Abstract

Grating-based X-ray differential phase contrast imaging (GDPCI) typically employs the phase-stepping technique to extract an object’s phase information. This method requires heavy radiation dosage and is time consuming. Another potential approach is the reverse projection (RP) method, which, however, relies on a synchrotron radiation source to obtain highly sensitive differential phase contrast(DPC) signal. Here, we present an alternative approach that enables the RP method to be used with a conventional X-ray source and substantially improves the sensitivity of the DPC signal by replacing the analyzer grating of the GDPCI with a sampling grating. This development represents a significant step towards obtaining fast and low-dosage DPC images in medical, biological, and industrial applications.

© 2015 Optical Society of America

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  1. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
    [Crossref]
  2. 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]
  3. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(Part 2, No. 7B), L866–L868 (2003).
    [Crossref]
  4. 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]
  5. 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]
  6. 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]
  7. Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
    [Crossref] [PubMed]
  8. A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
    [Crossref]
  9. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative X-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size,” Opt. Lett. 36(1), 55–57 (2011).
    [Crossref] [PubMed]
  10. K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative single-exposure X-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19(20), 19781–19789 (2011).
    [Crossref] [PubMed]
  11. 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]
  12. P. Zhu, W. Huang, Q. Yuan, Z. Wang, and K. Zhang, “Generalization of DEI methods in grating-based phase-contrast imaging,” in AIP Conf. Proc.1365 (AIP, 2011), pp. 329–332.
    [Crossref]
  13. P. P. Zhu, Z. Z. Zhu, Y. L. Hong, K. Zhang, W. X. Huang, Q. X. Yuan, X. J. Zhao, Z. Q. Ju, Z. Y. Wu, Z. Wei, S. Wiebe, and L. D. Chapman, “Common characteristics shared by different differential phase contrast imaging methods,” Appl. Opt. 53(5), 861–867 (2014).
    [Crossref] [PubMed]
  14. D. M. Paganin, Coherent X-ray Optics (Oxford University, 2006).
  15. 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]
  16. M. Das and Z. Liang, “Approximated transport-of-intensity equation for coded-aperture x-ray phase-contrast imaging,” Opt. Lett. 39(18), 5395–5398 (2014).
    [Crossref]
  17. 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]
  18. H. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
    [Crossref] [PubMed]
  19. Y. Ge, K. Li, J. Garrett, and G. H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
    [Crossref] [PubMed]
  20. N. Bevins, J. Zambelli, K. Li, and G.-H. Chen, “Comparison of phase contrast signal extraction techniques,” in AIP Conf. Proc.1466 (AIP, 2012), pp. 169–174.
    [Crossref]
  21. Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (2011).
    [Crossref] [PubMed]
  22. Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
    [Crossref] [PubMed]
  23. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
    [Crossref] [PubMed]
  24. Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
    [Crossref]

2014 (4)

2013 (2)

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

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

2012 (2)

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

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

2011 (4)

2010 (2)

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]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

2009 (1)

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]

2008 (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]

2007 (1)

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

2006 (1)

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

2003 (1)

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

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]

1995 (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Adamo, N. M.

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

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, F. Pfeiffer, and T. Weitkamp, “Interlaced phase stepping in phase-contrast x-ray tomography,” Appl. Phys. Lett. 98(9), 094101 (2011).
[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. Miao, L. Chen, E. E. Bennett, N. M. Adamo, A. A. Gomella, A. M. DeLuca, A. Patel, N. Y. Morgan, and H. Wen, “Motionless phase stepping in x-ray phase contrast imaging with a compact source,” Proc. Natl. Acad. Sci. U.S.A. 110(48), 19268–19272 (2013).
[Crossref] [PubMed]

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]

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. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Chapman, L. D.

Chen, G. H.

Y. Ge, K. Li, J. Garrett, and G. H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[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]

Chen, J.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Chen, L.

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

Chen, Z.

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]

Das, M.

David, 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]

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]

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

DeLuca, A. M.

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

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]

Du, Y.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (2011).
[Crossref] [PubMed]

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]

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]

Gao, D.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Gao, K.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Garrett, J.

Ge, X.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Ge, Y.

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]

Gomella, A. A.

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

Grünzweig, C.

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

Guo, J.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (2011).
[Crossref] [PubMed]

Gureyev, T. E.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Hamaishi, Y.

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

Hong, Y. L.

Huang, J.

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

Huang, W. X.

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]

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]

Ju, Z. Q.

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]

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. 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.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. 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]

Lei, Y.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (2011).
[Crossref] [PubMed]

Li, J.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Li, K.

Y. Ge, K. Li, J. Garrett, and G. H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[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]

Liang, Z.

Lin, D.

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

Liu, X.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (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]

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]

Miao, H.

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

Momose, A.

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

Morgan, K. S.

Morgan, N. Y.

