Abstract

A method of tomographic phase retrieval is developed for multi-material objects whose components each have a distinct complex refractive index. The phase-retrieval algorithm, based on the Transport-of-Intensity equation, utilizes propagation-based X-ray phase contrast images acquired at a single defocus distance for each tomographic projection. The method requires a priori knowledge of the complex refractive index for each material present in the sample, together with the total projected thickness of the object at each orientation. The requirement of only a single defocus distance per projection simplifies the experimental setup and imposes no additional dose compared to conventional tomography. The algorithm was implemented using phase contrast data acquired at the SPring-8 Synchrotron facility in Japan. The three-dimensional (3D) complex refractive index distribution of a multi-material test object was quantitatively reconstructed using a single X-ray phase-contrast image per projection. The technique is robust in the presence of noise, compared to conventional absorption based tomography.

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2008 (3)

2007 (3)

2006 (3)

F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
[CrossRef]

O. M. Bucci, L. Crocco, M. D'Urso, and T. Isernia, “Inverse scattering from phaseless measurements of the total field open lines,” J. Opt. Soc. Am. A 23(10), 2566–2577 (2006).
[CrossRef]

2005 (3)

X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30(4), 379–381 (2005).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

2004 (1)

D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19(3), 472–480 (2002).
[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]

2001 (3)

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
[CrossRef]

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

1999 (3)

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[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]

A. V. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171(4-6), 239–244 (1999).
[CrossRef]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

1997 (2)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[CrossRef]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

1996 (3)

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]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
[CrossRef]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
[CrossRef]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

1983 (1)

1980 (1)

E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15(8), 937–945 (1980).
[CrossRef]

1965 (1)

U. Bonse and M. Hart, “An x-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[CrossRef]

Abrami, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Arfelli, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Asano, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Balaic, D. X.

C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
[CrossRef]

Barnea, Z.

C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
[CrossRef]

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
[CrossRef]

Barroso, R. C.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[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]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
[CrossRef]

Bayat, S.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Belkerbir, K.

Bergamaschi, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Berruyer, G.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Bille, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Boistel, R.

Bonse, U.

U. Bonse and M. Hart, “An x-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
[CrossRef]

Bregant, P.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Brizzi, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Bronnikov, A. V.

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19(3), 472–480 (2002).
[CrossRef]

A. V. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171(4-6), 239–244 (1999).
[CrossRef]

Bucci, O. M.

Buffière, J.-Y.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Casarin, K.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
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A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
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J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
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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).
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P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
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C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
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D’Urso, M.

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A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

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F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

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Dreossi, D.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
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Fava, C.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
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S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
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M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
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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).
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Garbow, J.

D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004).
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E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15(8), 937–945 (1980).
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Goto, S.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Guigay, J. P.

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007).
[CrossRef] [PubMed]

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]

Guigay, J.-P.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
[CrossRef]

Gureyev, T. E.

G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16(14), 10736–10749 (2008).
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T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
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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).
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T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
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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).
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T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
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M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
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U. Bonse and M. Hart, “An x-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965).
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B. Driehuys and L. W. Hedlund, “Imaging techniques for small animal models of pulmonary disease: MR microscopy,” Toxicol. Pathol. 35(1), 49–58 (2007).
[CrossRef] [PubMed]

Hooper, S. B.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
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Ishikawa, T.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
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S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Kaiser, S. R.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

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S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Kitchen, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
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A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Kovacs, A.

D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004).
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Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
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Langer, M.

Le Duc, G.

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Lewis, R. A.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Litman, A.

Liu, H.

Longo, R.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[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]

Malre, E.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

Mancini, L.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Matsushita, T.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Mayo, S. C.

Menk, R.-H.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Miller, P. R.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[CrossRef] [PubMed]

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]

Monfraix, S.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Montanari, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Morgan, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Myers, G. R.

G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16(14), 10736–10749 (2008).
[CrossRef] [PubMed]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
[CrossRef]

Nemoz, C.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Nesterets, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
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Nugent, K. A.

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997).
[CrossRef]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
[CrossRef]

Ohashi, H.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Olivo, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Paganin, D.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[CrossRef] [PubMed]

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]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[CrossRef]

Paganin, D. M.

G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16(14), 10736–10749 (2008).
[CrossRef] [PubMed]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
[CrossRef]

Pani, S.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Paterson, D.

C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
[CrossRef]

Peix, G.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

Pernot-Rejmánková, P.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

Pfeiffer, F.

F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Pillon, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Piwnica-Worms, D.

D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004).
[CrossRef] [PubMed]

Pogany, A.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[CrossRef] [PubMed]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[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]

Porra, L.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Quai, E.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Rigon, L.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Rokvic, T.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Salomé-Pateyron, M.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

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]

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999).
[CrossRef]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996).
[CrossRef]

Schuster, D. P.

