Abstract

Grating-based phase-contrast imaging has been a hot topic for several years due to its excellent imaging capability for low-density materials and easy implementation with a laboratory x-ray source. Compared with traditional x-ray computed tomography (CT) systems, the standard data collection procedure, “phase-stepping” (PS), in the grating-based phase-contrast CT (GPC-CT) is time consuming. The imaging time of a GPC-CT scan is usually up to hours. It is unacceptable in clinical CT examinations, and will cause serious motion artifacts in the reconstructed images. Additionally, the radiation dose delivered to the object with the PS-based GPC-CT is several times larger than that by a conventional CT scan. To address these problems, in this paper, we followed the interlaced PS method and proposed a novel image reconstruction method, namely the inner-focusing (IF) reconstruction method. With the interlaced PS method, the sample rotation and the grating stepping in GPC-CT occur at the same time. Thus, the interlaced GPC-CT scan can have a comparable temporal resolution with existing CT systems. Without any additional requirements, the proposed IF reconstruction method can prevent the artifacts existing in the conventional interlaced PS method. Both numerical simulations and real experiments were carried out to verify the proposed IF reconstruction method. And the results demonstrated it was effective in archiving a fast and low-dose GPC-CT.

© 2013 OSA

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  1. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
    [CrossRef] [PubMed]
  2. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express11(19), 2303–2314 (2003).
    [CrossRef] [PubMed]
  3. D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
    [PubMed]
  4. 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]
  5. 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]
  6. M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol.46(12), 801–806 (2011).
    [CrossRef] [PubMed]
  7. A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2012 (5)

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (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]

Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE8506, 85061P, 85061P-6 (2012).
[CrossRef]

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[CrossRef]

2011 (3)

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[CrossRef]

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

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

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 (1)

2007 (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

2006 (2)

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 (1)

2003 (2)

A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express11(19), 2303–2314 (2003).
[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]

1998 (1)

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

1997 (1)

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

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]

Arfelli, F.

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

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]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[CrossRef]

Bevins, N.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

Bevins, N. B.

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[CrossRef]

Börner, M.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Bruyndonckx, P.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

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

Chapman, D.

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

Chen, G. H.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[CrossRef]

Cloetens, P.

David, C.

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]

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

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Diaz, A.

Gao, D.

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

Gmür, N.

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

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]

Hattori, T.

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]

Hauser, N.

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

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]

Hohl, M. K.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol.46(12), 801–806 (2011).
[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. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[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.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Kottler, C.

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

Kou, B.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[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]

Kubik-Huch, R. A.

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

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.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[CrossRef]

Liu, X.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[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]

Liu, Y.

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.

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.

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

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]

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

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. Express17(15), 12540–12545 (2009).
[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]

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, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express11(19), 2303–2314 (2003).
[CrossRef] [PubMed]

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]

Pauwels, B.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Pfeiffer, F.

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]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Pisano, E.

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

Pogany, A.

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

Qi, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Qi, Z.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

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]

Roessl, E.

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

Sasov, A.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Sayers, D.

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

Schulz, J.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Singer, G.

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

Stampanoni, M.

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Stevenson, A. W.

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

Sun, H.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Sun, J.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Suzuki, Y.

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(Part 2, No. 7B), 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(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. Express17(15), 12540–12545 (2009).
[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]

Tapfer, A.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Thomlinson, W.

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

Thüring, T.

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

Trippel, M.

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

Walter, M.

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[CrossRef] [PubMed]

Wang, Y.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Wang, Z.

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

Washburn, D.

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

Weitkamp, T.

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]

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[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. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Wilkins, S. W.

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

Wu, Z.

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]

Xi, Y.

Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE8506, 85061P, 85061P-6 (2012).
[CrossRef]

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Xiao, T.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Xu, L. X.

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[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. Express17(15), 12540–12545 (2009).
[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]

Zambelli, J.

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

Zambelli, J. N.

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[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]

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[CrossRef]

Zhang, K.

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]

Zhao, J.

Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE8506, 85061P, 85061P-6 (2012).
[CrossRef]

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Zhong, Z.

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

Zhu, P.

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]

Ziegler, E.

