Abstract

Many mathematical methods have been so far proposed in order to separate absorption, refraction and ultra-small angle scattering information in phase-contrast analyzer-based images. These algorithms all combine a given number of images acquired at different positions of the crystal analyzer along its rocking curve. In this paper a comprehensive quantitative comparison between five of the most widely used phase extraction algorithms based on the geometrical optics approximation is presented: the diffraction-enhanced imaging (DEI), the extended diffraction-enhanced imaging (E-DEI), the generalized diffraction-enhanced (G-DEI), the multiple-image radiography (MIR) and the Gaussian curve fitting (GCF). The algorithms are theoretically analyzed in terms of their validity conditions and experimentally compared by using geometrical phantoms providing various amounts of absorption, refraction and scattering. The presented work shows that, due to their specific validity conditions, the considered algorithms produce results that may greatly differ, especially in the case of highly refracting and/or highly scattering materials. The various extraction algorithms are also applied to images of a human bone-cartilage sample. The aim is to validate the results obtained on geometrical phantoms and prove the efficiency of the different algorithms for applications on biological samples.

© 2010 OSA

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  1. K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
    [CrossRef]
  2. A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (2003).
    [CrossRef]
  3. T. J. Davis, “A unified treatment of small-angle X-ray scattering, X-ray refraction and absorption using the Rytov approximation,” Acta Crystallogr. A 50(6), 686–690 (1994).
    [CrossRef]
  4. 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]
  5. 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(Pt 4), 296–308 (2006).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
    [CrossRef]
  9. 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]
  10. 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]
  11. E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
    [CrossRef]
  12. Z. F. Huang, K. J. Kang, and Y. G. Yang, “Extraction methods of phase information for X-ray diffraction enhanced imaging,” Nucl. Instrum. Meth. A 579(1), 218–222 (2007).
    [CrossRef]
  13. A. Maksimenko, “Nonlinear extension of the x-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90(3), 154106 (2007).
    [CrossRef]
  14. C. H. 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).
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  15. 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(11), 114102 (2007).
    [CrossRef]
  16. P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
    [CrossRef] [PubMed]
  17. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
    [CrossRef]
  18. O. Oltulu, Z. Zhong, M. O. 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]
  19. M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
    [CrossRef]
  20. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
    [CrossRef]
  21. C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
    [CrossRef]
  22. C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
    [CrossRef] [PubMed]

2008

2007

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(11), 114102 (2007).
[CrossRef]

Z. F. Huang, K. J. Kang, and Y. G. Yang, “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(3), 154106 (2007).
[CrossRef]

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

2006

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

2005

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
[CrossRef]

2004

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]

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]

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

2003

O. Oltulu, Z. Zhong, M. O. 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]

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (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]

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

1999

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

1997

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

1994

T. J. Davis, “A unified treatment of small-angle X-ray scattering, X-ray refraction and absorption using the Rytov approximation,” Acta Crystallogr. A 50(6), 686–690 (1994).
[CrossRef]

1979

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Anastasio, M. A.

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, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultrasmall-angle scattering,” Appl. Phys. Lett. 90(11), 114102 (2007).
[CrossRef]

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[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]

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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Brankov, J. G.

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.

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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[CrossRef] [PubMed]

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (2003).
[CrossRef]

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

Chapman, D.

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

O. Oltulu, Z. Zhong, M. O. 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]

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(Pt 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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Coan, P.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[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(Pt 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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Davis, T. J.

T. J. Davis, “A unified treatment of small-angle X-ray scattering, X-ray refraction and absorption using the Rytov approximation,” Acta Crystallogr. A 50(6), 686–690 (1994).
[CrossRef]

Fedotov, S. I.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Fiedler, S.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Förster, E.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[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]

Gao, D.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

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]

Goetz, K.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
[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]

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]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Hasnah, M. O.

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

O. Oltulu, Z. Zhong, M. O. 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]

Heitner, G.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Hu, C. H.

Huang, Z. F.