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

Niu, H.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

Y. Du, X. Liu, Y. Lei, J. Guo, and H. Niu, “Non-absorption grating approach for x-ray phase contrast imaging,” Opt. Express 19(23), 22669–22674 (2011).
[Crossref] [PubMed]

Olivo, A.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Paganin, D. M.

Pan, Z.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Patel, A.

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

Pfeiffer, F.

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, 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]

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]

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]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[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]

Siu, K. K. W.

Speller, R.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

Stampanoni, M.

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]

Stevenson, A. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Suzuki, Y.

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

Takai, H.

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

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]

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Wang, D.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Wang, Z.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[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]

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]

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]

Wei, Z.

Weitkamp, T.

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]

Wen, H.

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

Wiebe, S.

Wilkins, S. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Wu, Z.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[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]

Wu, Z. Y.

Yuan, Q. X.

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]

Zanette, I.

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

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

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

Zhang, L.

Z. 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]

Zhao, X. J.

Zhao, Z.

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

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.

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[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]

Zhu, P. P.

Zhu, Z. Z.

Anal. Bioanal. Chem. (1)

Y. Du, J. Huang, D. Lin, and H. Niu, “Analysis of field of view limited by a multi-line x-ray source and its improvement for grating interferometry,” Anal. Bioanal. Chem. 404(3), 793–797 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91(7), 074106 (2007).
[Crossref]

J. Micromech. Microeng. (1)

Y. Lei, Y. Du, J. Li, Z. Zhao, X. Liu, J. Guo, and H. Niu, “Fabrication of x-ray absorption gratings via micro-casting for grating-based phase contrast imaging,” J. Micromech. Microeng. 24(1), 015007 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(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]

Z. Wu, K. Gao, Z. Wang, X. Ge, J. Chen, D. Wang, Z. Pan, K. Zhang, P. Zhu, and Z. Wu, “A new method to retrieve phase information for equiangular fan beam differential phase contrast computed tomography,” Med. Phys. 40(3), 031911 (2013).
[Crossref] [PubMed]

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. 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]

Nature (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373(6515), 595–598 (1995).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

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. A (1)

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

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

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]

Rev. Sci. Instrum. (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81(7), 073709 (2010).
[Crossref] [PubMed]

Other (3)

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

P. Zhu, W. Huang, Q. Yuan, Z. Wang, and K. Zhang, “Generalization of DEI methods in grating-based phase-contrast imaging,” in AIP Conf. Proc.1365 (AIP, 2011), pp. 329–332.
[Crossref]

D. M. Paganin, Coherent X-ray Optics (Oxford University, 2006).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the configuration of a GDPCI.
Fig. 2
Fig. 2 (a) Procedure for sampling fringe at the up-slope region. (b) Procedure for sampling fringe at the down-slope region. (c) Grating shifting curve.
Fig. 3
Fig. 3 Simulation results of a protein pellet. (a) DPC image by a sampling grating. (b) DPC image by an analyzer grating. (c) Line profiles of (a) and (b). The rear sight of the picture width is 200 μm.
Fig. 4
Fig. 4 SEM image of the sampling grating: (a) front view, and (b) lateral view.
Fig. 5
Fig. 5 X-ray imaging of two samples consisting of a polyurethane tube and two peanuts. (a) Plot of intensity oscillation (grating shifting curve) for a detector pixel when the phase grating is scanned along xg without sample. (b) Absorption images of a polyurethane tube, and (c) its DPC image. (d) Absorption images of two peanuts, and (e) their DPC image. The rear sight is 5 mm.

Equations (12)

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

α= λ c 2π φ( x,y ) x ,
I( m,n ) a 0 ( m,n )+ a 1 ( m,n )cos[ 2π p m ( mcosθ+nsinθ )+ϕ ],
ϕ= λ c d t p 2 φ( x,y ) x ,
I x g d t = I 0 S( x g d t ),
I x g d t = I 0 exp[ μ( x,y ) ]S[ x g d t + θ x ( x,y ) ],
S[ x 0 d t + θ x ( x,y ) ]=S( x 0 d t )+ dS d( x g / d t ) ( x 0 d t ) θ x ( x,y ).
I up ( x,y )= I 0 exp[ μ( x,y ) ][ S( p 2 4 d t )+ dS d( x g / d t ) ( p 2 4 d t ) θ x ( x,y ) ],
I down ( x,y )= I 0 exp[ μ( x,y ) ][ S( p 2 4 d t )+ dS d( x g / d t ) ( p 2 4 d t ) θ x ( x,y ) ].
S( p 2 4 d t )=S( p 2 4 d t ),
dS d( x g / d t ) ( p 2 4 d t )= dS d( x g / d t ) ( p 2 4 d t ).
I a ( x,y )=ln[ 2 I 0 S( p 2 4 d t ) I up ( x,y )+ I down ( x,y ) ],
θ x ( x,y )= C g I down ( x,y ) I up ( x,y ) I down ( x,y )+ I up ( x,y ) ,

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