AIP Conf. Proc. (1)

N. B. Bevins, J. N. Zambelli, K. Li, and G. H. Chen, “Comparison of phase contrast signal extraction techniques,” AIP Conf. Proc.1466, 169–174 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

I. Zanette, M. Bech, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett.98(9), 094101 (2011).
[CrossRef]

Invest. Radiol. (1)

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

J. Synchrotron Radiat. (1)

Y. Xi, B. Kou, H. Sun, J. Qi, J. Sun, J. Mohr, M. Börner, J. Zhao, L. X. Xu, T. Xiao, and Y. Wang, “X-ray grating interferometer for biomedical imaging applications at Shanghai Synchrotron Radiation Facility,” J. Synchrotron Radiat.19(5), 821–826 (2012).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (2)

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(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

Med. Phys. (2)

N. Bevins, J. Zambelli, K. Li, Z. Qi, and G. H. Chen, “Multicontrast x-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping,” Med. Phys.39(1), 424–428 (2012).
[CrossRef] [PubMed]

A. Tapfer, M. Bech, B. Pauwels, X. Liu, P. Bruyndonckx, A. Sasov, J. Kenntner, J. Mohr, M. Walter, J. Schulz, and F. Pfeiffer, “Development of a prototype gantry system for preclinical x-ray phase-contrast computed tomography,” Med. Phys.38(11), 5910–5915 (2011).
[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 (3)

Phys. Med. Biol. (1)

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

Phys. Rev. Lett. (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98(10), 108105 (2007).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

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. 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]

Proc. SPIE (1)

Y. Xi and J. Zhao, “Fast imaging method for grating-based x-ray computed tomography,” Proc. SPIE8506, 85061P, 85061P-6 (2012).
[CrossRef]

Radiographics (1)

D. Gao, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast radiography,” Radiographics18(5), 1257–1267 (1998).
[PubMed]

Other (1)

G. A. F. Seber and C. J. Wild, Nonlinear Regression (LibreDigital, 2003), pp. 624.

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic representation of GPC-CT with synchrotron x-rays. The data collection schemes with PS, and interlaced PS methods are illustrated in (b). The red dashed boxes indicate the data collection procedure at each projection angle.

Fig. 2
Fig. 2

(a-b) Data analysis of the interlaced PS method where neighboring projection images { P i } are utilized to retrieve differential phase-contrast signals. The red triangle indicates the physical rotation center. Black and grey lines in (a) are captured projection images with different projection angles and different grating positions. In the proposed IF method, to reconstruct a local area in object f as marked by red dashed circle in (c), neighboring projections are firstly shifted along horizontal direction making f( r ) being a virtual rotation center (red triangle) where r is the position vector from the physical rotation center to the virtual rotation center. In (b) and (d), red dashed lines indicate projection positions of physical and virtual rotation centers and the black dashed line in (d) suggests the projection of physical rotation center of (c).

Fig. 3
Fig. 3

A geometrical illumination of imaging processes for parallel beam GPC-CT (a) and fan beam GPC-CT (b).

Fig. 4
Fig. 4

Numerical phantom used in simulations. (a) is its absorption coefficient map and (b) the distribution of refractive index.

Fig. 5
Fig. 5

Reconstructed phase-contrast images with the interlaced PS method (a–b) and IF reconstruction method (d–e). The display window is the same with Fig. 4(b). The number of projections (NP) in (a), (d) is 360 and (b), (e) 1080. (c) and (f) Plots of the line profile indicated by the red line in (a) with the interlaced PS method and IF reconstruction method respectively. The red triangle in (d) marks the virtual rotation center (–200, 200) in IF reconstruction, and red circles show the reconstruction region. The images are displayed with the same window as in Fig. 4(b).

Fig. 6
Fig. 6

Reconstructed phase-contrast images with interlaced PS method and IF reconstruction method are shown in (a) and (b) respectively. The two images are shown with the same display window as that in Fig. 4(b). The red arrow in (a) marks blurred boundary. The two-dimensional red-triangle array in (b) shows virtual rotational centers used in IF reconstruction method. The complete image is a montage of these reconstructed areas around virtual rotation points. (c) and (d) are their corresponding residual error images displayed with a narrow window.

Fig. 7
Fig. 7

Reconstructed phase-contrast images using real experimental data. Images reconstructed with interlaced PS method and IF method are shown in (a) and (b) respectively. Bar: 1 mm. (c) and (d) are their corresponding residue errors, compared with the image reconstructed by standard PS method.

Equations (1)

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P x ( t )= k a k ( t )cos( 2π g 2 x+ φ k ) a 0 ( t )+ a 1 ( t )cos( 2π g 2 x+ φ 1 ),

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