Abstract

We have developed two phase-retrieval techniques for analyser-based phase contrast imaging that provide information about an object’s X-ray absorption, refraction and scattering properties. The first requires rocking curves to be measured with and without the sample and improves upon existing techniques by accurately fitting the curves with Pearson type VII functions. The second employs an iterative approach using two simultaneously recorded images by exploiting the Laue crystal geometry. This technique provides a substantial reduction in X-ray dose and enables quantitative phase retrieval to be performed on images of moving objects.

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
  3. D. M. Paganin, Coherent X-ray optics (Oxford University Press, Oxford, UK, 2006).
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  5. M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
    [CrossRef] [PubMed]
  6. E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
    [CrossRef]
  7. H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
    [CrossRef] [PubMed]
  8. Y. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008).
    [CrossRef]
  9. C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
    [CrossRef]
  10. O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
    [CrossRef]
  11. M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
    [CrossRef]
  12. Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
    [CrossRef] [PubMed]
  13. L. Rigon, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D: Appl. Phys. 40(10), 3077–3089 (2007).
    [CrossRef]
  14. C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
    [CrossRef] [PubMed]
  15. Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
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    [CrossRef]
  19. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
    [CrossRef]
  27. M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  29. D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
    [CrossRef]
  30. M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  33. R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (3)

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[CrossRef]

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18(4), 3494–3509 (2010).
[CrossRef] [PubMed]

2009 (2)

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

2008 (5)

S.-A. Zhou and A. Brahme, “Development of phase-contrast X-ray imaging techniques and potential medical applications,” Phys. Medica 24(3), 129–148 (2008).
[CrossRef]

Y. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008).
[CrossRef]

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

C. Hu, L. Zhang, H. Li, and S. Lo, “Comparison of refraction information extraction methods in diffraction enhanced imaging,” Opt. Express 16(21), 16704–16710 (2008).
[CrossRef] [PubMed]

2007 (6)

Z. Huang, K. Kejun, and Y. Yigang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
[CrossRef]

A. Maksimenko, “Nonlinear extension of the X-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90(15), 154106 (2007).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

L. Rigon, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D: Appl. Phys. 40(10), 3077–3089 (2007).
[CrossRef]

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

2005 (3)

V. A. Bushuev and M. A. Guskova, “Image reconstruction in X-ray phase contrast method with crystal analyser in Laue geometry,” Bull. Russ. Acad. Sci. Phys. 69, 253–259 (2005).

S. Nadarajah and D. K. Dey, “Convolutions of the Pearson type VII distribution,” Comput. Math. Appl. 50(3-4), 339–346 (2005).
[CrossRef]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

2004 (3)

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

2003 (3)

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

2001 (1)

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
[CrossRef]

1997 (1)

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

1996 (1)

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

1995 (1)

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D: Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

1992 (1)

J. M. Boone, “Parametrized x-ray absorption in diagnostic radiology from Monte Carlo calculations: implications for x-ray detector design,” Med. Phys. 19(6), 1467–1473 (1992).
[CrossRef] [PubMed]

1977 (1)

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

1962 (1)

1926 (1)

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[CrossRef]

Anastasio, M. A.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Arfelli, F.

L. Rigon, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D: Appl. Phys. 40(10), 3077–3089 (2007).
[CrossRef]

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Baruchel, J.

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Beliaevskaya, E. A.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D: Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Boone, J. M.

J. M. Boone, “Parametrized x-ray absorption in diagnostic radiology from Monte Carlo calculations: implications for x-ray detector design,” Med. Phys. 19(6), 1467–1473 (1992).
[CrossRef] [PubMed]

Brahme, A.

S.-A. Zhou and A. Brahme, “Development of phase-contrast X-ray imaging techniques and potential medical applications,” Phys. Medica 24(3), 129–148 (2008).
[CrossRef]

Brankov, J. G.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Bravin, A.

P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18(4), 3494–3509 (2010).
[CrossRef] [PubMed]

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Brey, E. M.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

Bushuev, V. A.

