Abstract

Microscopy techniques using visible photons, x-rays, neutrons, and electrons have made remarkable impact in many scientific disciplines. The microscopic data can often be expressed as the convolution of the spatial distribution of certain properties of the specimens and the inherent response function of the imaging system. The x-ray grating interferometer (XGI), which is sensitive to the deviation angle of the incoming x-rays, has attracted significant attention in the past years due to its capability in achieving x-ray phase contrast imaging with low brilliance source. However, the comprehensive and analytical theoretical framework is yet to be presented. Herein, we propose a theoretical framework termed angular signal radiography (ASR) to describe the imaging process of the XGI system in a classical, comprehensive and analytical manner. We demonstrated, by means of theoretical deduction and synchrotron based experiments, that the spatial distribution of specimens’ physical properties, including absorption, refraction and scattering, can be extracted by ASR in XGI. Implementation of ASR in XGI offers advantages such as simplified phase retrieval algorithm, reduced overall radiation dose, and improved image acquisition speed. These advantages, as well as the limitations of the proposed method, are systematically investigated in this paper.

© 2016 Optical Society of America

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2015 (1)

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (4)

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express 21(16), 19401–19411 (2013).
[Crossref] [PubMed]

2012 (3)

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

P. C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three x-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express 20(3), 2789–2805 (2012).
[Crossref] [PubMed]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (1)

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

2009 (3)

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[Crossref] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[Crossref] [PubMed]

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(9), 094105 (2009).
[Crossref]

2008 (3)

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16(5), 3223–3241 (2008).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

2007 (1)

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

2006 (4)

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

2005 (2)

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]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

2003 (3)

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

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

Adamo, N. M.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Anastasio, M. A.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Andrews, J. C.

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

Arfelli, F.

Auweter, S.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Bamberg, F.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Bao, Y.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Bech, M.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bellotti, R.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

Bennett, E. E.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[Crossref] [PubMed]

Brankov, J. G.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Bravin, A.

Brey, E. M.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bukreeva, I.

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

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]

Cedola, A.

Chabior, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Chapman, D.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

Chapman, L. D.

Chen, B.

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Chen, G. H.

Chen, H.

Chen, L.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Chen, Z. Q.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

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(9), 094105 (2009).
[Crossref]

Chou, C. Y.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

Cloetens, P.

Coan, P.

Connor, D. M.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

David, C.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

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]

DeLuca, A. M.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Diaz, A.

Diemoz, P. C.

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Endo, T.

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

Fujino, S.

Galatsanos, N. P.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Gao, B.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Gao, K.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Z. Wang, K. Gao, D. Wang, Z. Wu, H. Chen, S. Wang, and Z. Wu, “Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors,” Opt. Lett. 39(4), 877–879 (2014).
[Crossref] [PubMed]

Garrett, J.

Ge, Y.

Glaser, C.

Gomella, A. A.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Gureyev, T. E.

Hamaishi, Y.

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

Harada, J.

Harasse, S.

Hasnah, M.

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

Hattori, T.

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

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

Hegedus, M. M.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[Crossref] [PubMed]

Herzen, J.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Holzner, C.

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

Honda, C.

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

Hong, Y. L.

Hosoi, T.

Hu, T.

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Hu, T. D.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Huang, W.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Huang, W. X.

P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
[Crossref] [PubMed]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Huang, Z. F.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

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(9), 094105 (2009).
[Crossref]

Ito, T.

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

Jiang, X. L.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

Ju, Z.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Ju, Z. Q.

Kang, K. J.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

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(9), 094105 (2009).
[Crossref]

Kawamoto, S.

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

Khelashvili, G.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

Kido, K.

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

Kiyohara, J.

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

Koyama, I.

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

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Kuwabara, H.

Lang, S.

Le Duc, G.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

Li, K.

Li, P.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Liu, X.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

Maikusa, H.

Makifuchi, C.

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

Marone, F.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

McDonald, S. A.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

Menk, R. H.

Miao, H.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Miller, P. R.

Modregger, P.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

Mohr, J.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

Momose, A.

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

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19(9), 8423–8432 (2011).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[Crossref] [PubMed]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

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

Morgan, N. Y.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Morimoto, N.

Muehleman, C.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Nagashima, M.

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

Nagatsuka, S.

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

Nelson, J.

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

Nesterets, Y. I.

Noda, D.

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

Ohshima, K.

Oltulu, O.

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Patel, A.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

Pelliccia, D.

Pfeiffer, F.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

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]

Pianetta, P.

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

Pinzer, B. R.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

Pogany, A.

