Abstract

We examine the projection approximation in the context of propagation-based phase contrast imaging using hard x-rays. Specifically, we consider the case of a cylinder or a rounded edge, as a simple model for the edges of many biological samples. The Argand-plane signature of a propagation-based phase contrast fringe from the edge of a cylinder is studied, and the evolution of this signature with propagation. This, along with experimental images obtained using a synchrotron source, reveals how propagation within the scattering volume is not fully described in the projection approximation's ray-based approach. This means that phase contrast fringes are underestimated by the projection approximation at a short object-to-detector propagation distance, namely a distance comparable to the free-space propagation within the volume. This failure of the projection approximation may become non-negligible in the detailed study of small anatomical features deep within a large body. Nevertheless, the projection approximation matches the exact solution for a larger propagation distance typical of those used in biomedical phase contrast imaging.

© 2010 OSA

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    [CrossRef]
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2008 (3)

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

2004 (1)

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

2002 (1)

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

1999 (4)

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[CrossRef]

G. Margaritondo and G. Tromba, “Coherence-based edge diffraction sharpening of x-ray images: A simple model,” J. Appl. Phys. 85(7), 3406–3408 (1999).
[CrossRef]

1998 (1)

1996 (2)

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(1), 133–146 (1996).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

1995 (1)

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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

1974 (1)

D. F. Lynch, M. A. O'Keefe, and A. F. Moodie, “n-beam lattice images. V. “The use of the charge-density approximation in the interpretation of lattice images,” Acta Crystallogr. 31, 300–307 (1974).

1962 (1)

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. A 52(2), 116–130 (1962).
[CrossRef]

1896 (1)

W. C. Röntgen, “On a new kind of rays,” Nature 53(1369), 274–276 (1896).
[CrossRef]

Barrett, R.

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(1), 133–146 (1996).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (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(1), 133–146 (1996).
[CrossRef]

Boucher, R.

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

Boucher, R. C.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

Buffière, J.-Y.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Cloetens, P.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (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(1), 133–146 (1996).
[CrossRef]

Crosbie, J.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

Delen, N.

Donnelley, M.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

Fouras, A.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Gao, D.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Guigay, J. P.

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(1), 133–146 (1996).
[CrossRef]

Guigay, J.-P.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Gureyev, T. E.

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Habib, A.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Hooker, B.

Hooper, S. B.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Keller, J. B.

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. A 52(2), 116–130 (1962).
[CrossRef]

Kitchen, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

Kohmura, Y.

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Kohn, V.

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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Kuznetsov, S.

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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Lewis, R. A.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Lynch, D. F.

D. F. Lynch, M. A. O'Keefe, and A. F. Moodie, “n-beam lattice images. V. “The use of the charge-density approximation in the interpretation of lattice images,” Acta Crystallogr. 31, 300–307 (1974).

Maire, E.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Margaritondo, G.

G. Margaritondo and G. Tromba, “Coherence-based edge diffraction sharpening of x-ray images: A simple model,” J. Appl. Phys. 85(7), 3406–3408 (1999).
[CrossRef]

Mayo, S. C.

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

Miller, P. R.

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

Moodie, A. F.

D. F. Lynch, M. A. O'Keefe, and A. F. Moodie, “n-beam lattice images. V. “The use of the charge-density approximation in the interpretation of lattice images,” Acta Crystallogr. 31, 300–307 (1974).

Morgan, K. S.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

Morgan, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Mudie, S. T.

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

O'Keefe, M. A.

D. F. Lynch, M. A. O'Keefe, and A. F. Moodie, “n-beam lattice images. V. “The use of the charge-density approximation in the interpretation of lattice images,” Acta Crystallogr. 31, 300–307 (1974).

Paganin, D. M.

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

Parsons, D. W.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

Peix, G.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Pernot-Rejmánková, P.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Pogany, A.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Raven, C.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[CrossRef]

Röntgen, W. C.

W. C. Röntgen, “On a new kind of rays,” Nature 53(1369), 274–276 (1896).
[CrossRef]

Salomé-Pateyron, M.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

Schelokov, I.

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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (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(1), 133–146 (1996).
[CrossRef]

Siew, M. L.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Siu, K. K. W.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

Snigirev, A.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Snigireva, I.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Stevenson, A. W.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Suzuki, Y.

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Tromba, G.

G. Margaritondo and G. Tromba, “Coherence-based edge diffraction sharpening of x-ray images: A simple model,” J. Appl. Phys. 85(7), 3406–3408 (1999).
[CrossRef]

Uesugi, K.

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

Umetani, K.

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Wallace, M. J.

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Wilkins, S. W.

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys. 32(5), 563–567 (1999).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

Williams, I.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

Yagi, N.

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Yamasaki, K.

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Acta Crystallogr. (1)

D. F. Lynch, M. A. O'Keefe, and A. F. Moodie, “n-beam lattice images. V. “The use of the charge-density approximation in the interpretation of lattice images,” Acta Crystallogr. 31, 300–307 (1974).

Eur. J. Radiol. (1)

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008).
[CrossRef] [PubMed]

J. Anat. (1)

D. W. Parsons, K. S. Morgan, M. Donnelley, A. Fouras, J. Crosbie, I. Williams, R. C. Boucher, K. Uesugi, N. Yagi, and K. K. W. Siu, “High-resolution visualization of airspace structures in intact mice via synchrotron phase-contrast X-ray imaging (PCXI),” J. Anat. 213(2), 217–227 (2008).
[CrossRef]

J. Appl. Phys. (1)

G. Margaritondo and G. Tromba, “Coherence-based edge diffraction sharpening of x-ray images: A simple model,” J. Appl. Phys. 85(7), 3406–3408 (1999).
[CrossRef]

J. Microsc. (1)

D. M. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

J. Phys. D Appl. Phys. (4)

P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Maire, and G. Peix, “Hard x-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 330–336 (1999).
[CrossRef]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. 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(1), 133–146 (1996).
[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,” J. Phys. D Appl. Phys. 29, 133–146 (1995).

