Abstract

We recently demonstrated how quantitative X-ray phase contrast imaging may be performed with laboratory sources using the coded aperture technique. This technique required the knowledge of system parameters such as, for example, the source focal spot size and distances between elements of the imaging system. The method also assumes that the absorbing regions of the apertures are perfectly absorbing. In this paper we demonstrate how quantitative imaging can be performed without knowledge of individual system parameters and with partially absorbing apertures. We also show that this method is analogous to that employed in analyser based imaging which uses the rocking curve of an analyser crystal.

© 2013 OSA

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  3. 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, 3360–3360 (1996).
  4. 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, 2015–2025 (1997).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an x-ray grating interferometer,” Opt. Express19, 1691–1698 (2011).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. 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, 181–342 (1993).
    [CrossRef]

2013

2012

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA109, 13922–13927 (2012).
[CrossRef] [PubMed]

2011

P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an x-ray grating interferometer,” Opt. Express19, 1691–1698 (2011).
[CrossRef] [PubMed]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

2010

2009

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

2007

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, 254110 (2007).
[CrossRef]

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91, 074106 (2007).
[CrossRef]

2006

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, 258–261 (2006).
[CrossRef]

A. Olivo and R. Speller, “Experimental validation of a simple model capable of predicting the phase contrast imaging capabilities of any x-ray imaging system,” Phys. Med. Biol.51, 3015–3030 (2006).
[CrossRef] [PubMed]

2005

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys.44, 6355–6367 (2005).
[CrossRef]

2004

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, 1262–1274 (2004).
[CrossRef]

2002

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

2001

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, 1610–1619 (2001).
[CrossRef] [PubMed]

1998

1997

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, 2015–2025 (1997).
[CrossRef] [PubMed]

1996

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, 3360–3360 (1996).

1995

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

1993

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, 181–342 (1993).
[CrossRef]

Allison, B. J.

Arfelli, F.

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, 1610–1619 (2001).
[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, 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, 3360–3360 (1996).

Borges, P. D. N.

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

Bravin, A.

Briod, I.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Bruder, J.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Bunk, O.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (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, 258–261 (2006).
[CrossRef]

Cantatore, G.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Castelli, E.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Chabior, M.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

Chapman, D.

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, 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, 3360–3360 (1996).

Coan, P.

David, C.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (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, 258–261 (2006).
[CrossRef]

Davis, J.

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, 181–342 (1993).
[CrossRef]

Davis, T.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

Diemoz, P. C.

Donath, T.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

Dreossi, D.

Endrizzi, M.

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

Foerster, E.

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, 254110 (2007).
[CrossRef]

Gao, D.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

Glaser, C.

Gmür, N.

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, 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, 3360–3360 (1996).

Gruenzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Gullikson, E.

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, 181–342 (1993).
[CrossRef]

Gureyev, T.

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, 1262–1274 (2004).
[CrossRef]

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

T. Gureyev and S. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A15, 579–585 (1998).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

Gureyev, T. E.

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]

Hagen, C. K.

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

Henke, B.

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, 181–342 (1993).
[CrossRef]

Hooper, S. B.

Ignatyev, K.

Johnson, R. E.

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, 3360–3360 (1996).

Johnston, R.

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, 2015–2025 (1997).
[CrossRef] [PubMed]

Kaufmann, R.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Kawabata, K.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

Kitchen, M.

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]

Kitchen, M. J.

Kottler, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Kraeusslich, J.

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, 254110 (2007).
[CrossRef]

Kuwabara, H.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

Lang, S.

Lewis, R. A.

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, 19994–20012 (2010).
[CrossRef] [PubMed]

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]

Longo, R.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Lopez, F. C.

Marenzana, M.

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

Mayo, S.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

Menk, R.

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, 1610–1619 (2001).
[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, 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, 3360–3360 (1996).

Miller, P.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

Momose, A.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys.44, 6355–6367 (2005).
[CrossRef]

Munro, P.