Rack, A.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

Rapacchi, S.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[Crossref] [PubMed]

Reiser, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Rigon, L.

Scattarella, F.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

Shao, Q.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Shimura, T.

Shu, H.

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Stampanoni, M.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett. 108(4), 048101 (2012).
[Crossref] [PubMed]

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 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(16), 6296–6304 (2005).
[Crossref] [PubMed]

Stevenson, A. W.

Suzuki, Y.

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

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

Tafforeau, P.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

Takai, K.

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

Takeda, Y.

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[Crossref] [PubMed]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

Takeuchi, A.

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

Tanaka, J.

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

Wang, D.

Wang, J.

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Wang, J. Y.

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Wang, S.

Wang, Y.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Wang, Z.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Z. Wang, K. Gao, D. Wang, Z. Wu, H. Chen, S. Wang, and Z. Wu, “Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors,” Opt. Lett. 39(4), 877–879 (2014).
[Crossref] [PubMed]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

Wang, Z. C.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

Wang, Z. T.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

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(9), 094105 (2009).
[Crossref]

Watanabe, H.

Wei, Z.

Weitkamp, T.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an x-ray grating interferometer,” Opt. Express 19(3), 1691–1698 (2011).
[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]

Wen, H.

H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, “Fourier X-ray scattering radiography yields bone structural information,” Radiology 251(3), 910–918 (2009).
[Crossref] [PubMed]

Wernick, M. N.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

Wiebe, S.

Wilkins, S. W.

Willner, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based x-ray phase contrast for biomedical imaging applications,” Z. Med. Phys. 23(3), 176–185 (2013).
[Crossref] [PubMed]

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Wu, Z.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Z. Wang, K. Gao, D. Wang, Z. Wu, H. Chen, S. Wang, and Z. Wu, “Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors,” Opt. Lett. 39(4), 877–879 (2014).
[Crossref] [PubMed]

Z. Wang, K. Gao, D. Wang, Z. Wu, H. Chen, S. Wang, and Z. Wu, “Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors,” Opt. Lett. 39(4), 877–879 (2014).
[Crossref] [PubMed]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Wu, Z. Y.

P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
[Crossref] [PubMed]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Yang, Y.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Yashiro, W.

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

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19(9), 8423–8432 (2011).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17(15), 12540–12545 (2009).
[Crossref] [PubMed]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[Crossref]

Yin, H. X.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

Yuan, Q.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Yuan, Q. X.

P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
[Crossref] [PubMed]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Zanette, I.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose x-ray tomography,” Proc. Natl. Acad. Sci. U.S.A. 109(26), 10199–10204 (2012).
[Crossref] [PubMed]

P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an x-ray grating interferometer,” Opt. Express 19(3), 1691–1698 (2011).
[Crossref] [PubMed]

Zhang, K.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
[Crossref] [PubMed]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

Zhang, L.

Z. T. Wang, Z. F. Huang, Z. Q. Chen, L. Zhang, X. L. Jiang, K. J. Kang, H. X. Yin, Z. C. Wang, and M. Stampanoni, “Low-dose multiple-information retrieval algorithm for x-ray grating-based imaging,” Nucl. Instrum. Methods Phys. Res., Sect. A 635(1), 103–107 (2011).

Zhao, X. J.

Zhong, Z.

C. Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[Crossref] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51(2), 221–236 (2006).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

Zhu, P.

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U.S.A. 107(31), 13576–13581 (2010).
[Crossref] [PubMed]

J. Wang, P. Zhu, Q. Yuan, W. Huang, H. Shu, B. Chen, T. Hu, and Z. Wu, “Reconstruction of the refractive index gradient by x-ray diffraction enhanced computed tomography,” Phys. Med. Biol. 51(14), 3391–3396 (2006).
[Crossref] [PubMed]

Zhu, P. P.

P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
[Crossref] [PubMed]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

Zhu, Z. Z.

Ziegler, E.

