Abstract

Phase retrieval is the key to quantitative x-ray phase-contrast imaging. To retrieve the phase image of an x-ray wave field, in general one needs multiple phase-contrast images. We have made a new observation of phase-attenuation duality for soft tissues, and we show how only a single phase-contrast image is needed for successful phase retrieval based on this duality. The phase-retrieval formula based on a single phase-contrast image of inhomogeneous soft tissue is derived and presented. We show the striking enhancement of the tissue contrast in simulated phase images that this new approach produces.

© 2005 Optical Society of America

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References

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  1. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
    [CrossRef]
  2. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
    [CrossRef]
  3. D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1997).
    [CrossRef]
  4. A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
    [CrossRef]
  5. X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).
  6. X. Wu and H. Liu, Med. Phys. 30, 2169 (2003).
    [CrossRef] [PubMed]
  7. E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
    [CrossRef] [PubMed]
  8. X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 35 (2004).
  9. X. Wu and H. Liu, Med. Phys. 31, 997 (2004).
    [CrossRef]
  10. X. Wu and H. Liu, Med. Phys. 31, 2378 (2004).
    [CrossRef] [PubMed]
  11. X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 284 (2004).
  12. X. Wu, A. Dean, and H. Liu, in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC Press, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.
  13. N. A. Dyson, X-Rays in Atomic and Nuclear Physics (Longman Scientific and Technical, Essex, UK, 1973).
  14. International Commission on Radiation Units and Measurements, “Tissue substitutes in radiation dosimetry and measurement,” (Internationl Commission on Radiation Units and Measurements, Bethesda, Md., 1989).

2004 (4)

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 35 (2004).

X. Wu and H. Liu, Med. Phys. 31, 997 (2004).
[CrossRef]

X. Wu and H. Liu, Med. Phys. 31, 2378 (2004).
[CrossRef] [PubMed]

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 284 (2004).

2003 (3)

X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).

X. Wu and H. Liu, Med. Phys. 30, 2169 (2003).
[CrossRef] [PubMed]

E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
[CrossRef] [PubMed]

1997 (2)

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1997).
[CrossRef]

A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

1996 (1)

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Dean, A.

X. Wu, A. Dean, and H. Liu, in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC Press, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.

Donnelly, E.

E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
[CrossRef] [PubMed]

Dyson, N. A.

N. A. Dyson, X-Rays in Atomic and Nuclear Physics (Longman Scientific and Technical, Essex, UK, 1973).

Gao, D.

A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Gureyev, T.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Liu, H.

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 284 (2004).

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 35 (2004).

X. Wu and H. Liu, Med. Phys. 31, 2378 (2004).
[CrossRef] [PubMed]

X. Wu and H. Liu, Med. Phys. 31, 997 (2004).
[CrossRef]

X. Wu and H. Liu, Med. Phys. 30, 2169 (2003).
[CrossRef] [PubMed]

X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).

X. Wu, A. Dean, and H. Liu, in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC Press, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.

Nugent, K. A.

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1997).
[CrossRef]

Paganin, D.

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1997).
[CrossRef]

Pickens, D.

E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
[CrossRef] [PubMed]

Pogany, A.

A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Price, R.

E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
[CrossRef] [PubMed]

Shelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Stevenson, A.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Wilkins, S.

A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Wu, X.

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 35 (2004).

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 284 (2004).

X. Wu and H. Liu, Med. Phys. 31, 2378 (2004).
[CrossRef] [PubMed]

X. Wu and H. Liu, Med. Phys. 31, 997 (2004).
[CrossRef]

X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).

X. Wu and H. Liu, Med. Phys. 30, 2169 (2003).
[CrossRef] [PubMed]

X. Wu, A. Dean, and H. Liu, in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC Press, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.

J. X-Ray Sci. Technol. (3)

X. Wu and H. Liu, J. X-Ray Sci. Technol. 11, 33 (2003).

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 284 (2004).

X. Wu and H. Liu, J. X-Ray Sci. Technol. 12, 35 (2004).

Med. Phys. (4)

X. Wu and H. Liu, Med. Phys. 31, 997 (2004).
[CrossRef]

X. Wu and H. Liu, Med. Phys. 31, 2378 (2004).
[CrossRef] [PubMed]

X. Wu and H. Liu, Med. Phys. 30, 2169 (2003).
[CrossRef] [PubMed]

E. Donnelly, R. Price, and D. Pickens, Med. Phys. 30, 2292 (2003).
[CrossRef] [PubMed]

Nature (1)

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, Nature 384, 335 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1997).
[CrossRef]

Rev. Sci. Instrum. (2)

A. Pogany, D. Gao, and S. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, Rev. Sci. Instrum. 66, 5486 (1995).
[CrossRef]

Other (3)

X. Wu, A. Dean, and H. Liu, in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC Press, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.

N. A. Dyson, X-Rays in Atomic and Nuclear Physics (Longman Scientific and Technical, Essex, UK, 1973).

International Commission on Radiation Units and Measurements, “Tissue substitutes in radiation dosimetry and measurement,” (Internationl Commission on Radiation Units and Measurements, Bethesda, Md., 1989).

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Figures (3)

Fig. 1
Fig. 1

Simulated image of projected electron density for a hypothetical breast of 4-cm thickness with very low tissue radiographic subject contrast, 0.083%, for x rays of 60 keV.

Fig. 2
Fig. 2

Simulated attenuation image with added random noise of 0.1% of A2r.

Fig. 3
Fig. 3

Retrieved phase image of a hypothetical breast from a noisy phase-contrast image Ir;R1+R2. See text for details.

Equations (4)

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

Arexp-σKN2ρer,zdz=exp-σKN2ρe,pr,
σKN=2πre21+ηη221+η1+2η-1ηlog1+2η+12ηlog1+2η-1+3η1+2η2.
ϕr=-λreρer,zdz=-λreρe,pr,
ρe,pr=-1σKNloge×Fˆ-1FˆM2IMr;R1+R2Iin[1+2πλ2reR2MσKNu2,

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