Abstract

Several x-ray phase contrast extraction algorithms use a set of images acquired along the rocking curve of a perfect flat analyzer crystal to study the internal structure of objects. By measuring the angular shift of the rocking curve peak, one can determine the local deflections of the x-ray beam propagated through a sample. Additionally, some objects determine a broadening of the crystal rocking curve, which can be explained in terms of multiple refraction of x rays by many subpixel-size inhomogeneities contained in the sample. This fact may allow us to differentiate between materials and features characterized by different refraction properties. In the present work we derive an expression for the beam broadening in the form of a linear integral of the quantity related to statistical properties of the dielectric susceptibility distribution function of the object.

© 2012 Optical Society of America

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References

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  1. R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53(7), 23–26 (2000).
    [CrossRef]
  2. R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
    [CrossRef]
  3. 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, 2015–2025 (1997).
    [CrossRef]
  4. 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, 3875–3895 (2003).
    [CrossRef]
  5. L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
    [CrossRef]
  6. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
    [CrossRef]
  7. J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
    [CrossRef]
  8. A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
    [CrossRef]
  9. A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981).
    [CrossRef]
  10. G. W. Faris and R. L. Byer, “Three-dimensional beam deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212 (1988).
    [CrossRef]
  11. V. A. Bushuev and A. A. Sergeev, “Inverse problem in the x-ray phase contrast method,” Tech. Phys. Lett. 25, 83–85 (1999).
    [CrossRef]
  12. C. M. Slack, “The refraction of x-rays in prisms of various materials,” Phys. Rev. 27, 691–695 (1926).
    [CrossRef]
  13. L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
    [CrossRef]
  14. M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
    [CrossRef]
  15. L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
    [CrossRef]
  16. M. Bech, “Scattering dependence on sample thickness” in X-ray Imaging with a Grating Interferometer, Ph.D. thesis (Faculty of Science, University of Copenhagen, 2009), p. 44.
  17. G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
    [CrossRef]
  18. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, “Propagation of waves in mediums with large-scale inhomogeneities. Geometrical optics method,” in Vol. 2 of Principles of Statistical Radiophysics (Springer-Verlag, 1988).
  19. A. S. Gurvich and M. A. Kallistratova, “Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations,” Radiophys. Quantum Electron. 11, 37–40 (1968).
    [CrossRef]
  20. L. Mandel and E. Wolf, “Radiation from some model sources,” in Optical Coherence and Quantum Optics (Cambridge University, 1995), p. 234.

2012 (1)

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

2010 (1)

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

2008 (3)

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

2007 (1)

L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
[CrossRef]

2006 (1)

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[CrossRef]

2004 (1)

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
[CrossRef]

2003 (2)

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, 3875–3895 (2003).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

2000 (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53(7), 23–26 (2000).
[CrossRef]

1999 (1)

V. A. Bushuev and A. A. Sergeev, “Inverse problem in the x-ray phase contrast method,” Tech. Phys. Lett. 25, 83–85 (1999).
[CrossRef]

1997 (1)

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, 2015–2025 (1997).
[CrossRef]

1988 (1)

1981 (1)

1968 (1)

A. S. Gurvich and M. A. Kallistratova, “Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations,” Radiophys. Quantum Electron. 11, 37–40 (1968).
[CrossRef]

1926 (1)

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

Anastasio, M. A.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[CrossRef]

Arfelli, F.

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

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, 2015–2025 (1997).
[CrossRef]

Astolfo, A.

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

Bamberg, F.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Bech, M.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

M. Bech, “Scattering dependence on sample thickness” in X-ray Imaging with a Grating Interferometer, Ph.D. thesis (Faculty of Science, University of Copenhagen, 2009), p. 44.

Besch, H.-J.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

Brankov, J. G.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[CrossRef]

Bravin, A.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Bronnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Brun, E.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Bunk, O.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Bushuev, V. A.

V. A. Bushuev and A. A. Sergeev, “Inverse problem in the x-ray phase contrast method,” Tech. Phys. Lett. 25, 83–85 (1999).
[CrossRef]

Byer, R. L.

Chapman, D.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[CrossRef]

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, 2015–2025 (1997).
[CrossRef]

Coan, P.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

David, C.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Devaney, A. J.

Diemoz, P. C.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Donath, T.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Faris, G. W.

Feidenhans, R.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

Fernandez, M.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Fiedler, S.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Fitzgerald, R.

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53(7), 23–26 (2000).
[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, 3875–3895 (2003).
[CrossRef]

Gmur, N.

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, 2015–2025 (1997).
[CrossRef]

Grunzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Gurvich, A. S.

A. S. Gurvich and M. A. Kallistratova, “Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations,” Radiophys. Quantum Electron. 11, 37–40 (1968).
[CrossRef]

Heitner, G.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

Johnston, R. E.

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, 2015–2025 (1997).
[CrossRef]

Kallistratova, M. A.