Appl. Opt. (1)

Appl. Phys. Express (1)

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, “Differential phase x-ray imaging microscopy with x-ray Talbot interferometer,” Appl. Phys. Express 1(11), 117002 (2008).
[Crossref]

Appl. Phys. Lett. (2)

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(9), 094105 (2009).
[Crossref]

P. P. Zhu, J. Y. Wang, Q. X. Yuan, W. X. Huang, H. Shu, B. Gao, T. D. Hu, and Z. Y. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87(26), 264101 (2005).
[Crossref]

J. Phys. D Appl. Phys. (2)

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D Appl. Phys. 36(17), 2152–2156 (2003).
[Crossref]

Y. Liu, J. Nelson, C. Holzner, J. C. Andrews, and P. Pianetta, “Recent advances in synchrotron-based hard x-ray phase contrast imaging,” J. Phys. D Appl. Phys. 46(49), 494001 (2013).
[Crossref]

J. Synchrotron Radiat. (1)

Y. Bao, Y. Wang, P. Li, Z. Wu, Q. Shao, K. Gao, Z. Wang, Z. Ju, K. Zhang, Q. Yuan, W. Huang, P. Zhu, and Z. Wu, “A novel crystal-analyzer phase retrieval algorithm and its noise property,” J. Synchrotron Radiat. 22(3), 786–795 (2015).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (2)

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

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Figures (11)

Fig. 1
Fig. 1 The pictures of (a) absorption, (b) refraction, and (c) scattering.
Fig. 2
Fig. 2 (a) Schematic imaging principle of the grating interferometer, (b) measured Shifting curve.
Fig. 3
Fig. 3 Projection images for (a) valley-image, (b) upslope-image, (c) peak-image, and (d) downslope-image.
Fig. 4
Fig. 4 Comparison between ASR and eight-step-PS methods. In the panels (a)-(c) we show absorption, refraction angle, and scattering variance images, respectively, extracted with the ASR method. The corresponding images extracted with the eight-step-PS method are shown in panels (d)-(f).
Fig. 5
Fig. 5 Comparison of profiles between ASR and eight-step-PS methods for (a) absorption, (b) refraction angle, and (c) scattering variance. The profiles correspond to the horizontal white dotted line across the sample in Fig. 4(a).
Fig. 6
Fig. 6 Comparison of the extracted images of ROI 1 between eight-step-PS, NS-ASR and NANS-ASR. Panels (a)-(b) contain absorption and refraction angle obtained by using eight-step-PS. The corresponding extracted images obtained by NS-ASR are shown in panels (c)-(d). The extracted refraction angle by NANS-ASR is shown in panel (e).
Fig. 7
Fig. 7 Comparison of extracted images of ROI 2 between eight-step-PS, NA-ASR and NANR-ASR. Panels (a)-(b) show the refraction angle and scattering variance by using the eight-step-PS method. The corresponding extracted images of the refraction angle and scattering variance obtained by NA-ASR are shown in panels (c)-(d). The extracted scattering variance by NANR-ASR is shown in panel (e).
Fig. 8
Fig. 8 Comparison of extracted images of ROI 3 among eight-step-PS, NR-ASR and NRNS-ASR. Panels (a)-(b) are absorption and scattering variance by using the eight-step-PS method. The corresponding extracted images of absorption and scattering variance obtained by NR-ASR are shown in panels (c)-(d). The extracted absorption by NRNS-ASR is shown in panel (e).
Fig. 9
Fig. 9 Comparison of the profiles, corresponding to the horizontal white solid line of ROI 1 in Fig. 6(a), between eight-step-PS, NS-ASR and NANS-ASR for (a) absorption, and (b) refraction angle.
Fig. 10
Fig. 10 Comparison of the profiles, corresponding to the horizontal white solid line of ROI 2 in Fig. 7(a), between eight-step-PS, NA-ASR and NANR-ASR for: (a) refraction angle, and (b) scattering variance.
Fig. 11
Fig. 11 Comparison of the profiles, corresponding to the horizontal white solid line of ROI 3 in Fig. 8(a), among eight-step-PS, NR-ASR and NRNS-ASR for: (a) absorption, and (b) the scattering variance.

Tables (2)

Tables Icon

Table 1 Calculated PPMCC between the new methods and eight-step-PS indicated by “—” mean ignorable information, A, R and S are the absorption, refraction angle and scattering variance, respectively.

Tables Icon

Table 2 Calculated ratio of SNR and ratio of projection images’ number needed to extract information, between the new methods and eight-step-PS indicated by “—” mean ignorable information, A, R and S are the absorption, refraction angle and scattering variance, respectively.

