Abstract

In this Letter, we present a single-shot approach to quantitatively retrieve x-ray absorption and phase shift in grating interferometry. The proposed approach makes use of the energy-resolving capability of x-ray photon-counting detectors. The retrieval method is derived and presented and is tested based on numerical simulations, including photon shot noise. The good agreement between retrieval results and theoretical values confirms the feasibility of the presented approach.

© 2014 Optical Society of America

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2012 (1)

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
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2011 (4)

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P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

2009 (1)

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
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2005 (1)

1997 (1)

J. M. Boone, T. R. Fewell, and R. J. Jennings, Med. Phys. 24, 1863 (1997).
[CrossRef]

1976 (1)

R. E. Alvarez and A. Macovski, Phys. Med. Biol. 21, 733 (1976).
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Abbene, L.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
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T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
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Alvarez, R. E.

R. E. Alvarez and A. Macovski, Phys. Med. Biol. 21, 733 (1976).
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A. Appel, M. Anastasio, and E. Brey, Tissue Eng. 17, 321 (2011).
[CrossRef]

Anton, G.

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A. Appel, M. Anastasio, and E. Brey, Tissue Eng. 17, 321 (2011).
[CrossRef]

Ballabriga, R.

Barber, W. C.

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

Bayer, F.

Bech, M.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Bevins, N.

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

Boone, J. M.

J. M. Boone, T. R. Fewell, and R. J. Jennings, Med. Phys. 24, 1863 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[CrossRef]

Brey, E.

A. Appel, M. Anastasio, and E. Brey, Tissue Eng. 17, 321 (2011).
[CrossRef]

Bruyndonckx, P.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

Campbell, M.

Caroli, E.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Chen, G.

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

Cloetens, P.

Coan, P.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[CrossRef]

Das, M.

David, C.

Den, T.

Diaz, A.

Druart, G.

Fewell, T. R.

J. M. Boone, T. R. Fewell, and R. J. Jennings, Med. Phys. 24, 1863 (1997).
[CrossRef]

Gabor, T.

Guerineau, N.

Gürsoy, D.

Haas, W.

Handa, S.

Harasse, S.

Horn, F.

Hubbell, J. H.

J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interest (NIST, 1996).

Idir, M.

Itoh, H.

Iwanczyk, J. S.

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

Jennings, R. J.

J. M. Boone, T. R. Fewell, and R. J. Jennings, Med. Phys. 24, 1863 (1997).
[CrossRef]

Kondoh, T.

Kuwabara, H.

Liu, X.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Liu, Y.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Llopart, X.

Macovski, A.

R. E. Alvarez and A. Macovski, Phys. Med. Biol. 21, 733 (1976).
[CrossRef]

Mancini, A. M.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Marone, F.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Mcdonald, S. A.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Meiser, J.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Mercere, P.

Michel, N.

Michel, T.

Mohr, J.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Mollenbauer, U.

Momose, A.

Nagai, K.

Nakamura, T.

Ouchi, C.

Pauwels, B.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Pelzer, G.

Pfeiffer, F.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
[CrossRef]

Primot, J.

Qi, Z.

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

Rieger, J.

Ritter, A.

Ritter, I.

Rizzi, J.

Sasov, A.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Sato, G.

Schulz, J.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Seltzer, S. M.

J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interest (NIST, 1996).

Seo, Y.

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

Setomoto, Y.

Sievers, P.

Silva, P.

Sordo, S. D.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Stampanoni, M.

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, Opt. Express 13, 6296 (2005).
[CrossRef]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[CrossRef]

Taper, A.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Teshima, T.

Thuering, T.

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

Ubertini, P.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Velroyen, A.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Vincent, G.

Walter, M.

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

Wang, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Weber, T.

Weitkamp, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wolfel, S.

Wong, W. S.

Wu, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Yamaguchi, K.

Yashiro, W.

Zambelli, J.

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

Zang, A.

Zappettini, A.

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Zhang, K.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Zhu, P.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Ziegler, E.

Appl. Phys. Lett. (1)

T. Thuering, W. C. Barber, Y. Seo, F. Alhassen, J. S. Iwanczyk, and M. Stampanoni, Appl. Phys. Lett. 102, 191113 (2013).
[CrossRef]

Med. Phys. (1)

J. M. Boone, T. R. Fewell, and R. J. Jennings, Med. Phys. 24, 1863 (1997).
[CrossRef]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Nat. Phys. 2, 258 (2006).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Med. Biol. (3)

Z. Qi, J. Zambelli, N. Bevins, and G. Chen, Phys. Med. Biol. 55, 2669 (2010).
[CrossRef]

R. E. Alvarez and A. Macovski, Phys. Med. Biol. 21, 733 (1976).
[CrossRef]

A. Bravin, P. Coan, and P. Suortti, Phys. Med. Biol. 58, R1 (2013).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

A. Taper, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, Proc. Natl. Acad. Sci. USA 109, 15691 (2012).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. Mcdonald, F. Marone, and M. Stampanoni, Proc. Natl. Acad. Sci. USA 107, 13576 (2010).
[CrossRef]

Sensors (1)

S. D. Sordo, L. Abbene, E. Caroli, A. M. Mancini, A. Zappettini, and P. Ubertini, Sensors 9, 3491 (2009).
[CrossRef]

Tissue Eng. (1)

A. Appel, M. Anastasio, and E. Brey, Tissue Eng. 17, 321 (2011).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interest (NIST, 1996).

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