Abstract

High-resolution hard X-ray grating-based imaging method with conventional X-ray sources provides attenuation, refraction and scattering information synchronously, and it is regarded as the next-generation X-ray imaging technology for medical and industrial applications. In this letter, a large phase-stepping approach with at least one order of magnitude lower resolution of the movement is presented to equivalently substitute the current high-positioning-resolution phase-stepping approach. Both the theoretical deduction and actual experiment prove that the new approach is available to relax the requirement of high positioning resolution and strict circumstances so as to benefit the future commercial applications of the grating-based multiple-information imaging technology.

© 2010 OSA

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  1. A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
    [CrossRef]
  2. S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10(7), 1575–1580 (1971).
    [CrossRef] [PubMed]
  3. O. Kafri, “Noncoherent method for mapping phase objects,” Opt. Lett. 5(12), 555–557 (1980).
    [CrossRef] [PubMed]
  4. J. F. Clauser and S. Li, ““Heisenberg microscope” decoherence atom interferometry,” Phys. Rev. A 50(3), 2430–2433 (1994).
    [CrossRef] [PubMed]
  5. C. David, B. Nohammer, 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]
  6. 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]
  7. A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
    [CrossRef]
  8. T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
    [CrossRef]
  13. Z.Huang, Z.Wang, L.Zhang, Z.Chen, K.Kang, “Attenuation-Refraction-Scattering Computed Tomographic Experimental System with a Conventional X-Ray Tube: System Optimization & Image Fusion,” IEEE NSS/MIC Record, 2347–2350 (2009)
  14. T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
    [CrossRef]
  15. Y. I. Nesterets and S. W. Wilkins, “Phase-contrast imaging using a scanning-double-grating configuration,” Opt. Express 16(8), 5849–5867 (2008).
    [CrossRef] [PubMed]
  16. M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
    [CrossRef] [PubMed]
  17. 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(6A6A), 5254–5262 (2006).
    [CrossRef]
  18. A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
    [CrossRef]
  19. W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25(8), 2025–2039 (2008).
    [CrossRef]
  20. Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
    [CrossRef]

2009

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

2008

Y. I. Nesterets and S. W. Wilkins, “Phase-contrast imaging using a scanning-double-grating configuration,” Opt. Express 16(8), 5849–5867 (2008).
[CrossRef] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (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]

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25(8), 2025–2039 (2008).
[CrossRef]

2006

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]

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(6A6A), 5254–5262 (2006).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

2005

2004

A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[CrossRef]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

2003

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

C. David, B. Nohammer, 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]

1994

J. F. Clauser and S. Li, ““Heisenberg microscope” decoherence atom interferometry,” Phys. Rev. A 50(3), 2430–2433 (1994).
[CrossRef] [PubMed]

1980

1971

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10(7), 1575–1580 (1971).
[CrossRef] [PubMed]

Baumann, J.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Bech, M.

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]

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.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (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]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (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]

Chabior, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Chen, Z.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

Clauser, J. F.

J. F. Clauser and S. Li, ““Heisenberg microscope” decoherence atom interferometry,” Phys. Rev. A 50(3), 2430–2433 (1994).
[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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

David, C.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (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]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

C. David, B. Nohammer, 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]

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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Ding, F.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Donath, T.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[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]

Engelhardt, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Fang, Q.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

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]

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(6A6A), 5254–5262 (2006).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

Hempel, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Hoheisel, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Huang, Z.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

Kafri, O.

Kang, K.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Z. Wang, K. Kang, Z. Huang, and Z. 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, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[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]

Kottler, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[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]

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]

Li, S.

J. F. Clauser and S. Li, ““Heisenberg microscope” decoherence atom interferometry,” Phys. Rev. A 50(3), 2430–2433 (1994).
[CrossRef] [PubMed]

Lohmann, A. W.

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

Mohr, J.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Momose, A.

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25(8), 2025–2039 (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(6A6A), 5254–5262 (2006).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[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]

Moritake, M.

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

Nesterets, Y. I.

Nohammer, B.

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

C. David, B. Nohammer, 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]

Pfeiffer, F.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (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]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Popescu, S.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Reznikova, E.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

Rohbeck, T.

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Schuster, M.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

Silva, D. E.

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

Solak, H. H.

C. David, B. Nohammer, 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]

Stampanoni, M.

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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Suzuki, T.

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(6A6A), 5254–5262 (2006).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[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]

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, Y.

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25(8), 2025–2039 (2008).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[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(6A6A), 5254–5262 (2006).
[CrossRef]

Takeuchi, A.

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

Tanaka, M.

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

Uesugi, K.

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

Wang, Z.

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Weitkamp, T.

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]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Wilkins, S. W.

Yashiro, W.

