕ ) ( 1 ) 4 k λ R 2 / M g p 1 2 sin ( 4 k 2 π λ R 2 / M g p 1 2 ) k π if m = 2 k , k 0 , i sin Δ ϕ sin [ ( 4 π λ R 2 / M g p 1 2 ) ( k + 1 / 2 ) 2 ] π ( k + 1 / 2 ) , if m = 2 k + 1 ,
I ( x ) = I in M g 2 { 1 + 2 k > 0 [ V ( 2 k ) sinc ( 2 k p d M g p 1 ) cos ( 2 π 2 k x M g p 1 ) + + V ( 2 k 1 ) sinc ( ( 2 k 1 ) p d M g p 1 ) sin ( 2 π ( 2 k 1 ) x M g p 1 ) ] } , V ( m ) S ( λ ) μ i n ( λ R 2 m / M g p 1 ) D ( m ; λ ) d λ ,
Circ ( | s | a ) exp ( i 2 π R 2 u M g R 1 ) d s = M g a R 1 R 2 | u | J 1 ( 2 π a R 2 | u | M g R 1 ) ,
μ in ( λ R 2 u M g ) = 2 J 1 ( 2 π a ( M g 1 ) | u | / M g ) 2 π a ( M g 1 ) | u | / M g × × m = N x N x n = N y N y exp [ i 2 π ( M g 1 ) p 0 ( m u x + n u y ) / M g ] ( 2 N x + 1 ) ( 2 N y + 1 ) .

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