V. A. Bushuev and M. A. Guskova, “Image reconstruction in X-ray phase contrast method with crystal analyser in Laue geometry,” Bull. Russ. Acad. Sci. Phys. 69, 253–259 (2005).

Chapman, D.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Chen, Z.-Q.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Chou, C.-Y.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

Cloetens, P.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Coan, P.

P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18(4), 3494–3509 (2010).
[CrossRef] [PubMed]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Connor, D. M.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

Davis, J. R.

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
[CrossRef]

Dey, D. K.

S. Nadarajah and D. K. Dey, “Convolutions of the Pearson type VII distribution,” Comput. Math. Appl. 50(3-4), 339–346 (2005).
[CrossRef]

Diemoz, P. C.

Ding, F.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Dubsky, S.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

Fernández, M.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Fiedler, S.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Förster, E.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Fouras, A.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

Galatsanos, N. P.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Glaser, C.

Gmür, N.

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Gureyev, T. E.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

Guskova, M. A.

V. A. Bushuev and M. A. Guskova, “Image reconstruction in X-ray phase contrast method with crystal analyser in Laue geometry,” Bull. Russ. Acad. Sci. Phys. 69, 253–259 (2005).

Habib, A.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

Hall, C. J.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Hall, M. M.

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

Härtwig, J.

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Hasnah, M.

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

Hooper, S. B.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Hu, C.

Huang, Z.

Z. Huang, K. Kejun, and Y. Yigang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
[CrossRef]

Huang, Z.-F.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Ingal, V. N.

V. N. Ingal and E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D: Appl. Phys. 28(11), 2314–2317 (1995).
[CrossRef]

Johnson, R. E.

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Johnston, R. E.

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

Kämpfe, T.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Karjalainen-Lindsberg, M.-L.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

Kejun, K.

Z. Huang, K. Kejun, and Y. Yigang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
[CrossRef]

Keller, J. B.

Kewish, C. M.

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
[CrossRef]

Keyriläinen, J.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Kitchen, M.

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Kitchen, M. J.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Kley, E.-B.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Leidenius, M.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

Lewis, R. A.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Li, H.

Lo, S.

Maksimenko, A.

A. Maksimenko, “Nonlinear extension of the X-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90(15), 154106 (2007).
[CrossRef]

Menk, R. H.

L. Rigon, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D: Appl. Phys. 40(10), 3077–3089 (2007).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Morgan, M. J.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
[CrossRef]

Muehleman, C.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Nadarajah, S.

S. Nadarajah and D. K. Dey, “Convolutions of the Pearson type VII distribution,” Comput. Math. Appl. 50(3-4), 339–346 (2005).
[CrossRef]

Nesterets, Y. I.

Y. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008).
[CrossRef]

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

Nugent, K. A.

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[CrossRef]

Oltulu, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

Paganin, D.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Paganin, D. M.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Pagot, E.

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Pavlov, K.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Pavlov, K. M.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
[CrossRef]

Pisano, E.

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Rigon, L.

L. Rigon, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D: Appl. Phys. 40(10), 3077–3089 (2007).
[CrossRef]

Rubin, H.

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

Sayers, D.

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Siew, M. L. L.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

Siu, K. K. W.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Slack, C. M.

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[CrossRef]

Suhonen, H.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Suortti, P.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Suzuki, Y.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Takeuchi, A.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Thomlinson, W.

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Tromba, G.

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

Uesugi, K.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Veeraraghavan, V. G.

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

Vine, D. J.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

von Smitten, K.

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

Wallace, M. J.

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Wang, Z.-C.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Washburn, D.

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Wernick, M. N.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Whitley, J.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Wilkins, S. W.

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

Williams, I.

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Winchell, P. G.

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Yagi, N.

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

Yang, Y.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

Yigang, Y.

Z. Huang, K. Kejun, and Y. Yigang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
[CrossRef]

Yin, H.-X.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Zhang, L.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

C. Hu, L. Zhang, H. Li, and S. Lo, “Comparison of refraction information extraction methods in diffraction enhanced imaging,” Opt. Express 16(21), 16704–16710 (2008).
[CrossRef] [PubMed]

Zhong, Z.

