Abstract

There are many variations of differential phase contrast imaging methods. Although these imaging methods are different in configuration, they are alike in imaging by extracting differential phase information through the evaluation of the refraction angles. In this paper, we investigate common characteristics shared by various different differential phase contrast imaging methods.

© 2014 Optical Society of America

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References

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  1. F. H. Smith, “Improvements in or relating to microscopy,” British patent639 014, Class 97(i), Group XX (August5, 1947).
  2. G. Nomarski, “Interféromètre à polarization,” French patent1.059.123 (May14, 1952).
  3. L. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015 (1997).
    [CrossRef]
  4. T. J. Davis, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
    [CrossRef]
  5. J. F. Clauser, “Ultrahigh resolution interferometric x-ray imaging,” US patent5812629 (September22, 1998).
  6. A. Momose, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
  7. 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, 258–261 (2006).
    [CrossRef]
  8. A. Olivo, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007).
    [CrossRef]
  9. Z. F. Huang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79, 013815 (2009).
    [CrossRef]
  10. N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
    [CrossRef]
  11. Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
    [CrossRef]
  12. Y. Hong, “X-ray phase contrast imaging research and application in X-ray microscopy,” Ph.D. thesis, Beijing: Institute of High Energy Physics (Chinese Academy of Sciences, 2012).
  13. P. P. Zhu, W. X. Huang, Q. X. Yuan, Z. L. Wang, and K. Zhang, “Generalization of DEI methods in grating-based phase-contrast imaging,” AIP Conf. Proc. 1365, 329–332 (2011).
    [CrossRef]
  14. M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
    [CrossRef]
  15. K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
    [CrossRef]
  16. 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. USA 107, 13576–13581 (2010).
  17. R. T. Peter, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA 109, 13922–13927 (2012).
  18. A. Töpler, “Beobachtungen nach einer neuen optischen Methode,” Pogg. Ann. Physik u. Chem 127, 556–580 (1866).
  19. L. Foucault, “Mémoire sur la construction des télescopes en verre argenté,” Ann. de l’Observatoire Imp. de Paris 5, 197–237 (1859).
  20. P. P. Zhu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
    [CrossRef]
  21. Z. F. Huang, “Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging,” Appl. Phys. Lett. 89, 041124 (2006).
    [CrossRef]

2012

R. T. Peter, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA 109, 13922–13927 (2012).

2011

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

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

2010

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. USA 107, 13576–13581 (2010).

2009

Z. F. Huang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79, 013815 (2009).
[CrossRef]

2008

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

2007

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

M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
[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, 258–261 (2006).
[CrossRef]

Z. F. Huang, “Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging,” Appl. Phys. Lett. 89, 041124 (2006).
[CrossRef]

2005

P. P. Zhu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

2003

A. Momose, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).

1997

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

1995

T. J. Davis, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

1866

A. Töpler, “Beobachtungen nach einer neuen optischen Methode,” Pogg. Ann. Physik u. Chem 127, 556–580 (1866).

1859

L. Foucault, “Mémoire sur la construction des télescopes en verre argenté,” Ann. de l’Observatoire Imp. de Paris 5, 197–237 (1859).

Aoki, S.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Arfelli, F.

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

Bunk, O.

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, 258–261 (2006).
[CrossRef]

Chapman, L. D.

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

Clauser, J. F.

J. F. Clauser, “Ultrahigh resolution interferometric x-ray imaging,” US patent5812629 (September22, 1998).

David, C.

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, 258–261 (2006).
[CrossRef]

Davis, T. J.

T. J. Davis, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Foucault, L.

L. Foucault, “Mémoire sur la construction des télescopes en verre argenté,” Ann. de l’Observatoire Imp. de Paris 5, 197–237 (1859).

Gmur, N.

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

Hong, Y.

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

Y. Hong, “X-ray phase contrast imaging research and application in X-ray microscopy,” Ph.D. thesis, Beijing: Institute of High Energy Physics (Chinese Academy of Sciences, 2012).

Huang, W.

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

Huang, W. X.

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

Huang, Z. F.

Z. F. Huang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79, 013815 (2009).
[CrossRef]

Z. F. Huang, “Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging,” Appl. Phys. Lett. 89, 041124 (2006).
[CrossRef]

Imai, Y.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Iwata, S.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Johnston, R. E.

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

Liu, X.

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

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. USA 107, 13576–13581 (2010).

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. USA 107, 13576–13581 (2010).

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. USA 107, 13576–13581 (2010).

Menk, R.

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

Momose, A.

A. Momose, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).

Nomarski, G.

G. Nomarski, “Interféromètre à polarization,” French patent1.059.123 (May14, 1952).

Olivo, A.

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

Peter, R. T.

R. T. Peter, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA 109, 13922–13927 (2012).

Pfeiffer, F.

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, 258–261 (2006).
[CrossRef]

Pisano, E.