Munro, P. R.

Nesterets, Y. I.

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, 1262–1274 (2004).
[CrossRef]

Olivo, A.

P. R. Munro, L. Rigon, K. Ignatyev, F. C. Lopez, D. Dreossi, R. D. Speller, and A. Olivo, “A quantitative, non-interferometric x-ray phase contrast imaging technique,” Opt. Express21, 647–661 (2013).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA109, 13922–13927 (2012).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[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, 4103–4117 (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, 19681–19692 (2010).
[CrossRef] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91, 074106 (2007).
[CrossRef]

A. Olivo and R. Speller, “Experimental validation of a simple model capable of predicting the phase contrast imaging capabilities of any x-ray imaging system,” Phys. Med. Biol.51, 3015–3030 (2006).
[CrossRef] [PubMed]

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Paganin, D.

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, 1262–1274 (2004).
[CrossRef]

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

D. Paganin, Coherent X-ray optics, Oxford series on synchrotron radiation (Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, 2006).
[CrossRef]

Paganin, D. M.

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, 19994–20012 (2010).
[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, 254110 (2007).
[CrossRef]

Pani, S.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Parry, D.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

Pavlov, K.

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, 1262–1274 (2004).
[CrossRef]

Pavlov, K. M.

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, 19994–20012 (2010).
[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, 254110 (2007).
[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]

Pfeiffer, F.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (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, 258–261 (2006).
[CrossRef]

Pisano, E.

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, 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, 3360–3360 (1996).

Pogany, A.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

Poropat, P.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Prest, M.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Rigon, L.

P. R. Munro, L. Rigon, K. Ignatyev, F. C. Lopez, D. Dreossi, R. D. Speller, and A. Olivo, “A quantitative, non-interferometric x-ray phase contrast imaging technique,” Opt. Express21, 647–661 (2013).
[CrossRef] [PubMed]

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Sayers, D.

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, 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, 3360–3360 (1996).

Schroer, C.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

Schuster, M.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[CrossRef] [PubMed]

Speller, R.

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA109, 13922–13927 (2012).
[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, 19681–19692 (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, 4103–4117 (2010).
[CrossRef] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91, 074106 (2007).
[CrossRef]

A. Olivo and R. Speller, “Experimental validation of a simple model capable of predicting the phase contrast imaging capabilities of any x-ray imaging system,” Phys. Med. Biol.51, 3015–3030 (2006).
[CrossRef] [PubMed]

Speller, R. D.

Stevenson, A.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

Szafraniec, M. B.

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[CrossRef] [PubMed]

Thomlinson, W.

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, 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, 3360–3360 (1996).

Tlustos, L.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Tromba, G.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Uesugi, K.

Uschmann, I.

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, 254110 (2007).
[CrossRef]

Vallazza, E.

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, 1610–1619 (2001).
[CrossRef] [PubMed]

Vine, D. J.

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, 254110 (2007).
[CrossRef]

Walt, H.

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Washburn, D.

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, 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, 3360–3360 (1996).

Wehrhan, O.

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, 254110 (2007).
[CrossRef]

Weitkamp, T.

P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an x-ray grating interferometer,” Opt. Express19, 1691–1698 (2011).
[CrossRef] [PubMed]

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (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, 258–261 (2006).
[CrossRef]

Wilkins, S.

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

T. Gureyev and S. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A15, 579–585 (1998).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature373, 595–598 (1995).
[CrossRef]

Wilkins, S. W.

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, 1262–1274 (2004).
[CrossRef]

Yashiro, W.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

Zanette, I.

Zhong, Z.

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, 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, 3360–3360 (1996).

Appl. Phys. Lett.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91, 074106 (2007).
[CrossRef]

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, 254110 (2007).
[CrossRef]

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, 181–342 (1993).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D Appl. Phys.

