Abstract

Phase retrieval extracts quantitative phase information from x-ray propagation-based phase-contrast images. Notwithstanding inherent approximations, phase retrieval using a single sample-to-detector distance (SDD) is very attractive, because it imposes no setup complications or additional radiation dose compared to absorption-based imaging. Considering the phase-attenuation duality (ε=δ/β, where ε is constant), a simple absorption correction factor is proposed for the modified Bronnikov algorithm in x-ray propagation-based phase-contrast computed tomography (PPCT). Moreover, a practical method for calculating the optimal ε value is proposed, which requires no prior knowledge of the sample. Tests performed on simulation and experimental data successfully distin guished different materials in a quasihomogeneous and weakly absorbing sample from a single SDD-PPCT data point.

© 2011 Optical Society of America

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L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, Opt. Express 18, 6423 (2010).
[CrossRef] [PubMed]

2007 (1)

2006 (3)

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, Opt. Express 14, 8103 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2002 (1)

2000 (1)

R. Fitzgerald, Phys. Today 53, 23 (2000).
[CrossRef]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

1996 (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Abela, R.

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Baruchel, J.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Bellotti, R.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Beltran, M. A.

Boistel, R.

Bronnikov, A. V.

Buffiere, J. Y.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

Cloetens, P.

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, Opt. Lett. 32, 1617 (2007).
[CrossRef] [PubMed]

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Davis, T. J.

De Caro, L.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Di Michiel, M.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

Ferrie, E.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

Fitzgerald, R.

R. Fitzgerald, Phys. Today 53, 23 (2000).
[CrossRef]

Giannini, C.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Groso, A.

Guigay, J. P.

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, Opt. Lett. 32, 1617 (2007).
[CrossRef] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Gureyev, T. E.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, Appl. Opt. 43, 2418 (2004).
[CrossRef] [PubMed]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

Kitchen, M. J.

Langer, M.

Liu, H.

Longo, R.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Ludwig, W.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Maire, E.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

Mayo, S. C.

Myers, G. R.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

Nesterets, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

Nugent, K. A.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Paganin, D.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Paganin, D. M.

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, Opt. Express 18, 6423 (2010).
[CrossRef] [PubMed]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

Pogany, A.

Rigon, L.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Salvo, L.

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

Scattarella, F.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Stampanoni, M.

Tangaro, S.

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Uesugi, K.

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, Appl. Opt. 43, 2418 (2004).
[CrossRef] [PubMed]

Wu, X. Z.

Yan, A. M.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, Appl. Phys. Lett. 75, 2912 (1999).
[CrossRef]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, Appl. Phys. Lett. 89 (2006).
[CrossRef]

Atomic Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data Nucl. Data Tables 54, 181 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

Med. Phys. (1)

L. De Caro, F. Scattarella, C. Giannini, S. Tangaro, L. Rigon, R. Longo, and R. Bellotti, Med. Phys. 37, 3817 (2010).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef] [PubMed]

Phys. Today (1)

R. Fitzgerald, Phys. Today 53, 23 (2000).
[CrossRef]

Scripta Mater. (1)

J. Baruchel, J. Y. Buffiere, P. Cloetens, M. Di Michiel, E. Ferrie, W. Ludwig, E. Maire, and L. Salvo, Scripta Mater. 55, 41 (2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the PPCT scanning geometry.

Fig. 2
Fig. 2

Simulation results: (a) 3D phantom and one PPCT projection. (b) Cross-sectional view of 3D phantom. (c) Corresponding reconstructed results of (b). (d) Profiles of the phantom and the reconstructed result along the line positions in Figs. 2b, 2c, respectively.

Fig. 3
Fig. 3

Experimental results: (a) reconstructed result of the wire sample and (b) histogram of Fig. 3a; the labels indicate the peak for each material.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I θ , z ( x , y ) = I θ , 0 ( x , y ) [ 1 λ z 2 π 2 ϕ θ ( x , y ) ] ,
δ ( x , y , z ) = 1 4 π 2 z 0 π [ q ( x , y ) * * g θ ( x , y ) ] d θ ,
Q ( ξ , η ) = | ξ | ξ 2 + η 2 + α ,
α = 1 π ε λ z .
F [ ( I z / I 0 1 ) / 2 ] ( ξ , η ) = γ ^ cos χ + ϕ ^ sin χ ,
ε = ϕ γ = F 1 { [ cos χ 1 F ( I z 2 1 2 ) cos χ 2 F ( I z 1 1 2 ) ] / sin ( χ 2 χ 1 ) } F 1 { [ sin χ 2 F ( I z 1 1 2 ) sin χ 1 F ( I z 2 1 2 ) ] / sin ( χ 2 χ 1 ) } ,

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