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

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

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Zhou, S.-A.

S.-A. Zhou and A. Brahme, “Development of phase-contrast X-ray imaging techniques and potential medical applications,” Phys. Medica 24(3), 129–148 (2008).
[CrossRef]

Zhu, P.-P.

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Acta Crystallogr. A (1)

Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A 62(4), 296–308 (2006).
[CrossRef] [PubMed]

Adv. Phys. (1)

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyzer-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

A. Maksimenko, “Nonlinear extension of the X-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90(15), 154106 (2007).
[CrossRef]

Bull. Russ. Acad. Sci. Phys. (1)

V. A. Bushuev and M. A. Guskova, “Image reconstruction in X-ray phase contrast method with crystal analyser in Laue geometry,” Bull. Russ. Acad. Sci. Phys. 69, 253–259 (2005).

Chinese Phys. C (1)

Z.-Q. Chen, F. Ding, Z.-F. Huang, L. Zhang, H.-X. Yin, Z.-C. Wang, and P.-P. Zhu, “Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging,” Chinese Phys. C 33(11), 969–974 (2009).
[CrossRef]

Comput. Math. Appl. (1)

S. Nadarajah and D. K. Dey, “Convolutions of the Pearson type VII distribution,” Comput. Math. Appl. 50(3-4), 339–346 (2005).
[CrossRef]

Eur. J. Radiol. (2)

M. Fernández, H. Suhonen, J. Keyriläinen, A. Bravin, S. Fiedler, M.-L. Karjalainen-Lindsberg, M. Leidenius, K. von Smitten, and P. Suortti, “USAXS and SAXS from cancer-bearing breast tissue samples,” Eur. J. Radiol. 68(3Suppl), S89–S94 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[CrossRef] [PubMed]

J. Appl. Cryst. (1)

M. M. Hall, V. G. Veeraraghavan, H. Rubin, and P. G. Winchell, “The approximation of symmetric X-ray peaks by Pearson type VII distributions,” J. Appl. Cryst. 10(1), 66–68 (1977).
[CrossRef]

J. Instrum. (1)

M. J. Kitchen, A. Habib, A. Fouras, S. Dubsky, R. A. Lewis, M. J. Wallace, and S. B. Hooper, “A new design for high stability pressure-controlled ventilation for small animal lung imaging,” J. Instrum. 5(02), T02002 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. D: Appl. Phys. (6)

K. M. Pavlov, C. M. Kewish, J. R. Davis, and M. J. Morgan, “A variant on the geometrical optics approximation in diffraction enhanced tomography,” J. Phys. D: Appl. Phys. 34(10A), A168–A172 (2001).
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[CrossRef]

O. Oltulu, Z. Zhong, M. Hasnah, M. N. Wernick, and D. Chapman, “Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging,” J. Phys. D: Appl. Phys. 36(17), 2152–2156 (2003).
[CrossRef]

Y. I. Nesterets, T. E. Gureyev, D. Paganin, K. M. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D: Appl. Phys. 37(8), 1262–1274 (2004).
[CrossRef]

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to X-ray phase-contrast imaging,” J. Phys. D: Appl. Phys. 37(19), 2746–2750 (2004).
[CrossRef]

J. Synchrotron Radiat. (1)

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

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J. M. Boone, “Parametrized x-ray absorption in diagnostic radiology from Monte Carlo calculations: implications for x-ray detector design,” Med. Phys. 19(6), 1467–1473 (1992).
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Nucl. Instrum. Meth. A (1)

Z. Huang, K. Kejun, and Y. Yigang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
[CrossRef]

Opt. Commun. (2)

Y. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008).
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D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun. 234(1-6), 87–105 (2004).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (5)