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, 1262–1274 (2004).
[CrossRef]

Journal of Microscopy-Oxford

S. Mayo, P. Miller, S. Wilkins, T. Davis, D. Gao, T. Gureyev, D. Paganin, D. Parry, A. Pogany, and A. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” Journal of Microscopy-Oxford207, 79–96 (2002).
[CrossRef]

Jpn. J. Appl. Phys.

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-based x-ray phase imaging using multiline x-ray source,” Jpn. J. Appl. Phys.48, 076512 (2009).
[CrossRef]

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys.44, 6355–6367 (2005).
[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, 1610–1619 (2001).
[CrossRef] [PubMed]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys.38, 1189–1195 (2011).
[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, 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, 595–598 (1995).
[CrossRef]

Opt. Commun.

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]

Opt. Express

Phys. Med. Biol.

A. Olivo and R. Speller, “Experimental validation of a simple model capable of predicting the phase contrast imaging capabilities of any x-ray imaging system,” Phys. Med. Biol.51, 3015–3030 (2006).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. D. N. Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based x-ray phase contrast imaging,” Phys. Med. Biol.57, 8173–8184 (2012).
[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, 2015–2025 (1997).
[CrossRef] [PubMed]

Phys. Status Solidi. A

C. Kottler, F. Pfeiffer, O. Bunk, C. Gruenzweig, J. Bruder, R. Kaufmann, L. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast x-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi. A204, 2728–2733 (2007).
[CrossRef]

Proc. Natl. Acad. Sci. USA

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent x-ray sources,” Proc. Natl. Acad. Sci. USA109, 13922–13927 (2012).
[CrossRef] [PubMed]

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, 3360–3360 (1996).

Other

D. Paganin, Coherent X-ray optics, Oxford series on synchrotron radiation (Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, 2006).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of a CAXPCI system which is not to scale (a) and specification of the coordinate systems used within this paper (b). The system is formed by two apertures A1 and A2. The sample is placed immediately after A1. A1 is translated by an amount Δξ in order to select the operating regime of the system. A1 is placed a distance zso from the source and A2 is placed a distance zod from A1. The detector has pixels with a width of P and A1 has a period of p1. The distance along the optical axis is denoted z and is considered to begin at the centre of the source focal spot. The lateral dimensions within the source focal spot and within the planes of A1 and A2 are denoted xs, ξ and x respectively. Each lateral dimension has its origin at the optical axis.

Fig. 2
Fig. 2

Plot of experimentally acquired ITC. The fitted curve was found by minimising the least square error with Fourier series containing four harmonic terms.

Fig. 3
Fig. 3

Plot of IΣ = ITC (−Δξ0 − Δξs) + ITCξ0 − Δξs), ITC (−Δξ0 − Δξs) and ITCξ0 − Δξs) using the fitted TC plotted in Fig. 2.

Fig. 4
Fig. 4

Plot of εξ0), a measure of the flatness of IΣ for particular values of Δξ0 when Δξs takes values in the range [−5 × 10−6, 5 × 10−6] m.

Fig. 5
Fig. 5

Plot of the derivative of the fitted ITCξ), the vertical lines denote Δξ = ±8μm.

Fig. 6
Fig. 6

Plot of ITCξ0 − Δξs) with Δξ0 = 8μm for a range of Δξs corresponding to |∂ϕ̄/∂x| < 10−5rad/m.

Fig. 7
Fig. 7

Plot of IΔ/IΣ versus Δξs. The domain of the plot is restricted to the non-shaded region so that there is a one-to-one mapping from Δξs to IΔ/IΣ. The plot was calculated using the fitted TC in Fig. 2.

Fig. 8
Fig. 8

Comparison of the inversion formulae. TC-approx is described by Eq. (23), TC-full by inverting Eq. (21) using the experimental TC in Fig. 2, Analytic-approx by Eq. (26) and Analytic-full by Eq. (25), TC (ideal)-full is found using an ideal TC, calculated assuming fully absorbing apertures.

