Abstract

When a very-low-absorbing sample is scanned at an x-ray computed tomography setup with a microfocus x-ray tube and a high-resolution detector, the obtained projection images contain not only absorption contrast but also phase contrast. While images without a phase signal can be reconstructed very well, such mixed phase and absorption images give rise to severe artifacts in the reconstructed slices. A method is described that applies a correction to these mixed projections to remove the phase signal. These corrected images can then be processed using a standard filtered backprojection algorithm to obtain reconstructions with only few or no phase artifacts. This new method, which we call the Bronnikov-aided correction (BAC), can be used in a broad variety of applications and without much additional effort. It is tested on a biological and a pharmaceutical sample, and results are evaluated and discussed by comparing them with those of conventional reconstruction methods.

© 2009 Optical Society of America

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References

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  1. X. Wu, “X-ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express 13, 6000-6014 (2005).
    [CrossRef] [PubMed]
  2. R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49, 3573-3583 (2004).
    [CrossRef] [PubMed]
  3. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).
  4. F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
    [CrossRef]
  5. C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
    [CrossRef] [PubMed]
  6. A. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171, 239-244 (1999).
    [CrossRef]
  7. D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
    [CrossRef] [PubMed]
  8. S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
    [CrossRef] [PubMed]
  9. G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
    [CrossRef]
  10. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
    [CrossRef]
  11. T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49-58 (2003).
    [CrossRef]
  12. M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103-8110 (2006).
    [CrossRef] [PubMed]
  16. B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
    [CrossRef]
  17. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  18. J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
    [CrossRef]
  19. N. Kardjilov, “Further developments and applications of radiography and tomography with thermal and cold neutrons,” Ph.D. dissertation (Technical University Munich, 2003).

2007 (5)

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

2006 (1)

2005 (2)

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

X. Wu, “X-ray cone-beam phase tomography formulas based on phase-attenuation duality,” Opt. Express 13, 6000-6014 (2005).
[CrossRef] [PubMed]

2004 (2)

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

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

1999 (1)

A. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171, 239-244 (1999).
[CrossRef]

1985 (1)

Abela, R.

Anastasio, M. A.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

Baumann, J.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Bronnikov, A.

A. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171, 239-244 (1999).
[CrossRef]

Bunk, O.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

Carlo, F. D.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

Cnudde, V.

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

David, C.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

Davis, T. J.

Dierick, M.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

Dreossi, D.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Engelhardt, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

Groso, A.

Grünzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

Gureyev, T.

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Gureyev, T. E.

T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49-58 (2003).
[CrossRef]

Jacobs, P.

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

Kardjilov, N.

N. Kardjilov, “Further developments and applications of radiography and tomography with thermal and cold neutrons,” Ph.D. dissertation (Technical University Munich, 2003).

Kottler, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[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] [PubMed]

Masschaele, B.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

Mayo, S. C.

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Miller, P. R.

S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Myers, G. R.

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
[CrossRef]

Olivo, A.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Paganin, D.

S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Paganin, D. M.

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

Pan, X.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

Pani, S.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Peterzol, A.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Pfeiffer, F.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

Pogany, A.

Rigon, L.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Schuster, M.

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

Shi, D.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

Stampanoni, M.

Stevenson, A.

Teague, M. R.

Van Hoorebeke, L.

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

Vlassenbroeck, J.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

Wilkins, S.

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

S. C. Mayo, T. J. Davis, T. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289-2302 (2003).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wu, X.

Appl. Phys. Lett. (1)

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[CrossRef]

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. Gureyev, P. R. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of homogeneous object,” J. Microsc. 206, 33-40 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Med. Phys. (1)

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617-3627 (2005).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (2)

B. Masschaele, V. Cnudde, M. Dierick, P. Jacobs, L. Van Hoorebeke, and J. Vlassenbroeck, “UGCT: New x-ray radiography and tomography facility,” Nucl. Instrum. Methods Phys. Res. A 580, 266-269 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography,” Nucl. Instrum. Methods Phys. Res. A 580, 442-445 (2007).
[CrossRef]

Opt. Commun. (2)

T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49-58 (2003).
[CrossRef]

A. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171, 239-244 (1999).
[CrossRef]

Opt. Express (3)

Phys. Med. Biol. (2)

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121-144 (2004).
[CrossRef] [PubMed]

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

Phys. Rev. A (1)

G. R. Myers, S. C. Mayo, T. Gureyev, D. M. Paganin, and S. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A 76, 045804 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, and C. David, “Grating interferometer based scanning setup for hard x-ray phase contrast imaging,” Rev. Sci. Instrum. 78, 043710 (2007).
[CrossRef] [PubMed]

Other (4)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).

F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001).
[CrossRef]

N. Kardjilov, “Further developments and applications of radiography and tomography with thermal and cold neutrons,” Ph.D. dissertation (Technical University Munich, 2003).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

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Figures (7)

Fig. 1
Fig. 1

Line profiles of the transition between the edge of the leg of a fly and the surrounding air for the original projection and for the BAC projection with different values of the parameter γ.

Fig. 2
Fig. 2

Left, original projection image of the fly leg. Middle, projection image after applying the Bronnikov phase filter. Right, projection image after BAC.

Fig. 3
Fig. 3

Slice of the reconstructed leg of a fly. Left, FBP; middle, MBA; right, BAC.

Fig. 4
Fig. 4

Horizontal cut through the 3D rendered model of the reconstructed fly leg. Left, FBP; middle, MBA; right, BAC.

Fig. 5
Fig. 5

Detail of the 3D rendered model of the reconstructed fly leg. Left, FBP; middle, MBA; right, BAC.

Fig. 6
Fig. 6

Reconstructed slice of the bead. Left, FBP; middle, MBA; right, BAC.

Fig. 7
Fig. 7

Detail of a cut through the 3D rendered model of the bead. Left, FBP; middle, MBA; right, BAC.

Equations (10)

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

I θ , d ( x , y , λ ) = I θ , d a ( x , y , λ ) [ 1 λ d 2 π M 2 ϕ θ ( x , y , λ ) ] ,
M = s + d s ,
q ( ξ , η ) = ξ ξ 2 + η 2 + α ,
q ( ξ , η ) = p ( ξ , η ) r ( ξ ) ,
ξ ,
p ( ξ , η ) = 1 ξ 2 + η 2 + α ,
ϕ ̃ θ ( x , y , λ ) = φ d L ,
ln [ I θ ( x , y , λ ) ] = μ d L .
I θ , d a ( x , y , λ ) = I θ , d ( x , y , λ ) 1 λ d 2 π M 2 ϕ ̃ θ ( x , y , λ ) .
C θ ( x , y , λ ) = 1 γ 2 ϕ ̃ θ ( x , y , λ ) ,

Metrics