Abstract

Differential phase-contrast tomography, also known as beam-deflection tomography, is a method for reconstructing an object’s refractive index distribution from knowledge of differential projection data that describe beam deflection angles. We describe and demonstrate an approach to determining regions of interest within an object from truncated differential projection data.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2006 (3)

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

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

Y. Song, B. Zhang, and Z. He, Appl. Opt. 45, 8092 (2006).
[CrossRef] [PubMed]

2005 (1)

X. Pan and Y. Zou, Inverse Probl. 21, 1169 (2005).
[CrossRef]

2004 (2)

Y. Zou and X. Pan, Phys. Med. Biol. 49, 941 (2004).
[CrossRef] [PubMed]

F. Noo, R. Clackdoyle, and J. Pack, Phys. Med. Biol. 49, 3903 (2004).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

1988 (1)

1987 (1)

1984 (1)

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Bunk, O.

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

Byer, R. L.

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Clackdoyle, R.

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

F. Noo, R. Clackdoyle, and J. Pack, Phys. Med. Biol. 49, 3903 (2004).
[CrossRef] [PubMed]

David, C.

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

Defrise, M.

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

Faris, G. W.

Gmur, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

He, Z.

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Kudo, H.

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

Lewis, R. W.

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Momose, A.

Noo, F.

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

F. Noo, R. Clackdoyle, and J. Pack, Phys. Med. Biol. 49, 3903 (2004).
[CrossRef] [PubMed]

Pack, J.

F. Noo, R. Clackdoyle, and J. Pack, Phys. Med. Biol. 49, 3903 (2004).
[CrossRef] [PubMed]

Pan, X.

X. Pan and Y. Zou, Inverse Probl. 21, 1169 (2005).
[CrossRef]

Y. Zou and X. Pan, Phys. Med. Biol. 49, 941 (2004).
[CrossRef] [PubMed]

Pfeiffer, F.

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

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Seder, T. A.

Sell, J. A

Song, Y.

Stricker, J.

Teets, R. E.

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Weitkamp, T.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Zhang, B.

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Zou, Y.

X. Pan and Y. Zou, Inverse Probl. 21, 1169 (2005).
[CrossRef]

Y. Zou and X. Pan, Phys. Med. Biol. 49, 941 (2004).
[CrossRef] [PubMed]

Appl. Opt. (4)

Inverse Probl. (2)

X. Pan and Y. Zou, Inverse Probl. 21, 1169 (2005).
[CrossRef]

M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Inverse Probl. 22, 1037 (2006).
[CrossRef]

Nat. Phys. (1)

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

Opt. Express (1)

Phys. Med. Biol. (3)

Y. Zou and X. Pan, Phys. Med. Biol. 49, 941 (2004).
[CrossRef] [PubMed]

F. Noo, R. Clackdoyle, and J. Pack, Phys. Med. Biol. 49, 3903 (2004).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, Phys. Med. Biol. 42, 2015 (1997).
[CrossRef] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

Thick solid line denotes the support segment of a chord at orientation θ.

Fig. 2
Fig. 2

a, Two-dimensional phantom, representing a transverse slice through a 3D object. b and c display two types of ROIs, as enclosed by the white lines, which are referred to as peripheral and central ROIs.

Fig. 3
Fig. 3

Left column: the reconstructed noiseless (upper row) and noisy (lower row) peripheral ROI images. Right column: the reconstructed noiseless (upper row) and noisy (lower row) central ROI images.

Equations (3)

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α ( x r , ϕ ; z ) x r d r 2 a ( r 2 ; z ) δ ( x r r 2 · s r ( ϕ ) ) ,
b θ ( r 2 ; z ) = θ θ + π d ϕ α ( r 2 s r ( θ ) , ϕ ; z ) .
a ( x r s r ( θ ) + y r s r ( θ ) ; z ) = 1 4 π 2 y r U x r y r L x r × L x r U x r d y r y r y r y r L x r y r U x r b θ ( x r s r ( θ ) + y r s r ( θ ) ; z ) ,

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