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25(8), 2025–2039 (2008).
[CrossRef]

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[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(6A6A), 5254–5262 (2006).
[CrossRef]

Yokozeki, S.

Zhang, L.

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

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. Nohammer, 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. Opt.

Appl. Phys. Lett.

C. David, B. Nohammer, 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]

Z. Wang, K. Kang, Z. Huang, and Z. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95(9), 094105 (2009).
[CrossRef]

J. Appl. Phys.

T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009).
[CrossRef]

J. Microsc.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

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(6A6A), 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]

Nat. Mater.

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. Phys.

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. Commun.

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. F. Clauser and S. Li, ““Heisenberg microscope” decoherence atom interferometry,” Phys. Rev. A 50(3), 2430–2433 (1994).
[CrossRef] [PubMed]

Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A 79(1), 013815 (2009).
[CrossRef]

Proc. SPIE

A. Momose, W. Yashiro, M. Moritake, Y. Takeda, K. Uesugi, A. Takeuchi, Y. Suzuki, M. Tanaka, and T. Hattori, “Biomedical imaging by Talbot-type x-ray phase tomography,” Proc. SPIE 6318, 63180T (2006).
[CrossRef]

A. Momose, S. Kawamoto, I. Koyama, and Y. Suzuki, “Phase tomography using an x-ray Talbot interferometer,” Proc. SPIE 5535, 352–360 (2004).
[CrossRef]

T. Weitkamp, A. Diaz, B. Nohammer, F. Pfeiffer, T. Rohbeck, P. Cloetens, M. Stampanoni, and C. David, “Hard x-ray phase imaging and tomography with a grating interferometer,” Proc. SPIE 5535, 137–142 (2004).
[CrossRef]

Other

Z.Huang, Z.Wang, L.Zhang, Z.Chen, K.Kang, “Attenuation-Refraction-Scattering Computed Tomographic Experimental System with a Conventional X-Ray Tube: System Optimization & Image Fusion,” IEEE NSS/MIC Record, 2347–2350 (2009)

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Figures (2)

Fig. 1
Fig. 1

The schematic diagram of the X-ray grating-based multiple-information imaging method.

Fig. 2
Fig. 2

The comparisons of experimental results by use of two phase-stepping approaches. (a), (d) and (g) are the attenuation, refraction and scattering images, respectively, retrieved by the current high-positioning-resolution phase-stepping approach (Approach I). (b), (e) and (h) are the attenuation, refraction and scattering images, respectively, retrieved by the large phase-stepping approach (Approach II). (c) is the comparison of profile values in two attenuation images. (f) is the comparison of profile values in two refraction images. (i) is the comparison of profile values in two scattering images.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

p0p2=LD,
p1p2=LL+D
p2p1/2=LLDT
T0(x)=nfne2πinp0x,
T1(x)=nane2πinp1x,
T2(x)=ntne2πinp2x,
ST(x)=S0(x)T0(x).
Is(x)=I1(x)S(x),
Js(x)=J1(x)S(x),
I1(x)=T1(LL+Dx),
J1(x)=T1'(LL+Dx),
S(x)=ST(LDx),
I1(x)=T1(LL+Dx)=nane2πinpx,
J1(x)=T1'(LL+Dx)=nan'e2πinp[x+Dϕ(x)],
S(x)=ST(LDx)=S0'(x)T0'(x)=S0(LDx)T0(LDx),
S(x)=S0'(x)T0'(x)=S0'(x)[nfne2πinpx]nfn'e2πinpx,
ID(x)=Is(x)T2(x),
JD(x)=Js(x)T2(x).
ID(x,χ)=Is(x,χ)T2(x)=[I1(x)S(x+χ)]T2(x)=[I1(x)(S0'(x)T0'(x+χ))]T2(x)=[(nane2πinpx)(S0'(x)mfme2πimp(x+χ))](ktke2πikpx)nanfn'tne2πinpχ,
JD(x,χ)=Js(x,χ)T2(x)=[J1(x)S(x+χ)]T2(x)=[J1(x)(S0'(x)T0'(x+χ))]T2(x)=[(nan'e2πinp[x+Dϕ(x)])(S0'(x)mfme2πimp(x+χ))](ktke2πikpx)nan'fn'tne2πinp[χ+Dϕ(x)],
ID'(x,χ)=Is(x)T2(x,χ)=[I1(x)S(x)]T2(x+χ)[(nane2πinpx)(mfm'e2πimpx)](ktke2πikp(x+χ))nanfn'tne2πinpχ,
JD'(x,χ)=Js(x)T2(x,χ)=[J1(x)S(x)]T2(x+χ)[(nan'e2πinp[x+Dϕ(x)])(mfm'e2πimpx)](ktke2πikp(x+χ))nan'fn'tne2πinp[χ+Dϕ(x)],

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