A. S. Gurvich and M. A. Kallistratova, “Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations,” Radiophys. Quantum Electron. 11, 37–40 (1968).
[CrossRef]

Karjalainen-Lindsberg, M. L.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Keyrilainen, J.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Khelashvili, G.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[CrossRef]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, “Propagation of waves in mediums with large-scale inhomogeneities. Geometrical optics method,” in Vol. 2 of Principles of Statistical Radiophysics (Springer-Verlag, 1988).

Leidenius, M.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Lewis, R. A.

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, “Radiation from some model sources,” in Optical Coherence and Quantum Optics (Cambridge University, 1995), p. 234.

Mayr, D.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Menk, R.

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, 2015–2025 (1997).
[CrossRef]

Menk, R. H.

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
[CrossRef]

Menk, R.-H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[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, 3875–3895 (2003).
[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, 3875–3895 (2003).
[CrossRef]

Pfeiffer, F.

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Pisano, E.

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, 2015–2025 (1997).
[CrossRef]

Plothow-Besch, H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

Reiser, M. F.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Rigon, L.

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, “Propagation of waves in mediums with large-scale inhomogeneities. Geometrical optics method,” in Vol. 2 of Principles of Statistical Radiophysics (Springer-Verlag, 1988).

Sayers, D.

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, 2015–2025 (1997).
[CrossRef]

Schlossbauer, T.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Sergeev, A. A.

V. A. Bushuev and A. A. Sergeev, “Inverse problem in the x-ray phase contrast method,” Tech. Phys. Lett. 25, 83–85 (1999).
[CrossRef]

Sipila, P.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Slack, C. M.

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

Suhonen, H.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Suortti, P.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Sztrokay, A.

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

Tatarskii, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, “Propagation of waves in mediums with large-scale inhomogeneities. Geometrical optics method,” in Vol. 2 of Principles of Statistical Radiophysics (Springer-Verlag, 1988).

Thomlinson, W.

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, 2015–2025 (1997).
[CrossRef]

Virkkunen, P.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

von Smitten, K.

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Washburn, D.

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, 2015–2025 (1997).
[CrossRef]

Wernick, M. N.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[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, 3875–3895 (2003).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, “Radiation from some model sources,” in Optical Coherence and Quantum Optics (Cambridge University, 1995), p. 234.

Yang, Y.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[CrossRef]

Zhong, Z.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[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, 3875–3895 (2003).
[CrossRef]

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, 2015–2025 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Rigon, F. Arfelli, and R. H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90, 114102 (2007).
[CrossRef]

Eur. J. Radiol. (1)

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol. 68, S3–S7 (2008).
[CrossRef]

J. Phys. D (1)

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D 36, A107–A112 (2003).
[CrossRef]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Bronnimann, C. Grunzweig, and C. David, “Hard-x-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (6)

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573–3583 (2004).
[CrossRef]

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, 2015–2025 (1997).
[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, 3875–3895 (2003).
[CrossRef]

A. Sztrokay, P. C. Diemoz, T. Schlossbauer, E. Brun, F. Bamberg, D. Mayr, M. F. Reiser, A. Bravin, and P. Coan, “High resolution breast tomography at high energy: a feasibility study of phase contrast imaging on a whole breast,” Phys. Med. Biol. 57, 2931–2942 (2012).
[CrossRef]

M. Bech, O. Bunk, T. Donath, R. Feidenhans, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[CrossRef]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol. 51, 221–236 (2006).
[CrossRef]

Phys. Rev. (1)

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

Phys. Today (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53(7), 23–26 (2000).
[CrossRef]

Radiology (1)

J. Keyrilainen, M. Fernandez, M. L. Karjalainen-Lindsberg, P. Virkkunen, M. Leidenius, K. von Smitten, P. Sipila, S. Fiedler, H. Suhonen, P. Suortti, and A. Bravin, “Towards high-contrast breast CT at low radiation dose,” Radiology 249, 321–327 (2008).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. S. Gurvich and M. A. Kallistratova, “Experimental study of the fluctuations in angle of incidence of a light beam under conditions of strong intensity fluctuations,” Radiophys. Quantum Electron. 11, 37–40 (1968).
[CrossRef]

Tech. Phys. Lett. (1)

V. A. Bushuev and A. A. Sergeev, “Inverse problem in the x-ray phase contrast method,” Tech. Phys. Lett. 25, 83–85 (1999).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, “Radiation from some model sources,” in Optical Coherence and Quantum Optics (Cambridge University, 1995), p. 234.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, “Propagation of waves in mediums with large-scale inhomogeneities. Geometrical optics method,” in Vol. 2 of Principles of Statistical Radiophysics (Springer-Verlag, 1988).

M. Bech, “Scattering dependence on sample thickness” in X-ray Imaging with a Grating Interferometer, Ph.D. thesis (Faculty of Science, University of Copenhagen, 2009), p. 44.