Equations (29)

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I ( ψ ; x , y ) = f ( ψ ; x , y ) S ( ψ ) ,
I = I 0 δ ˜ ( ψ ) exp ( M ( x , y ) ) ,
I = I 0 δ ˜ ( ψ θ ( x , y ) ) ,
I = I 0 1 2 π σ ( x , y ) exp [ 1 2 ( ψ ) 2 σ 2 ( x , y ) ] ,
M ( x , y ) = μ ( x , y , z ) d z ,
θ ( x , y ) = δ ( x , y , z ) x d z ,
σ 2 ( x , y ) = i σ i 2 ( x , y ) = i ω i ( x , y , z ) Δ z i = ω ( x , y , z ) d z ,
f ( ψ ; x , y ) = I 0 exp ( M ( x , y ) ) 2 π σ ( x , y ) exp [ 1 2 ( ψ θ ( x , y ) ) 2 σ 2 ( x , y ) ] .
S ( ψ ) = S ( x g / D ) .
S ( ψ ) = S ¯ [ 1 V 0 cos ( 2 π D p ( ψ + ψ 0 ) + η π 2 ) ] ,
I V ( x , y ) = I 0 S ¯ e M ( x , y ) [ 1 V 0 e 2 π 2 D 2 σ 2 ( x , y ) / p 2 cos ( 2 π D p ( θ ( x , y ) + ψ 0 ) ) ] ,
I U ( x , y ) = I 0 S ¯ e M ( x , y ) [ 1 + V 0 e 2 π 2 D 2 σ 2 ( x , y ) / p 2 sin ( 2 π D p ( θ ( x , y ) + ψ 0 ) ) ] ,
I P ( x , y ) = I 0 S ¯ e M ( x , y ) [ 1 + V 0 e 2 π 2 D 2 σ 2 ( x , y ) / p 2 cos ( 2 π D p ( θ ( x , y ) + ψ 0 ) ) ] ,
I D ( x , y ) = I 0 S ¯ e M ( x , y ) [ 1 V 0 e 2 π 2 D 2 σ 2 ( x , y ) / p 2 sin ( 2 π D p ( θ ( x , y ) + ψ 0 ) ) ] .
M ( x , y ) = ln ( I U b ( x , y ) + I D b ( x , y ) I U s ( x , y ) + I D s ( x , y ) ) ,
θ ( x , y ) = p 2 π D ( arc tan ( I U s ( x , y ) I D s ( x , y ) I V s ( x , y ) I P s ( x , y ) ) arc tan ( I U b ( x , y ) I D b ( x , y ) I V b ( x , y ) I P b ( x , y ) ) ) ,
σ 2 ( x , y ) = p 2 2 π 2 D 2 ln ( ( I U s ( x , y ) I D s ( x , y ) ) 2 + ( I V s ( x , y ) I P s ( x , y ) ) 2 V 0 ( I U s ( x , y ) + I D s ( x , y ) ) ) + p 2 2 π 2 D 2 ln ( ( I U b ( x , y ) I D b ( x , y ) ) 2 + ( I V b ( x , y ) I P b ( x , y ) ) 2 V 0 ( I U b ( x , y ) + I D b ( x , y ) ) ) .
I P + I V = I U + I D .
σ 2 ( x , y ) = 0.
M ( x , y ) = ln ( I U b ( x , y ) + I D b ( x , y ) I U s ( x , y ) + I D s ( x , y ) ) ,
θ N S ( x , y ) = p 2 π D arc sin ( 1 V 0 I D s ( x , y ) I U s ( x , y ) I D s ( x , y ) + I U s ( x , y ) ) p 2 π D arc sin ( 1 V 0 I D b ( x , y ) I U b ( x , y ) I D b ( x , y ) + I U b ( x , y ) ) .
I U ( o r D ) ( x , y , φ ; ψ 0 = 0 ) = I D ( o r U ) ( x , y , φ + π ; ψ 0 = 0 ) .
M ( x , y ) = 0.
θ ( x , y ) = 0.
S N R A / S = A ( I o b j I b a c k ) s t d 2 ( I o b j ) + s t d 2 ( I b a c k ) ,
S N R R = y 0 y 1 d y x 0 x 1 d x | I ( x , y ) I b a c k | 2 y 0 y 1 d y x 0 x 1 d x I b a c k ,
