Abstract

We present a simplified acquisition and processing method for X-ray grating interferometry computed tomography (CT). The proposed approach eliminates the need to scan the gratings, thus allowing for a faster CT acquisition compared to methods presently in use. The contrast in the reconstructed images can be expressed as a linear combination of the absorption and refraction within the sample. Experimental images of a test phantom made of known materials and a human bone-cartilage sample prove the correctness of the method and show very good agreement with the theory. The here proposed approach might be highly interesting in many fields where a reduced imaging acquisition time is requested and/or where the radiation dose delivered to the sample has to be kept low, such as, for example, in in-vivo imaging.

© 2011 OSA

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2010 (2)

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

2009 (3)

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

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]

2008 (3)

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]

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

A. Olivo and R. Speller, “Image formation principles in coded-aperture based x-ray phase contrast imaging,” Phys. Med. Biol. 53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

2006 (2)

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

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

2005 (1)

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]

2003 (2)

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

2002 (1)

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

2000 (1)

R. Fitzgerald, “Phase sensitive X-ray imaging,” Phys. Today 53(7), 23 (2000).
[CrossRef]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

1996 (1)

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

Adam-Neumair, S.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Bamberg, F.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Baruchel, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Bech, M.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

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]

Bennett, E. E.

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]

Bernard, P.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Bravin, A.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (2003).
[CrossRef]

P. C. Diemoz, A. Bravin, C. Glaser, and P. Coan, “Comparison of analyzer-based imaging computed tomography extraction algorithms and application to bone-cartilage imaging,” Phys. Med. Biol. (to be published).
[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]

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]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Cloetens, P.

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. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Coan, P.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

P. C. Diemoz, A. Bravin, C. Glaser, and P. Coan, “Comparison of analyzer-based imaging computed tomography extraction algorithms and application to bone-cartilage imaging,” Phys. Med. Biol. (to be published).
[PubMed]

David, C.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

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]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Deyhle, H.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Diaz, A.

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]

Diemoz, P. C.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

P. C. Diemoz, A. Bravin, C. Glaser, and P. Coan, “Comparison of analyzer-based imaging computed tomography extraction algorithms and application to bone-cartilage imaging,” Phys. Med. Biol. (to be published).
[PubMed]

Donath, T.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

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]

Fernández, M.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Fiedler, S.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

Fitzgerald, R.

R. Fitzgerald, “Phase sensitive X-ray imaging,” Phys. Today 53(7), 23 (2000).
[CrossRef]

Glaser, C.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

P. C. Diemoz, A. Bravin, C. Glaser, and P. Coan, “Comparison of analyzer-based imaging computed tomography extraction algorithms and application to bone-cartilage imaging,” Phys. Med. Biol. (to be published).
[PubMed]

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[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]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[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]

Hintermüller, C.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

Hirano, K.

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

Itai, Y.

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

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Karjalainen-Lindsberg, M. L.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Kenntner, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Keyriläinen, J.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[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(Part 2, No. 7B), 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]

Labiche, J. C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

Lang, S.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Leidenius, M.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Maikusa, H.

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]

Marone, F.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

McDonald, S. A.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

Menk, R. H.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Mikuljan, G.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

Mohr, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Momose, A.

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]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

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

Müller, B.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Mützel, E.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Nöhammer, B.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Olivo, A.

A. Olivo and R. Speller, “Image formation principles in coded-aperture based x-ray phase contrast imaging,” Phys. Med. Biol. 53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

Peterzol, A.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

Pfeiffer, F.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

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]

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Ponchut, C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

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]

Raya, J. G.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Reiser, M. F.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Reznikova, E.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Rutishauser, S.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Schulz, G.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Sipilä, P.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Solak, H. H.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Speller, R.

A. Olivo and R. Speller, “Image formation principles in coded-aperture based x-ray phase contrast imaging,” Phys. Med. Biol. 53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

Stampanoni, M.

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[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]

Suhonen, H.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Suortti, P.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Takeda, T.

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

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]

Tapfer, A.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Timpert, K.

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

Valade, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Virkkunen, P.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

von Smitten, K.

J. Keyriläinen, M. Fernández, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipilä, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Toward high-contrast breast CT at low radiation dose,” Radiology 249(1), 321–327 (2008).
[CrossRef] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Weitkamp, T.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[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]

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. 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]

Yashiro, W.

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]

Zanette, I.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J. Valade, “Recent developments in X-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE 7804, 780406 (2010).
[CrossRef]

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Ziegler, E.

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]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Invest. Radiol. (1)

P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol. 45(7), 437–444 (2010).
[PubMed]

J. Phys. D Appl. Phys. (1)

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (2003).
[CrossRef]

J. Synchrotron Radiat. (2)

S. A. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 4, 562–572 (2009).
[CrossRef]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 3, 260–270 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Nat. Mater. (1)

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]

Nat. Med. (1)

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

Nat. Phys. (1)

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

Opt. Express (2)

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]

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Figures (4)

Fig. 1
Fig. 1

(a) Scheme of the XGI setup used for this study, with gratings lines perpendicular to the sample rotation axis. (b) Sinusoidal fringe pattern measured with the phase stepping method, the linear approximation of the curve around the point x0 is indicated. V represents the visibility, I0 the intensity incident on the object and IT the transmitted intensity.

Fig. 2
Fig. 2

Reconstructed axial slices for the two cylinders containing ethanol (a,b,c) and formalin (d,e,f): absorption (a,d) and refraction (b,e) images obtained with phase stepping method and combined absorption-refraction images (c,f) obtained for one fixed gratings position.

Fig. 3
Fig. 3

Profiles across the cylinder containing ethanol (line 1 in Fig. 2(a)). In (a), absorption and refraction profiles extracted with phase stepping method are reported (the latter multiplied by 105 for visualization purposes), together with absorption-refraction combined profile obtained from a single gratings position. In (b), the absorption-refraction combined profile is compared to that theoretically expected from Eq. (6) (see text).

Fig. 4
Fig. 4

Images of a human bone-cartilage sample calculated by using the combined absorption-refraction reconstruction: (a) reconstructed CT vertical plane of the bone and cartilage tissues (respectively at the top and bottom parts of the image), (b) expanded view of a cartilage tissue region.

Equations (6)

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ln [ I T ( x , y r ) / I 0 ( x , y r ) ] = d z r μ ( x , y r , z r ) ,
Δ θ R ( x , y r ) = d z r δ x ( x , y r , z r ) .
I ( x G ; x , y r ) = T G R ( x , y r ) I T ( x , y r ) [ 1 + V ( x , y r ) sin ( ψ ( x , y r ) + 2 π p 2 x G + 2 π S Δ θ R ( x , y r ) ) ] = = T G R ( x , y r ) I T ( x , y r ) G ( x G ; Δ θ R ; x , y r ) ,
ln I ( x , y r ) I 0 ( x , y r ) T G R ( x , y r ) = d z r μ ( x , y r , z r ) ln [ G ( x G ; Δ θ R ) ] .
ln [ G ( x G ; Δ θ R ) ] ln [ G ( x G ; Δ θ R = 0 ) ] + 1 G ( x G ; Δ θ R = 0 ) G ˙ ( x G ; Δ θ R = 0 ) Δ θ R ( x , y r ) = = K 1 ( x G ) + K 2 ( x G ) d z r δ x ( x , y r , z r ) ,
f ( x , y , z ) = μ ( x , y , z ) K 1 ( x G ) L K 2 ( x G ) δ x ( x , y , z ) ,

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