Abstract

We introduce theoretically and demonstrate experimentally a contrast transfer function based phase retrieval algorithm that reconstructs the projected thickness of an homogeneous sample using a polychromatic x-ray source. We show excellent quantitative recovery of test samples in 2D using a synchrotron source with significant harmonic contamination, and in 3D using a laboratory source.

© 2011 OSA

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  1. 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]
  2. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
    [CrossRef]
  3. H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30(13), 1638–1640 (2005).
    [CrossRef] [PubMed]
  4. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
    [CrossRef] [PubMed]
  5. L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12(13), 2960–2965 (2004).
    [CrossRef] [PubMed]
  6. L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
    [CrossRef]
  7. B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
    [CrossRef]
  8. R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
    [CrossRef]
  9. B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic x-ray laboratory source,” Opt. Express 16(24), 19950–19956 (2008).
    [CrossRef] [PubMed]
  10. T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
    [CrossRef]
  11. J. P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik (Stuttg.) 49, 121–125 (1977).
  12. C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
    [CrossRef]
  13. D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
    [CrossRef] [PubMed]
  14. D. M. Paganin, Coherent X-ray Optics (Oxford Science Publications, 2006).
  15. J. Baruchel, J. Y. Buffiere, E. Maire, P. Merle, and G. Peix, X-Ray Tomography in Material Science (Hermes Science Publications, 2000).
  16. J. Hseh, Computed Tomography: Principle, Design, Artifacts, and Recent Advances (SPIE-The International Society for Optical Engineering, 2002).

2009 (3)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

2008 (1)

2006 (2)

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (1)

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

1996 (1)

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]

1977 (1)

J. P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik (Stuttg.) 49, 121–125 (1977).

Abbey, B.

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

Arhatari, B. D.

Balaur, E.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic x-ray laboratory source,” Opt. Express 16(24), 19950–19956 (2008).
[CrossRef] [PubMed]

Barnea, Z.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Chantler, C. T.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

Chen, B.

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

Cookson, D.

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

Cookson, D. J.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Dao, L. V.

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

deJonge, M. D.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Dhal, B.

Dhal, B. B.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Dilanian, R. A.

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[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]

Guigay, J. P.

J. P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik (Stuttg.) 49, 121–125 (1977).

Gureyev, T. E.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

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]

Hannaford, P.

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

Hannah, K.

Hayes, J.

Kirby, N.

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

Knott, R.

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

Lee, M.

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

Mancuso, A.

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

McNulty, I.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

Nesterets, Y. I.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

Nugent, K.

Nugent, K. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30(13), 1638–1640 (2005).
[CrossRef] [PubMed]

Paganin, D.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

Paganin, D. M.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

Paterson, D.

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: Demonstration of extended conditions for homogeneous objects,” Opt. Express 12(13), 2960–2965 (2004).
[CrossRef] [PubMed]

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Peele, A.

Peele, A. G.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic x-ray laboratory source,” Opt. Express 16(24), 19950–19956 (2008).
[CrossRef] [PubMed]

H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30(13), 1638–1640 (2005).
[CrossRef] [PubMed]

Pogany, A.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[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]

Quiney, H. M.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

H. M. Quiney, K. A. Nugent, and A. G. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30(13), 1638–1640 (2005).
[CrossRef] [PubMed]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

Scholten, R.

Schultz, D.

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

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]

Teichmann, S.

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

Tran, C.

Tran, C. Q.

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Turner, L.

Van Dao, L.

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

Vine, D. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

Whitehead, L. W.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

Wilkins, S. W.

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

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]

Williams, G. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

J. Appl. Phys. (1)

R. A. Dilanian, B. Chen, G. J. Williams, H. M. Quiney, K. A. Nugent, S. Teichmann, P. Hannaford, L. V. Dao, and A. G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106(2), 023110–023115 (2009).
[CrossRef]

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

J. Synchrotron Radiat. (1)

D. Cookson, N. Kirby, R. Knott, M. Lee, and D. Schultz, “Strategies for data collection and calibration with a pinhole-geometry SAXS instrument on a synchrotron beamline,” J. Synchrotron Radiat. 13(6), 440–444 (2006).
[CrossRef] [PubMed]

Nature (2)

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]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[CrossRef]

Opt. Commun. (1)

T. E. Gureyev, Y. I. Nesterets, D. M. Paganin, A. Pogany, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination,” Opt. Commun. 259(2), 569–580 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Optik (Stuttg.) (1)