( f ( ψ ) ) = I 0 e M e i 2 π υ θ e 2 π 2 υ 2 σ 2 , a n d ( S ( ψ ) ) = 1 2 [ δ ( v D p ) + δ ( v + D p ) ] e j v ( ψ 0 + η p 4 π D ) . f ( ψ ) S ( ψ ) = 1 ( ( f ( ψ ) ) ( S ( ψ ) ) ) | ψ = 0 = I 0 S ¯ e M [ 1 V 0 e 2 π 2 D 2 σ 2 / p 2 cos ( 2 π D p ( θ + ψ 0 ) + η π 2 ) ] . I V = f ( ψ ) S ( ψ ) | η = 0 = I 0 S ¯ e M [ 1 V 0 e 2 π 2 D 2 σ 2 / p 2 cos ( 2 π D p ( θ + ψ 0 ) ) ] , a n d I U = f ( ψ ) S ( ψ ) | η = 1 = I 0 S ¯ e M [ 1 + V 0 e 2 π 2 D 2 σ 2 / p 2 sin ( 2 π D p ( θ + ψ 0 ) ) ] , a n d I P = f ( ψ ) S ( ψ ) | η = 2 = I 0 S ¯ e M [ 1 + V 0 e 2 π 2 D 2 σ 2 / p 2 cos ( 2 π D p ( θ + ψ 0 ) ) ] , a n d I D = f ( ψ ) S ( ψ ) | η = 3 = I 0 S ¯ e M [ 1 V 0 e 2 π 2 D 2 σ 2 / p 2 sin ( 2 π D p ( θ + ψ 0 ) ) ] .
{ M ( x , y ) = ln ( k = 1 4 I k b ( x , y ) k = 1 4 I k s ( x , y ) ) = ln ( I 1 b ( x , y ) + I 2 b ( x , y ) + I 3 b ( x , y ) + I 4 b ( x , y ) I 1 s ( x , y ) + I 2 s ( x , y ) + I 3 s ( x , y ) + I 4 s ( x , y ) ) , θ ( x , y ) = p 2 π D arg ( k = 1 4 I k s ( x , y ) exp ( i 2 π k 4 ) k = 1 4 I k b ( x , y ) exp ( i 2 π k 4 ) ) = p 2 π D arg ( i I 1 s ( x , y ) I 2 s ( x , y ) i I 3 s ( x , y ) + I 4 s ( x , y ) i I 1 b ( x , y ) I 2 b ( x , y ) i I 3 b ( x , y ) + I 4 b ( x , y ) ) = p 2 π D ( arc tan ( I 1 s ( x , y ) I 3 s ( x , y ) I 4 s ( x , y ) I 2 s ( x , y ) ) arc tan ( I 1 b ( x , y ) I 3 b ( x , y ) I 4 b ( x , y ) I 2 b ( x , y ) ) ) , σ 2 ( x , y ) = p 2 2 π 2 D 2 ln ( | k = 1 4 I k b ( x , y ) exp ( i 2 π k 4 ) | k = 1 4 I k b ( x , y ) k = 1 4 I k s ( x , y ) | k = 1 4 I k s ( x , y ) exp ( i 2 π k 4 ) | ) = p 2 2 π 2 D 2 ln ( | i I 1 b ( x , y ) I 2 b ( x , y ) i I 3 b ( x , y ) + I 4 b ( x , y ) | I 1 b ( x , y ) + I 2 b ( x , y ) + I 3 b ( x , y ) + I 4 b ( x , y ) I 1 s ( x , y ) + I 2 s ( x , y ) + I 3 s ( x , y ) + I 4 s ( x , y ) | i I 1 s ( x , y ) I 2 s ( x , y ) i I 3 s ( x , y ) + I 4 s ( x , y ) | ) = p 2 2 π 2 D 2 ln ( ( I 1 b ( x , y ) I 3 b ( x , y ) ) 2 + ( I 4 b ( x , y ) I 2 b ( x , y ) ) 2 I 1 b ( x , y ) + I 2 b ( x , y ) + I 3 b ( x , y ) + I 4 b ( x , y ) I 1 s ( x , y ) + I 2 s ( x , y ) + I 3 s ( x , y ) + I 4 s ( x , y ) ( I 1 s ( x , y ) I 3 s ( x , y ) ) 2 + ( I 4 s ( x , y ) I 2 s ( x , y ) ) 2 ) .
{ M ( x , y ) = ln ( I U b ( x , y ) + I D b ( x , y ) I U s ( x , y ) + I D s ( x , y ) ) , θ ( x , y ) = p 2 π D ( arc tan ( I U s ( x , y ) I D s ( x , y ) I V s ( x , y ) I P s ( x , y ) ) arc tan ( I U b ( x , y ) I D b ( x , y ) I V b ( x , y ) I P b ( x , y ) ) ) , σ 2 ( x , y ) = p 2 2 π 2 D 2 ln ( ( I U b ( x , y ) I D b ( x , y ) ) 2 + ( I V b ( x , y ) I P b ( x , y ) ) 2 I U b ( x , y ) + I D b ( x , y ) I U s ( x , y ) + I D s ( x , y ) ( I U s ( x , y ) I D s ( x , y ) ) 2 + ( I V s ( x , y ) I P s ( x , y ) ) 2 ) .

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