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A quantitative, non-interferometric X-ray phase contrast imaging techniquePeter R.T. Munro, Luigi Rigon, Konstantin Ignatyev, Frances C.M. Lopez, Diego Dreossi, Robert D. Speller, and Alessandro Olivo »View Author Affiliations
Peter R.T. Munro,1,2,*
Luigi Rigon,3
Konstantin Ignatyev,4
Frances C.M. Lopez,3,5
Diego Dreossi,6
Robert D. Speller,4
and Alessandro Olivo4
1Optical + Biomedical Engineering Laboratory, School of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia 2Centre for Microscopy, Characterisation and Analysis, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia, 6009, Australia 3INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy 4Department of Medical Physics and Bioengineering, University College London, Malet Place, Gower Street, London WC1E 6BT, UK 5Physics Department, University of Trieste, Via Valerio 2, 34127 Trieste, Italy 6Sincrotrone Trieste SCpA, S.S. 14 km 163.5, 34012 Basovizza (TS), Italy *Corresponding author: peter.munro@uwa.edu.au |
Optics Express, Vol. 21, Issue 1, pp. 647-661 (2013)
http://dx.doi.org/10.1364/OE.21.000647
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Abstract
We present a quantitative, non-interferometric, X-ray differential phase contrast imaging technique based on the edge illumination principle. We derive a novel phase retrieval algorithm which requires only two images to be acquired and verify the technique experimentally using synchrotron radiation. The technique is useful for planar imaging but is expected to be important for quantitative phase tomography also. The properties and limitations of the technique are studied in detail.
© 2012 OSA
OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(340.6720) X-ray optics : Synchrotron radiation
ToC Category:
X-ray Optics
History
Original Manuscript: August 30, 2012
Revised Manuscript: October 8, 2012
Manuscript Accepted: October 9, 2012
Published: January 7, 2013
Virtual Issues
Vol. 8, Iss. 2 Virtual Journal for Biomedical Optics
Citation
Peter R.T. Munro, Luigi Rigon, Konstantin Ignatyev, Frances C.M. Lopez, Diego Dreossi, Robert D. Speller, and Alessandro Olivo, "A quantitative, non-interferometric X-ray phase contrast imaging technique," Opt. Express 21, 647-661 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-1-647
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- K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996). [CrossRef] [PubMed]
- 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, 133–146 (1996). [CrossRef]
- A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005). [CrossRef]
- P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. 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, 133–146 (1996). [CrossRef]
- F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011). [CrossRef]
- L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010). [CrossRef]
- L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009). [CrossRef]
- A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005). [CrossRef]
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Atom. Data Nucl. Data
- B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993). [CrossRef]
Contemp. Phys.
- K. Nugent, “The measurement of phase through the propagation of intensity: an introduction,” Contemp. Phys.52, 55–69 (2011). [CrossRef]
J. Appl. Phys.
- T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009). [CrossRef]
J. Instrum.
- F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011). [CrossRef]
J. Microsc.-Oxford
- D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002). [CrossRef]
J. Phys. D Appl. Phys.
- T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (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, 133–146 (1996). [CrossRef]
- Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004). [CrossRef]
Jpn. J. Appl. Phys.
- A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003). [CrossRef]
Med. Phys.
- A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001). [CrossRef] [PubMed]
Nat. Phys.
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
Nature
- T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995). [CrossRef]
- S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996). [CrossRef]
Nucl. Instrum. Meth. A
- A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995). [CrossRef]
- A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005). [CrossRef]
- L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009). [CrossRef]
- L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010). [CrossRef]
Opt. Express
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010). [CrossRef]
Opt. Commun.
- A. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun.2(9), 413–415 (1971). [CrossRef]
- D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004). [CrossRef]
- T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004). [CrossRef]
- T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005). [CrossRef]
Opt. Express
- M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010). [CrossRef]
- P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express18, 3494–3509 (2010). [CrossRef] [PubMed]
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(5), 4103–4117 (2010). [CrossRef] [PubMed]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
Phys. Med. Biol.
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010). [CrossRef] [PubMed]
- A. Olivo and R. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008). [CrossRef] [PubMed]
- A. Olivo and R. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007). [CrossRef] [PubMed]
- D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
Phys. Rev. A
- Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009). [CrossRef]
Phys. Rev. Lett.
- K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996). [CrossRef] [PubMed]
Proc. Natl. Acad. Sci. U. S. A.
- P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010). [CrossRef]
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012). [CrossRef]
Prog. Optics
- K. Creath, “Phase-measurement interferometry techniques,” Prog. OpticsXXVI, 349–393 (1988). [CrossRef]
Rev. Sci. Instrum.
- 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]
- F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995). [CrossRef]
The 9th National Conference on Synchrotron Radiation Instrumentation
- D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).
Other
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2012, Munro, Proc. Natl. Acad. Sci. U. S. A.
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012). [CrossRef]
- K. Nugent, “The measurement of phase through the propagation of intensity: an introduction,” Contemp. Phys.52, 55–69 (2011). [CrossRef]
- F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011). [CrossRef]
- L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010). [CrossRef]
- P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010). [CrossRef]
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010). [CrossRef] [PubMed]
- P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010). [CrossRef]
- M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010). [CrossRef]
- Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009). [CrossRef]
- T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009). [CrossRef]
- L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009). [CrossRef]
- A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009). [CrossRef]
- A. Olivo and R. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008). [CrossRef] [PubMed]
- A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007). [CrossRef]
- A. Olivo and R. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007). [CrossRef] [PubMed]
- D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007). [CrossRef]
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
- T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005). [CrossRef]
- A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005). [CrossRef]
- T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004). [CrossRef]
- D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004). [CrossRef]
- Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004). [CrossRef]
- A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003). [CrossRef]
- D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002). [CrossRef]
- A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001). [CrossRef] [PubMed]
- P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. 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]
- T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999). [CrossRef]
- D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
- D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).
- 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, 133–146 (1996). [CrossRef]
- S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996). [CrossRef]
- K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996). [CrossRef] [PubMed]
- T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995). [CrossRef]
- A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995). [CrossRef]
- 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]
- F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995). [CrossRef]
- B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993). [CrossRef]
- K. Creath, “Phase-measurement interferometry techniques,” Prog. OpticsXXVI, 349–393 (1988). [CrossRef]
- A. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun.2(9), 413–415 (1971). [CrossRef]
- U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]
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