Fig. 9
Fig. 9

(left) an image of IΔ/IΣ for a 125μm titanium wire, (top right) line profiles of ϕ̄x through the titanium wire and (bottom right) a zoomed in version of the top right plots. Line profiles were calculated using the three inversion formula indicated by the legend. Ē is the estimated mean energy of the spectrum and ϕx at Ē is the theoretical value of ϕx at the mean energy.

Fig. 10
Fig. 10

Plots of the source spectrum (left) and refractive index of PEEK (right) as employed in the simulation.

Fig. 11
Fig. 11

Plots of the translation and inversion curves for the four aperture thicknesses employed which are indicated in the legend. Plots a) and c) correspond to the polychromatic case whilst plots b) and d) correspond to the monochromatic case at the spectrum mean energy of 18keV.

Fig. 12
Fig. 12

Plots of integrated refraction angle across the simulated PEEK fiber of 100μm radius. Plot a) and c) correspond to the polychromatic case whilst plots b) and d) correspond to the monochromatic case at the spectrum mean energy of 18keV. Plots a) and b) have been obtained using the TC inversion technique whilst plots c) and d) have been obtained using the linear approximation. The analytic sample phase at the spectrum mean energy has been plotted on all axes for reference.

Tables (1)

Tables Icon

Table 1 Numerically determined values of δ̄ for four different values of aperture gold thickness. Ēδ̄ is the photon energy at which PEEK has δ = δ̄.

Equations (26)