R. A. Lewis, N. Yagi, M. J. Kitchen, M. J. Morgan, D. Paganin, K. K. W. Siu, K. Pavlov, I. Williams, K. Uesugi, M. J. Wallace, C. J. Hall, J. Whitley, and S. B. Hooper, “Dynamic imaging of the lungs using x-ray phase contrast,” Phys. Med. Biol. 50(21), 5031–5040 (2005).
[CrossRef] [PubMed]

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

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[CrossRef]

C.-Y. Chou, M. A. Anastasio, J. G. Brankov, M. N. Wernick, E. M. Brey, D. M. Connor, and Z. Zhong, “An extended diffraction-enhanced imaging method for implementing multiple-image radiography,” Phys. Med. Biol. 52(7), 1923–1945 (2007).
[CrossRef] [PubMed]

M. J. Kitchen, K. M. Pavlov, K. K. W. Siu, R. H. Menk, G. Tromba, and R. A. Lewis, “Analyser-based phase contrast image reconstruction using geometrical optics,” Phys. Med. Biol. 52(14), 4171–4187 (2007).
[CrossRef] [PubMed]

Phys. Medica (1)

S.-A. Zhou and A. Brahme, “Development of phase-contrast X-ray imaging techniques and potential medical applications,” Phys. Medica 24(3), 129–148 (2008).
[CrossRef]

Phys. Rev. (1)

C. M. Slack, “The refraction of X-rays in prisms of various materials,” Phys. Rev. 27(6), 691–695 (1926).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Vine, D. M. Paganin, K. M. Pavlov, K. Uesugi, A. Takeuchi, Y. Suzuki, N. Yagi, T. Kämpfe, E.-B. Kley, and E. Förster, “Deterministic retrieval of complex Green’s functions using hard X rays,” Phys. Rev. Lett. 102(4), 043901 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. H. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” Rev. Sci. Instrum. 67(9), 1–5 (1996).
[CrossRef]

Other (2)

A. Authier, Dynamical theory of X-ray diffraction, rev. ed. (Oxford University Press, Oxford, UK, 2005).

D. M. Paganin, Coherent X-ray optics (Oxford University Press, Oxford, UK, 2006).

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Figures (15)

Fig. 1
Fig. 1

Schematic of the experimental analyser-based X-ray imaging setup used in this research (not to scale).

Fig. 2
Fig. 2

(a) Measured rocking curves (RCs) for the transmitted and diffracted beams through the Si(1 1 1) Laue analyser using 26 keV X-rays. This plot shows the intrinsic rocking curves measured with no sample in the beam and with the beam transmitted through the lung of a mouse. The rocking curves measured through the lung show reduced intensity due to absorption; a shift in peak position due to refraction; and broadening by USAXS within the sample. Each curve is measured using a single pixel from 260 angular measurements in 0.1 arc second angular steps. The vertical (dashed) orange line shows the angle at which images in Fig. 3 were recorded. (b) The diffracted (intrinsic) rocking curve from (a) is here symmetrised by mirroring the intensity on the positive side of the curve to the negative side. Both a symmetric Gaussian and Pearson type VII function are fit to the experimental data.

Fig. 4
Fig. 4

Flow-chart for the dual-image iterative phase retrieval algorithm. * represents an optional step.

Fig. 3
Fig. 3

(a) Diffracted and (b) transmitted images of a mouse thorax recorded using a Si(1 1 1) Laue analyser crystal with 26 keV X-rays. Field-of-view (FOV): 21×21 mm2. The mouse is submerged in a tube of water, hence the attenuation is similar everywhere but appears darker through the more attenuating bones and brighter through the air filled (low density) lung tissue. The bright curved (horizontal) line through the lung reveals the ventral edge of the lung following the shape of the diaphragm. The centers of the black circles on the ventral edge indicate the position at which the rocking curves in Fig. 2 were recorded.

Fig. 5
Fig. 5

Angular X-ray scattering distribution P ( θ ) (thick black curve) of a section of mouse lung tissue highlighted in Fig. 3. The thin red curve shows the Pearson type VII function fit to the scattering distribution.