J. P. Guigay, “Fourier transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik (Stuttg.) 49, 121–125 (1977).

Phys. Rev. A (1)

B. Chen, R. A. Dilanian, S. Teichmann, B. Abbey, A. G. Peele, G. J. Williams, P. Hannaford, L. Van Dao, H. M. Quiney, and K. A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79(2), 023809 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[CrossRef]

X-Ray Spectrom. (1)

C. Q. Tran, Z. Barnea, M. D. deJonge, B. B. Dhal, D. Paterson, D. J. Cookson, and C. T. Chantler, “Quantitative determination of major systematics in synchrotron x-ray experiments: seeing through harmonic components,” X-Ray Spectrom. 32(1), 69–74 (2003).
[CrossRef]

Other (3)

D. M. Paganin, Coherent X-ray Optics (Oxford Science Publications, 2006).

J. Baruchel, J. Y. Buffiere, E. Maire, P. Merle, and G. Peix, X-Ray Tomography in Material Science (Hermes Science Publications, 2000).

J. Hseh, Computed Tomography: Principle, Design, Artifacts, and Recent Advances (SPIE-The International Society for Optical Engineering, 2002).

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Figures (4)

Fig. 1
Fig. 1

a) Spectrum of the x-ray beam measured at the sample position; b) a 1D plot across a 2D diffracted intensity measured at 3.37 m resulting from a 100 nm thick Cu sample; c) Reconstructed thickness using two approaches; Eq. (5) (blue, dash line), and Eq. (14) (red, line)

Fig. 2
Fig. 2

a) a combined spectral and detection response distribution;

Fig. 3
Fig. 3

a) 2D Diffraction pattern of a hollow polyimide tube with an outer diameter of 168 µm and an inner diameter of 122 µm; b) 2D reconstructed thickness using Eq. (14); c) profiles of the reconstructed thickness across the white dashed line shown in (b) for different approaches described in the text. There was a small feature on the wall the tube; it can be seen as a small region in the middle of the tube in both the diffraction pattern (a) and in the reconstruction (b). The polychromatic CTF is not only able to reconstruct the correct projected thickness but also be able to reconstruct a small feature on the wall of the tube.

Fig. 4
Fig. 4

a. ) the 3D distribution of the density of the sample; b) the distribution of the density for 1 slice; c) a 1D plot along the dashed line in (b).

Equations (16)

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t h i c k n e s s ρ ( r , z ) d z = ρ o T ( r ) ,
ψ λ ( r , 0 ) = ψ o , λ exp { μ ( r ) i ϕ ( r ) }
{ I λ ( r , z ) } = I o , λ + exp { μ + μ + i ϕ i ϕ + } exp { 2 π i r u } d r
| μ + + μ | 2 μ < < 1   and   | ϕ ϕ + | < < 1.
{ I λ ( r , z ) I o , λ } = I o , λ C T F λ ( u , z ) { T ( r ) }
C T F λ ( u , z ) 4 π δ 2 + β 2 λ sin ( π λ z u 2 arctan [ β δ ] ) ,
I p o l y ( r , z ) = λ I λ ( r , z ) D ( λ ) d λ ,
I o , p o l y ( r , 0 ) = λ I o , λ D ( λ ) d λ
I o , λ = S ( λ ) I o
{ I λ ( r , z ) D ( λ ) d λ I o , λ D ( λ ) d λ } = [ I o , λ D ( λ , z ) d λ ] C T F λ ( u , z ) { T ( r ) } .
{ I p o l y ( r , z ) I o , p o l y } = { T } ( λ I o S ( λ ) D ( λ ) C T F λ ( u , z ) d λ )
C T F p o l y ( u , z ) ( λ S ( λ ) D ( λ , z ) C T F λ ( u , z ) d λ ) ( λ S ( λ ) D ( λ , z ) d λ ) 1 .
{ I p o l y ( r , z ) I o , p o l y } = { T ( r ) } I o ( λ S ( λ ) D ( λ , 0 ) d λ ) C T F p o l y ( u , z )                 = { T ( r ) } I o , p o l y C T F p o l y ( u , z ) .
T ( r ) = 1 [ 1 C T F p o l y ( u , z ) { I p o l y ( r , z ) I o , p o l y 1 } ] .
z < 0.5 N Δ x 2 λ max 1 .
I / I o = α exp { μ f t } + ( 1 α ) exp { μ h t } ,

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