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

Sasaya, T.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Sayers, D.

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

Smith, F. H.

F. H. Smith, “Improvements in or relating to microscopy,” British patent639 014, Class 97(i), Group XX (August5, 1947).

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. USA 107, 13576–13581 (2010).

Thomlinson, W.

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

Töpler, A.

A. Töpler, “Beobachtungen nach einer neuen optischen Methode,” Pogg. Ann. Physik u. Chem 127, 556–580 (1866).

Wang, M.

M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
[CrossRef]

Wang, Z.

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

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

Wang, Z. L.

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

Washburn, D.

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

Watanabe, N.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[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, 258–261 (2006).
[CrossRef]

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. USA 107, 13576–13581 (2010).

Yuan, Q.

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

Yuan, Q. X.

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

Zama, K.

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Zhang, K.

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

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

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

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
[CrossRef]

Zhong, Z.

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

Zhu, P.

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

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

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
[CrossRef]

Zhu, P. P.

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

P. P. Zhu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Zhu, Z.

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

AIP Conf. Proc.

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

N. Watanabe, T. Sasaya, Y. Imai, S. Iwata, K. Zama, and S. Aoki, “Observation of phase objects by using an x-ray microscope with a Foucault knife-edge,” AIP Conf. Proc. 1365, 313–316 (2011).
[CrossRef]

Y. Hong, P. Zhu, K. Zhang, Z. Wang, and Z. Zhu, “Analysis of absorption and phase difference images from differential interference contrast microscopy,” AIP Conf. Proc. 1365, 246–249 (2011).
[CrossRef]

Ann. de l’Observatoire Imp. de Paris

L. Foucault, “Mémoire sur la construction des télescopes en verre argenté,” Ann. de l’Observatoire Imp. de Paris 5, 197–237 (1859).

Appl. Phys. Lett.

P. P. Zhu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Z. F. Huang, “Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging,” Appl. Phys. Lett. 89, 041124 (2006).
[CrossRef]

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

J. Phys.

M. Wang, P. Zhu, and K. Zhang, “A new method to extract angle of refraction in diffraction enhanced imaging computed tomography,” J. Phys. 40, 6917–6921 (2007).
[CrossRef]

Jpn. J. Appl. Phys.

A. Momose, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).

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, 258–261 (2006).
[CrossRef]

Nature

T. J. Davis, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Phys. Med. Biol.

K. Zhang, P. Zhu, W. Huang, and Q. Yuan, “Investigation of misalignment in analyzer crystal based-CT and its effect,” Phys. Med. Biol. 53, 5757–5766 (2008).
[CrossRef]

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

Phys. Rev. A

Z. F. Huang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x-rays,” Phys. Rev. A 79, 013815 (2009).
[CrossRef]

Pogg. Ann. Physik u. Chem

A. Töpler, “Beobachtungen nach einer neuen optischen Methode,” Pogg. Ann. Physik u. Chem 127, 556–580 (1866).

Proc. Natl. Acad. Sci. USA

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. USA 107, 13576–13581 (2010).

R. T. Peter, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA 109, 13922–13927 (2012).

Other

Y. Hong, “X-ray phase contrast imaging research and application in X-ray microscopy,” Ph.D. thesis, Beijing: Institute of High Energy Physics (Chinese Academy of Sciences, 2012).

J. F. Clauser, “Ultrahigh resolution interferometric x-ray imaging,” US patent5812629 (September22, 1998).

F. H. Smith, “Improvements in or relating to microscopy,” British patent639 014, Class 97(i), Group XX (August5, 1947).

G. Nomarski, “Interféromètre à polarization,” French patent1.059.123 (May14, 1952).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of DEI.

Fig. 2.
Fig. 2.

Rocking curve.

Fig. 3.
Fig. 3.

Schematic of grating-based imaging.

Fig. 4.
Fig. 4.

Shifting curve.

Fig. 5.
Fig. 5.

Schematic of DIC microscope.

Fig. 6.
Fig. 6.

Shifting curve.

Fig. 7.
Fig. 7.

Schematic of differential phase contrast x-ray microscope.

Fig. 8.
Fig. 8.

Shifting curve.

Fig. 9.
Fig. 9.

Schematic of differential phase contrast x-ray microscope [10].

Fig. 10.
Fig. 10.

Shifting curve.