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

Issever, A. S.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

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]

Kalashnikov, M. P.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Kang, K. J.

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

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]

Kohn, V.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Kuettner, K. E.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Labiche, J. C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[CrossRef] [PubMed]

Lewis, R. A.

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.

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Majumdar, S.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Maksimenko, A.

A. Maksimenko, “Nonlinear extension of the x-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90(3), 154106 (2007).
[CrossRef]

Menk, R. H.

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(11), 114102 (2007).
[CrossRef]

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[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]

Metge, J.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Mikhailov, Yu. A.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Mollenhauer, J.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Morgan, M. J.

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]

Muehleman, C.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[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]

Nesterets, Y. I.

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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
[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]

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. O. 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.

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]

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]

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 analyser-based X-ray phase contrast imaging,” Appl. Phys. Lett. 82(20), 3421–3423 (2003).
[CrossRef]

Parham, C.

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

Pavlov, K. M.

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]

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]

Peterzol, A.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[CrossRef] [PubMed]

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]

Pogany, A.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Ponchut, C.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[CrossRef] [PubMed]

Raven, C.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Reime, B.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Rigon, L.

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(11), 114102 (2007).
[CrossRef]

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

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]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Sklizkov, G. V.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Snigirev, A.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Snigireva, I.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Souvorov, A.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Spanne, P.

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

Stevenson, A. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

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 analyser-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]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

Wagner, A.

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

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]

Wernick, M. N.

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. O. 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]

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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
[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]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[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]

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]

Yang, Y. G.

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

Zaumseil, P.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

Zhang, H.

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

Zhang, L.

Zhong, Z.

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

O. Oltulu, Z. Zhong, M. O. 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]

Acta Crystallogr. A

T. J. Davis, “A unified treatment of small-angle X-ray scattering, X-ray refraction and absorption using the Rytov approximation,” Acta Crystallogr. A 50(6), 686–690 (1994).
[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(Pt 4), 296–308 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett.

E. Pagot, P. Cloetens, S. Fiedler, A. Bravin, P. Coan, J. Baruchel, J. Härtwig, and W. Thomlinson, “A method to extract quantitative information in analyser-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(3), 154106 (2007).
[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(11), 114102 (2007).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999).
[CrossRef]

C. Raven, A. Snigirev, I. Snigireva, P. Spanne, A. Souvorov, and V. Kohn, “Phase-contrast microtomography with coherent high-energy synchrotron X rays,” Appl. Phys. Lett. 69(13), 1826–1828 (1996).
[CrossRef]

J. Phys. D Appl. Phys.

O. Oltulu, Z. Zhong, M. O. 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]

Y. I. Nesterets, T. E. Gureyev, and S. W. Wilkins, “Polychromaticity in the combined propagation-based/analyser-based phase-contrast imaging,” J. Phys. D Appl. Phys. 38(24), 4259–4271 (2005).
[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]

A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys. 36(10A), A24–A29 (2003).
[CrossRef]

J. Synchrotron Radiat.

P. Coan, A. Peterzol, S. Fiedler, C. Ponchut, J. C. Labiche, and A. Bravin, “Evaluation of imaging performance of a taper optics CCD; FReLoN’ camera designed for medical imaging,” J. Synchrotron Radiat. 13(Pt 3), 260–270 (2006).
[CrossRef] [PubMed]

Nature

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Nucl. Instrum. Meth. A

M. O. Hasnah, Z. Zhong, C. Parham, H. Zhang, and D. Chapman, “Compositional images from the diffraction enhanced Imaging technique,” Nucl. Instrum. Meth. A 572(2), 953–957 (2007).
[CrossRef]

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

Opt. Commun.

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

Osteoarthritis Cartilage

C. Muehleman, S. Majumdar, A. S. Issever, F. Arfelli, R. H. Menk, L. Rigon, G. Heitner, B. Reime, J. Metge, A. Wagner, K. E. Kuettner, and J. Mollenhauer, “X-ray detection of structural orientation in human articular cartilage,” Osteoarthritis Cartilage 12(2), 97–105 (2004).
[CrossRef] [PubMed]

Phys. Med. Biol.