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𝒯 i ( x + n P ) = { 1 | x | < η i P / 2 exp ( μ c a T i ) otherwise ,
T ( x ) = exp ( i k ϕ ( x ) 1 2 𝒪 μ ( x , z ) d z )
U ( x ) = C 𝒯 1 ( M ( ξ Δ ξ ) ) T ( ξ ) exp ( i k ξ 2 z so + z od 2 z so z od ) exp ( i k ξ x z od ) d ξ
C = U 0 i λ z so z od ( z so + z od ) exp ( i k ( z so + z od ) ) exp ( i k ( x 2 2 z od ) )
I = P / 2 P / 2 𝒯 2 ( x ) | U ( x ) | 2 d x
T ( x ) T ˜ ( x ) = exp ( i k ( ϕ ( 0 ) + ϕ x ( 0 ) x ) 1 2 𝒪 μ ( 0 , z ) d z )
U 0 ( x ) ~ U 0 exp ( i k ( z so + z od ) ) z so + z od exp ( i k ( x 2 2 z od ) ) exp ( 1 2 𝒪 μ ( 0 , z ) d z ) 𝒯 1 ( z od ϕ x ( 0 ) + x M Δ ξ ) exp ( i k z so 2 z od ( z so + z od ) ( z od ϕ x ( 0 ) + x ) 2 )
I = | U 0 | 2 ( z so + z od ) 2 exp ( 𝒪 μ ( 0 , z ) d z ) P / 2 P / 2 𝒯 2 ( x ) 𝒯 1 ( z od ϕ x ( 0 ) + x M Δ ξ ) d x
I = | U 0 | 2 ( z so + z od ) 2 spectrum exp ( 𝒪 μ ( 0 , z ) d z ) P / 2 P / 2 𝒯 2 ( x ) [ 𝒯 1 ( z od ϕ x ( 0 ) + x M Δ ξ ) * S ( x z so z od ) ] d x σ ( E ) d E
I P ( ϕ ¯ x , μ ¯ , Δ ξ ) = | U 0 | 2 ( z so + z od ) 2 exp ( 𝒪 μ ¯ d z ) P / 2 P / 2 𝒯 ¯ 2 ( x ) [ 𝒯 ¯ 1 ( z od ϕ ¯ x + x M Δ ξ ) * S ( x z so z od ) ] d x
I TC ( Δ ξ ) = | U 0 | 2 ( z so + z od ) 2 P / 2 P / 2 𝒯 ¯ 2 ( x ) [ 𝒯 ¯ 1 ( x M Δ ξ ) * S ( x z so z od ) ] d x
I P ( ϕ ¯ x , μ ¯ , Δ ξ ) = exp ( 𝒪 μ ¯ d z ) I TC ( Δ ξ z od ϕ ¯ x / M ) ,
F ( z od ϕ ¯ x ( 0 ) ) = P / 2 P / 2 𝒯 ¯ 2 ( x ) [ ( 𝒯 ¯ 1 ( z od ϕ ¯ x ( 0 ) + x M Δ ξ 1 ) + 𝒯 ¯ 1 ( z od ϕ ¯ x ( 0 ) + x M Δ ξ 2 ) ) * S ( x z so z od ) ] d x
| P / 2 P / 2 𝒯 ¯ 2 ( x ) [ ( δ ( x ˜ 1 + η 1 P / 2 ) δ ( x ˜ 1 η 1 P / 2 ) + δ ( x ˜ 2 + η 1 P / 2 ) δ ( x ˜ 2 η 1 P / 2 ) ) * S ( x z so z od ) d x ] |
I TC ( Δ ξ ) = M | U 0 | 2 ( z so + z od ) 2 P / 2 P / 2 𝒯 ¯ 2 ( x ) [ S ( ( x M Δ ξ + η 1 P / 2 ) z so z od ) S ( ( x M Δ ξ η 1 P / 2 ) z so z od ) ] d x
I L = I P ( ϕ ¯ x , μ ¯ , Δ ξ 0 ) = exp ( 𝒪 μ ¯ d z ) I TC ( Δ ξ 0 z od ϕ ¯ x / M )
I R = I P ( ϕ ¯ x , μ ¯ , Δ ξ 0 ) = exp ( 𝒪 μ ¯ d z ) I TC ( Δ ξ 0 z od ϕ ¯ x / M ) .
I Σ = I L + I R = exp ( 𝒪 μ ¯ d z ) [ I TC ( Δ ξ 0 z od ϕ ¯ x / M ) + I TC ( Δ ξ 0 z od ϕ ¯ x / M ) ]
I Δ = I L I R = exp ( 𝒪 μ ¯ d z ) [ I TC ( Δ ξ 0 z od ϕ ¯ x / M ) I TC ( Δ ξ 0 z od ϕ ¯ x / M ) ]
𝒪 μ ¯ d z = log [ 2 I TC ( Δ ξ 0 ) I ^ Σ ] .
f : Ω Δ ξ Ω O Δ ξ s I TC ( Δ ξ 0 Δ ξ s ) I TC ( Δ ξ 0 Δ ξ s ) I TC ( Δ ξ 0 Δ ξ s ) + I TC ( Δ ξ 0 Δ ξ s )
I Δ I Σ ( z od ϕ ¯ x / M ) I TC ( Δ ξ 0 ) ( z od ϕ ¯ x / M ) I TC ( Δ ξ 0 ) + O ( ( z od ϕ ¯ x ) 3 ) 2 I TC ( Δ ξ 0 ) = z od ϕ ¯ x M I TC ( Δ ξ 0 ) I TC ( Δ ξ 0 )
ϕ ¯ x = M z od I ^ Δ I ^ Σ I TC ( Δ ξ 0 ) I TC ( Δ ξ 0 )
ε ( Δ ξ 0 ) = max Δ ξ s Ω Δ ξ s ( I Σ ( Δ ξ 0 , Δ ξ s ) ) max Δ ξ s Ω Δ ξ s ( I Σ ( Δ ξ 0 , Δ ξ s ) ) mean Δ ξ s Ω Δ ξ s ( I Σ ( Δ ξ 0 , Δ ξ s ) )
ϕ ¯ x = erf 1 ( I ^ Δ I ^ Σ ) σ d z od
π 2 I ^ Δ I ^ Σ σ d z od

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