Equations (51)

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

IθA=I0R(θA),
IθA(x,y)=I0exp[M(x,y)]R[θAθx(x,y)],
M(x,y)=μ(x,y,z)dz,
θx(x,y)=δ(x,y,z)xdz,
IU(x,y)=I0exp[M(x,y)]R(θD2)[1CUcθx(x,y)],
ID(x,y)=I0exp[M(x,y)]R(θD2)[1CDcθx(x,y)],
R(θD2)=R(θD2),dR(θD2)/dθA=dR(θD2)/dθA,
CUc=CDc,
M(x,y)=ln(2I0R(θD2)ID(x,y)+IU(x,y))=μ(x,y,z)dz,
θx(x,y)=1CDcID(x,y)IU(x,y)ID(x,y)+IU(x,y)=δ(x,y,z)xdz.
IU(x,y,φ)=ID(x,y,φ+π),
M(x,y,φ)=ln(2I0R(θD2)ID(x,y,φ)+ID(x,y,φ+π))=μ(x,y,z,φ)dz,
θx(x,y,φ)=1CDcID(x,y,φ)ID(x,y,φ+π)ID(x,y,φ)+ID(x,y,φ+π)=δ(x,y,z,φ)xdz.
IxgD=I0S(xgD),
IxgD(x,y)=I0exp[M(x,y)]S[xgDθx(x,y)],
IU(x,y)=I0exp[M(x,y)]S(p4D)[1CUgθx(x,y)],
ID(x,y)=I0exp[M(x,y)]S(p4D)[1CDgθx(x,y)],
S(p4D)=S(p4D),dS(p4D)/d(xgD)=dS(p4D)/d(xgD),
CUg=CDg,
M(x,y)=ln(2I0S(p4D)ID(x,y)+IU(x,y))=μ(x,y,z)dz,
θx(x,y)=1CDgID(x,y)IU(x,y)ID(x,y)+IU(x,y)=δ(x,y,z)xdz.
IU(x,y,φ)=ID(x,y,φ+π),
M(x,y,φ)=ln(2I0S(p4D)ID(x,y,φ)+ID(x,y,φ+π))=μ(x,y,z,φ)dz,
θx(x,y,φ)=1CDgID(x,y,φ)ID(x,y,φ+π)ID(x,y,φ)+ID(x,y,φ+π)=δ(x,y,z,φ)xdz.
I2θ=I0S(2θ)=I0[1212cos(2θ)],
I2θ(x,y)=I0exp[M(x,y)]S[2θΔΦ(x,y)]=I0exp[M(x,y)][1212cos(2θΔΦ(x,y))],
ΔΦ(x,y)=Φ(x+Δx,y)Φ(xΔx,y)=2πΔxλδ(x,y,z)xdz,
ΔΦ(x,y)Δx2πλθx(x,y).
ID(x,y)=I0exp[M(x,y)]1+sin(ΔΦ(x,y))2,
IU(x,y)=I0exp[M(x,y)]1sin(ΔΦ(x,y))2.
M(x,y)=ln(I0ID(x,y)+IU(x,y))=μ(x,y,z)dz,
ΔΦ(x,y)=arcsin(ID(x,y)IU(x,y)ID(x,y)+IU(x,y))=2πΔxλδ(x,y,z)xdz.
IU(x,y,φ)=ID(x,y,φ+π),
M(x,y,φ)=ln(I0ID(x,y,φ)+ID(x,y,φ+π))=μ(x,y,z,φ)dz,
ΔΦ(x,y,φ)=arcsinID(x,y,φ)ID(x,y,φ+π)ID(x,y,φ)+ID(x,y,φ+π)=2πΔxλδ(x,y,z,φ)xdz.
IxaF=I0S(xaF),
IxaF(x,y)=I0exp[M(x,y)]S[xaFθx(x,y)],
ID(x,y)=I0exp[M(x,y)]S(w2F)[1CDmθx(x,y)],
IU(x,y)=I0exp[M(x,y)]S(w2F)[1CUmθx(x,y)],
S(w2F)=S(w2F),dS(w2F)/d(xaF)=dS(w2F)/d(xaF),
CDm=CUm,
M(x,y)=ln(2I0S(w2F)ID(x,y)+IU(x,y))=μ(x,y,z)dz,
θx(x,y)=1CDmID(x,y)IU(x,y)ID(x,y)+IU(x,y)=δ(x,y,z)xdz.
IU(x,y,φ)=ID(x,y,φ+π),
M(x,y,φ)=ln(2I0S(w2F)ID(x,y,φ)+ID(x,y,φ+π))=μ(x,y,z,φ)dz,
θx(x,y,φ)=1CDmID(x,y,φ)ID(x,y,φ+π)ID(x,y,φ)+ID(x,y,φ+π)=δ(x,y,z,φ)xdz.
IxeF=I0S(xeF),
IxeF(x,y)=I0exp[M(x,y)]S[xeFθx(x,y)],
IH(x,y)=I0exp[M(x,y)]S(0)[1CHmθx(x,y)],
M(x,y,φ)=ln(2I0S(0)IH(x,y,φ)IH(x,y,φ+π))=μ(x,y,z,φ)dz,
θx(x,y,φ)=1CHmIH(x,y,φ)IH(x,y,φ+π)IH(x,y,φ)+IH(x,y,φ+π)=δ(x,y,z,φ)xdz.

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