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]

Sov. J. Quantum Electr.

K. Goetz, M. P. Kalashnikov, Yu. A. Mikhaĭlov, G. V. Sklizkov, S. I. Fedotov, E. Förster, and P. Zaumseil, “Measurements of the parameters of shell targets for laser thermonuclear fusion using an X-ray Schlieren method,” Sov. J. Quantum Electr. 9(5), 607–610 (1979).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Example of the finite sampling of a ‘reference’ RC (FWHMref = 2.94 μrad), of a first ‘object’ RC characterized by refraction (Δθz = 1 μrad) and a second ‘object’ RC characterized by refraction and USAXS (Δθz = 1 μrad, FWHMobj = 1.5 FWHMref). The calculated refraction angle is Δθest,1 = 0.88 μrad and Δθest,2 = 0.62 μrad respectively in the absence and in the presence of scattering.

Fig. 2
Fig. 2

Sketches of the phantoms used in the experiment: 200 μm and 350 μm diameter nylon wires with overlapped paper layers (a), and Lucite grooves phantom with overlapped paper layers (b).

Fig. 3
Fig. 3

Calculated absorption, refraction angle and ultra-small angle images of the 350 μm diameter nylon wire overlapped to the newspaper layers.

Fig. 4
Fig. 4

Cross-sections of phase images of the 350 μm diameter wire, when (a) no overlapping paper layers are present and when (b) 8 overlapping paper layers are present. The results extracted by DEI, E-DEI, G-DEI, MIR and GCF algorithms are compared with the theoretical profile. The plotted values are obtained by taking the average over 30 horizontal pixels.

Fig. 5
Fig. 5

Extracted phase values (a) at the centre of the 350 μm diameter wire and (b) at the centre of groove 5, plotted with respect to the number of overlapping paper layers. Results obtained with the DEI, E-DEI, G-DEI, MIR and GCF algorithms are shown. The plotted values are obtained by taking the average over 30 horizontal pixels; the error bars represent the standard deviation of the mean. The theoretical value is also shown for comparison.

Fig. 6
Fig. 6

Cross-sections of absorption images of groove 5 (depth 1.44 mm). Values extracted by the DEI, E-DEI, G-DEI, MIR and GCF algorithms are compared with the theoretical profile.

Fig. 7
Fig. 7

USAXS profiles from a horizontal line across images in Fig. 3. The results from G-DEI algorithm, MIR algorithm and GCF algorithm are shown.

Fig. 8
Fig. 8

Images calculated by applying MIR algorithm to the human bone-cartilage sample: (a) maximum absorption, (b) integrated absorption, (c) refraction angle and (d) USAXS images.

Fig. 9
Fig. 9

Comparison of cartilage refraction angle values extracted by DEI, MIR and GCF algorithms. Profiles position corresponds to line 1 in Fig. 8.

Fig. 10
Fig. 10

Comparison of bone refraction angle values extracted by DEI, MIR and GCF algorithms. Profiles position corresponds to line 2 in Fig. 8.

Tables (1)

Tables Icon

Table 1 Some physical parameters of the groove phantom. The absorption contrast is calculated at the groove centre with respect to the maximum thickness of the groove phantom. For Lucite at 26 keV, δ=3.94 × 10−7; β=1.39 × 10−10

Equations (3)

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I 1 , 2 = I a b s A exp [ ( Δ θ z + θ 1 , 2 ) 2 σ 2 ]
I = I a b s [ R ( θ ) + d R ( θ ) d θ Δ θ z + 1 2 d 2 R d θ 2 ( θ ) Δ θ z 2 + 1 2 d 2 R d θ 2 ( θ ) σ Δ θ s 2 ]
I r e f , o b j = A r e f , o b j exp [ ( Δ θ z r e f , o b j + θ A ) 2 σ r e f , o b j 2 ]

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