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of an ABI experiment. (a) An x-ray wave propagates through an object that is composed of several large-scale structures that can be uniform or containing subpixel inhomogeneities. The wavefront is then analyzed by a perfect Bragg crystal before being recorded by a pixilated detector. The wavefront can be considered divided in small portions, which are associated with the detector pixels (marked as A, B, C). Two rocking curves are measured: one without [dotted (thick black) line in (b)] and one with the object in the x-ray beam, respectively. Depending on the characteristics of the internal structures of the sample, the rocking curve acquired with the object (in different pixels) can be compared to the curve without object: A, broadened, if the medium consists of many random inhomogeneities [solid (thin red) line in (b)]; C, shifted, if the x rays are deflected from the initial propagation direction when the wave crosses the interface (l) between two parts of the object with different indexes of refraction [dashed line in (b)]; B, shifted and broadened, if the x rays experience both regular refraction on large-scale structures and the interaction with many subpixel-size features [dotted–dashed line in (b)].

Fig. 2.
Fig. 2.

Integration region after change of variables in Eq. (12).

Fig. 3.
Fig. 3.

Change of variables in Eq. (15), performed to describe the propagation of a nonplane wave in the medium with variable mean dielectric susceptibility.

Fig. 4.
Fig. 4.

Unperturbed vector t0 and the decomposition of the first correction term t1 in the plane tangential to the unperturbed wavefront.

Equations (35)

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u+k2ϵ(r)u=0,
u=AeiS=Aeikϕ.
(ϕ)2=ϵ.
rs=t,ts=12ϵ[ϵt(tϵ)],
t=ϕϵ.
ϕ=0Lϵds=0Lϵ[r(s)]ds,
ϕ=ϕ0+ϕ1+ϕ2+,
(ϕ0)2=ϵ˜,
2(ϕ0ϕ1)=ϵ˜.
ϕ1=120sϵ˜ϵ¯ds.
ψϕ(r1,r2)=ϕ˜(r1)ϕ˜(r2)=ϕ1(r1)ϕ1(r2).
ψϕ(r1,r2)=140z1dz0z2dzψϵ(ρ1ρ2,zz),
ψϕ(r1,r2)=14Σψϵ(ρ1ρ2,ζ)dζdη,
ψϕ(r1,r2)140z1dηdζψϵ(ρ1ρ2,ζ)=z1/20ψϵ(ρ1ρ2,ζ)dζ.
ψϕ(r1,r2)=z<20ψϵ(ρ,ζ)dζ,
ψϕ(r1,r2)=L<20ψϵ(σ+tζ)dζ,
ψϕ(r1,r2)=120L<dsϵ¯0ψϵ[δ(s)+t0ζ]ζ.
ψϵ(r,r)=ψϵ(rr,R)=σϵ2(R)Kϵ(rr,R),
ψϕ(r1,r2)=120L<dsϵ¯[r0(s)]0ψϵ[δ(s)+t0(s)ζ;r0(s)]dζ.
σϕ(L)=120Ldsϵ¯[r0(s)]0ψϵ[t0(s)ζ;r0(s)]dζ=120Ldsσϵ2[r0(s)]ϵ¯[r0(s)]0Kϵ[t0(s)ζ;r0(s)]dζ.
leff(s)=0Kϵ[t0(s)ζ;r0(s)]dζ,
σϕ2(L)=120Lσϵ2[r0(s)]leff(s)ϵ¯[r0(s)]ds,
t=ϕϵ=(ϕ0+ϕ1+)ϵ¯+ϵ˜=ϕ0ϵ¯+1ϵ¯[ϕ1ϵ˜ϕ02ϵ¯].
tt0+1ϵ¯[ϕ1t0(t0ϕ1)].
t1=tt0=1ϵ¯[ϕ1t0(t0ϕ1)]ϕ1ϵ¯,
Θαt1α=1ϵ¯(αϕ1)=1ϵ¯ϕ1ρα,
ϕαβΘ(ρ1,ρ2)Θα(ρ1)Θβ(ρ2)=1ϵ¯2ψ(ρ1,ρ2)ρ1αρ1β,
ψ(ρ,L)=120Ldsϵ¯[r0(s)]0ψϵ[ρ;ζ;r0(s)]dζ.
ϕαβΘ(ρ)=12ϵ¯2ψ(ρ)ρ1αρ1β=12ϵ¯2D(ρ)ρ1αρ1β.
Θα2=ψααΘ(0)=12ϵ¯2ψ(0)ρ1α2=12ϵ¯2D(0)ρ1α2,Θβ2=12ϵ¯2D(0)ρ1β2.
Θ2[r0(s)]=140Ldsϵ¯2[r(s)][0ψϵ[ρ;ζ;r(s)]dζ]ρ0,
Θ2=140Ldzϵ¯2(z)[0ψϵ(ρ;ζ;z)dζ]ρ0.
ψϵ(ρ)=σϵ2eρ2/2lϵ2.
σϕ(z)=π221ϵ¯σϵ2lϵz,
Θ2=π221ϵ¯2σϵ2lϵz.

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