D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004).
[CrossRef] [PubMed]

Siew, M. L.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Siu, K. K. W.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Sovijärvi, A. R. A.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Standertskjöld-Nordenstam, C. G.

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Stevenson, A. W.

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[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]

Suortti, P.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Suzuki, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Takeshita, K.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Teague, M. R.

Thomlinson, W.

S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005).
[CrossRef] [PubMed]

S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001).
[CrossRef]

Tonutti, M.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Tran, C. Q.

C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001).
[CrossRef]

Tromba, G.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Uesugi, K.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Umetani, K.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

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]

Vascotto, A.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Venanzi, C.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Wallace, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006).
[CrossRef]

S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003).
[CrossRef] [PubMed]

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]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[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]

Wu, X.

Yagi, N.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Yamazaki, H.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Yan, A.

Yoneda, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001).
[CrossRef]

Zanconati, F.

A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005).
[CrossRef]

Zanetti, A.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup showing the imaging geometry and coordinate system, for propagation-based phase contrast tomography of a multi-material object from a single propagation-based phase contrast image per projection.

Fig. 2
Fig. 2

Top view of the object, used as a test object to demonstrate interface-specific phase-retrieval tomography, using a single propagation-based X-ray phase contrast image per projection.

Fig. 3
Fig. 3

Projection images of the multi-material test sample. (a) Absorption contrast image. The numbered regions correspond to the different interfaces in the object (Air/PMMA (Green), Al/PMMA (Red) and PTFE/PMMA (Blue)). (b) Phase contrast image acquired at d=1 m. (c) Phase retrieved image of (b) using Eq. (2). (d) and (e) Phase retrieved images of (b) using Eq. (9) with appropriate values of δ and µ for the Al/PMMA and PTFE/PMMA interface, respectively (see Table 1). Line profiles from the centre of the images on the left column are shown in (f), (g), (h), (i) and (j), respectively.

Fig. 4
Fig. 4

Tomographic reconstruction of the multi-material test sample using (a) conventional absorption contrast images reconstructed via FBP; (b) phase contrast images reconstructed by applying FBP to raw PCI data. (c) Phase contrast images reconstructed using Eq. (2) to calculate T 1 ( r , θ ) for each projection ( j = 1 ), followed by FBP. (d) and (e) are reconstructions using same procedure as (c), after calculating T 2 ( r , θ ) and T 3 ( r , θ ) with Eq. (9) for both Al and PTFE for each projection ( j = 2 and j = 3 ). (f), (g), (h), (i) and (j) respectively, show line profiles from left-to-right across the centre of the images in (a), (b), (c), (d) and (e). Numbered regions correspond to different interfaces in the object (Air/PMMA (Green), Al/PMMA (Red) and PTFE/PMMA (Blue)).

Fig. 5
Fig. 5

(a) Spliced tomographic reconstruction. (b) Line profile of the different interfaces in (a).

Tables (1)

Tables Icon

Table 1 Values of δ and µ at 24 keV for materials used to construct the test object in Fig. 2. Values obtained from http://henke.lbl.gov/optical_constants/ (accessed Nov. 4, 2009).

Equations (13)

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[ I ( r , z ) φ ( r , z ) ] = k z I ( r , z ) .
T 1 ( r ) = 1 μ 1 log e ( F 1 { 1 ( d δ 1 / μ 1 ) k 2 + 1 F [ I ( r , z = d ) I 0 ] } ) .
A ( r ) = T j ( r ) + T 1 ( r ) .
I ( r , z = 0 ) = I 0 exp [ μ j T j ( r ) μ 1 T 1 ( r ) ] ,
φ ( r , z = 0 ) = k [ δ j T j ( r ) + δ 1 T 1 ( r ) ] .
( δ j δ 1 ) I 0 exp [ μ 1 A ( r ) ] { exp [ ( μ j μ 1 ) T j ( r ) ] T j ( r ) } = z I ( r , z ) .
{ exp [ ( μ j μ 1 ) T j ( r ) ] T j ( r ) } = 1 μ j μ 1 2 exp [ ( μ j μ 1 ) T j ( r ) ] ,
[ d ( δ j δ 1 ) ( μ j μ 1 ) 2 + 1 ] exp [ ( μ j μ 1 ) T j ( r ) ] = I ( r , z = d ) I 0 exp [ μ 1 A ( r ) ] .
T j ( r ) = 1 μ j μ 1 log e ( F 1 { 1 [ d ( δ j δ 1 ) / ( μ j μ 1 ) ] k 2 + 1 F [ I ( r , z = d ) I 0 exp [ μ 1 A ( r ) ] ] } ) .
1 α k 2 + 1 = 1 ε k 2 + 1 × ε k 2 + 1 α k 2 + 1 .
Δ x Δ k 1 ,
Δ x α .
3 α Δ x 5 α .

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