Med. Phys. (1)

N. Yagi, Y. Suzuki, K. Umetani, Y. Kohmura, and K. Yamasaki, “Refraction-enhanced x-ray imaging of mouse lung using synchrotron radiation source,” Med. Phys. 26(10), 2190–2193 (1999).
[CrossRef] [PubMed]

Nature (2)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384(6607), 335–338 (1996).
[CrossRef]

W. C. Röntgen, “On a new kind of rays,” Nature 53(1369), 274–276 (1896).
[CrossRef]

Phys. Med. Biol. (2)

M. J. Kitchen, D. M. Paganin, R. A. Lewis, N. Yagi, K. Uesugi, and S. T. Mudie, “On the origin of speckle in x-ray phase contrast images of lung tissue,” Phys. Med. Biol. 49(18), 4335–4348 (2004).
[CrossRef] [PubMed]

M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008).
[CrossRef] [PubMed]

Other (3)

D. M. Paganin, Coherent X-ray Optics, Oxford University Press, New York, 2006.

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

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics, 2nd ed. (World Scientific Publishing, New Jersey, 2006).

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Figures (10)

Fig. 1
Fig. 1

Imaging geometry showing the projected thickness of a sample object, as used by the projection approximation, along with the associated exit plane.

Fig. 2
Fig. 2

Phase contrast fringes from the simulation for light of wavelength λ = 0.5 Angstrom incident on the left edge of a 3 mm diameter perspex cylinder (using δair = 4.13 × 10−10, βair = 0, δperspex = 4.00 × 10−7, βperspex = 3.1998 × 10−10), propagated 50 cm.

Fig. 3
Fig. 3

Phase contrast images show the projection approximation correctly predicts the fringes seen at sufficiently long propagation distances. Images taken at the upstream hutch of BL20XU, SPring-8, of a 3 mm diameter perspex cylinder at 25keV for a propagation of a) 50 cm and b) 100 cm. The observed profile is shown in black and the simulated in blue.

Fig. 4
Fig. 4

Argand plot of 1 Angstrom waves incident on a 3 mm cylinder, propagated 5 mm, corresponding to 8 micron either side of the cylinder's geometric shadow, producing a connected Cornu spiral (blue) and hypocyloid (black).

Fig. 5
Fig. 5

Propagation based phase contrast imaging of a cylinder separated into edge diffraction and a distorted transmitted wave.

Fig. 7
Fig. 7

Argand plot of 0.5 Angstrom waves incident on a 1 mm diameter cylinder, propagated 1 mm, corresponding 8 micron either side of the cylinder's geometric shadow, with significant attenuation by the cylinder (β Fig. 7 = 500 × β Fig. 4 ). The dotted circle indicates the uniform intensity of the unscattered wave.

Fig. 6
Fig. 6

Geometry of rays incident on a cylinder, showing the rays which interfere to form a Cornu spiral and a hypocycloid.

Fig. 8
Fig. 8

Argand plot of 0.5 Angstrom waves incident on a 3 mm cylinder, smoothed by a Gaussian of pixel size 0.18 micron, showing the introduction of multiple intense, wider fringes with propagation, viewing 1 micron either side of the interface.

Fig. 9
Fig. 9

Experimental phase contrast images show the projection approximation does not predict the fringes seen at very short propagation distances, but the simulated fringes become more accurate as the propagation distance increases. Images taken of the same 3 mm diameter perspex cylinder as Fig. 3, at 25keV for a propagation of a) contact, b) 1.5 mm, c) 3 mm. At these short propagation distances, the pixel size and point spread function prevent multiple fringes being resolved at the edge interface. The shorter propagation distance means that the signal to noise ratio is reduced. The observed profile is shown in black and that simulated using the projection approximation (then smoothed with detector characteristics as in Fig. 3) in blue.

Fig. 10
Fig. 10

A hypocycloid is traced by a circle turning, a) without slipping and b) with slipping, around the inside of a bigger circle.

Equations (15)

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

[2ikz+2+k2(n2(x,y,z)1)]ψ(x,y,z)=0,
ψexit surface=ψincident×exp(ijkδjTj)×exp(jkβjTj).
ψ{[1/2+C(u)][1/2+2(u)]}+{[1/2+C(u)][1/2+S(u)]}.
ψ{[1/2+C(u)]+[1/2+S(u)]}+i{[1/2+C(u)][1/2+S(u)]}+exp(ikδT)×exp(kβT){[1/2+C(u)]i[1/2+S(u)]}.
ψimage plane=eikz×eikδT+SeikR/R,
ψimage plane=eikz×eiφobject+SReiφedge.
φobject(x+Δx)φobject(x)=φobject'(x)×Δx,
2πd=2πSR(x)=φ'object(x)×Δx.
φ'edge(x)Δx2π.
φ'edge(x)2πSR(x)φ'object(x)2π.
Sφ'edge(x)R(x)φ'object(x).
SkR(x)R(x)kδT(x).
T(x)Sxδ(z2+x2)3/4.
T(x)Sxδz3/2.
xz 2aδ2S23.

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