Fig. 6
Fig. 6

Multiple image radiography of an adolescent mouse thorax. (a) Refraction angle image. (b) Scatter HWHM image. (c) Integrated absorption image. (d) Peak absorption image. FOV: 21 × 21 mm2. X-ray energy: 26 keV. Net exposure time: 78 s.

Fig. 7
Fig. 7

Multiple image radiography of two cylindrical cavities in a PMMA block. The lower cavity is filled with hollow glass microspheres. (a) Refraction angle image. (b) Scatter HWHM image. (c) Integrated absorption image. (d) Peak absorption image. FOV: 25 × 16 mm2. X-ray energy: 26 keV. Net exposure time: 78 s.

Fig. 8
Fig. 8

Refraction angle ( Δ θ ) images of the PMMA phantom calculated using two simultaneously recorded images. Here the diffracted intensity was approximately 10% of the Bragg peak reflectivity. FOV: 25 × 16 mm2. X-ray energy: 26 keV. Net exposure time: 300 ms.

Fig. 9
Fig. 9

Scattering width parameter a (see Eq. (1)) used for iterative phase retrieval of (a) the PMMA cavity containing hollow glass microspheres and (b) mouse lung tissue.

Fig. 10
Fig. 10

RMS differences between iteratively reconstructed and known projected glass microsphere thickness for the reconstruction shown in Fig. 8(c). Black dashed lines there show the corresponding positions L1 and L2.

Fig. 11
Fig. 11

Refraction angle ( Δ θ ) images of the PMMA phantom calculated using two simultaneously recorded images. Here the diffracted intensity was approximately 1% of the Bragg peak reflectivity. FOV: 25 × 16 mm2. X-ray energy: 26 keV. Net exposure time: 300 ms.

Fig. 12
Fig. 12

Apparent absorption images of the PMMA phantom reconstructed at (a) 10% and (b) 1% Bragg reflectivity, respectively. (c) and (d) are scatter HWHM images of the microsphere-filled cavity at the same respective reflectivities as (a) and (b). X-ray energy: 26 keV. Net exposure time: 300 ms.

Fig. 13
Fig. 13

Projected thickness profiles of the (a) hollow cavity and (b) microsphere filled cavity shown reconstructed using MIR (Fig. 7), and dual-image ABI at 10% reflectivity (Fig. 8) and 1% reflectivity (Fig. 11) (see white dashed lines in figures for profile locations).

Fig. 14
Fig. 14

Refraction angle images of the mouse thorax calculated using two simultaneously recorded images. Here the diffracted intensity was approximately 15% of the Bragg peak intensity. (a) Initial refraction angle reconstruction. (b) Best iterative refraction angle reconstruction. (c) Scatter HWHM image. (d) Apparent absorption image. FOV: 21 × 21 mm2. X-ray energy: 26 keV. Net exposure time: 300 ms.

Fig. 15
Fig. 15

(a) Optimal number of iterations used to generate the refraction angle map for the mouse lung shown in Fig. 14(b). (b) Projected lung volume calculated from Fig. 6(b) (MIR – thick black line) and Fig. 14(b) (dual-image iterative reconstruction – thin red line) summed along vertical columns.

Tables (1)

Tables Icon

Table 1 Volume fraction (%) and FOM (in parentheses) of the cylindrical cavities measured using MIR and dual-image reconstructions.

Equations (8)

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y = c [ 1 + ( x x ˜ ) 2 / ( m a 2 ) ] m
Δ θ = θ s θ 0 .
P ( θ S c a t ) H W H M = a m ( 2 1 / m 1 ) .
[ I T I D ] = I R [ T ( θ 0 + Δ θ ) R ( θ 0 + Δ θ ) ] ,
θ = ± a m [ ( c I T / I D ) 1 / m 1 ] .
I T = I R T ( θ ) = I R { f d [ 1 + θ 2 / ( n b 2 ) ] n } .
I R = I T { f d [ 1 + θ 2 / ( n b 2 ) ] n } 1 .
t ( y ) = ( 1 / δ ) Δ θ ( y ) d y .

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