Abstract

Imaging techniques employed to measure the structure of granular, particulate and porous materials are limited by scale, temporal resolution and, for biological samples, radiation exposure. This paper describes a technique for determining the distribution of particle sizes in opaque samples, for particle volume fractions less than ten percent, using a single projection radiograph. The method is based on the derived property of the additivity of the particles’ spatial autocorrelation function in projection images. Simulations and experiments demonstrate the ability to use this property to determine the distribution of particle sizes in a material.

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    [CrossRef] [PubMed]
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2010 (1)

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

2009 (1)

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

2008 (1)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

2007 (2)

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

2006 (1)

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

2004 (1)

M. J. Kitchen, D. 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]

2003 (1)

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

2002 (2)

M. E. Davis, “Ordered porous materials for emerging applications,” Nature 417(6891), 813–821 (2002).
[CrossRef] [PubMed]

D. 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]

2001 (2)

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A 467–468, 1005–1009 (2001).
[CrossRef]

1997 (2)

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[CrossRef]

1996 (1)

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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

1987 (1)

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

1963 (1)

R. A. Dobbins, L. Crocco, and I. Glassmans, “Measurement of Mean Particle Sizes of Sprays from Diffractively Scattered Light,” AIAA J. 1(8), 1882–1886 (1963).
[CrossRef]

Alaimo, M. D.

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

Arfelli, F.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Asano, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Besch, H.-J.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Bosecke, P.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

Bösecke, P.

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A 467–468, 1005–1009 (2001).
[CrossRef]

Bravin, A.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Carberry, J.

C. V. Nguyen, J. Carberry, and A. Fouras, “Volumetric-correlation PIV to measure particle concentration and velocity of microflows,” Exp. Fluids (in-press).

Cerbino, R.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

Crocco, L.

R. A. Dobbins, L. Crocco, and I. Glassmans, “Measurement of Mean Particle Sizes of Sprays from Diffractively Scattered Light,” AIAA J. 1(8), 1882–1886 (1963).
[CrossRef]

D’Amico, K. L.

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Davis, M. E.

M. E. Davis, “Ordered porous materials for emerging applications,” Nature 417(6891), 813–821 (2002).
[CrossRef] [PubMed]

Deckman, H. W.

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Diat, O.

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A 467–468, 1005–1009 (2001).
[CrossRef]

Dobbins, R. A.

R. A. Dobbins, L. Crocco, and I. Glassmans, “Measurement of Mean Particle Sizes of Sprays from Diffractively Scattered Light,” AIAA J. 1(8), 1882–1886 (1963).
[CrossRef]

Dubsky, S.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

Dusting, J.

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

Fernández, M.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Ferri, F.

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

Flannery, B. P.

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Fouras, A.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

C. V. Nguyen, J. Carberry, and A. Fouras, “Volumetric-correlation PIV to measure particle concentration and velocity of microflows,” Exp. Fluids (in-press).

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[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]

Giglio, M.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

Glassmans, I.

R. A. Dobbins, L. Crocco, and I. Glassmans, “Measurement of Mean Particle Sizes of Sprays from Diffractively Scattered Light,” AIAA J. 1(8), 1882–1886 (1963).
[CrossRef]

Goto, S.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Gureyev, T. E.

D. 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]

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]

Havlin, S.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[CrossRef]

Heitner, G.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Hourigan, K.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

Irvine, S. C.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

Ishikawa, T.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Isshiki, M.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Jamison, R. A.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

Keyriläinen, J.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Kimura, H.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

King, P. R.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[CrossRef]

Kitchen, M. J.

M. J. Kitchen, D. 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]

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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Lewis, R.

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

Lewis, R. A.

M. J. Kitchen, D. 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]

Lo Jacono, D.

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

Magatti, D.

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

Makse, H. A.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[CrossRef]

Matsushita, T.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Mayo, S. C.

D. 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]

Menk, R.-H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Miller, P. R.

D. 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]

Mudie, S. T.

M. J. Kitchen, D. 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]

Narayanan, T.

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A 467–468, 1005–1009 (2001).
[CrossRef]

Nguyen, C. V.

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

C. V. Nguyen, J. Carberry, and A. Fouras, “Volumetric-correlation PIV to measure particle concentration and velocity of microflows,” Exp. Fluids (in-press).

Ohashi, H.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Paganin, D.

M. J. Kitchen, D. 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. 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]

Peverini, L.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

Plothow-Besch, H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Pogany, A.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[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]

Potenza, M. A. C.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

Rigon, L.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

Roberge, W. G.

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Robert, A.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Siu, K. K. W.

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

Snigirev, A.

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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Snigireva, 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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

Stanley, H. E.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[CrossRef]

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]

Suhonen, H.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Suortti, P.

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Suzuki, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Takeshita, K.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Uesugi, K.

M. J. Kitchen, D. 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.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Wilkins, S. W.

D. 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]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[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]

Yagi, N.

M. J. Kitchen, D. 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]

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Yamazaki, H.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Yoneda, Y.

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

AIAA J. (1)

R. A. Dobbins, L. Crocco, and I. Glassmans, “Measurement of Mean Particle Sizes of Sprays from Diffractively Scattered Light,” AIAA J. 1(8), 1882–1886 (1963).
[CrossRef]

Appl. Phys. Lett. (2)

M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett. 88(19), 191101 (2006).
[CrossRef]

S. Dubsky, R. A. Jamison, S. C. Irvine, K. K. W. Siu, K. Hourigan, and A. Fouras, “Computed tomographic x-ray velocimetry,” Appl. Phys. Lett. 96(2), 023702 (2010).
[CrossRef]

Exp. Fluids (1)

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids 47(4-5), 569–577 (2009).
[CrossRef]

J. Appl. Phys. (1)

A. Fouras, J. Dusting, R. Lewis, and K. Hourigan, “Three-dimensional synchrotron x-ray particle image velocimetry,” J. Appl. Phys. 102(6), 064916 (2007).
[CrossRef]

J. Microsc. (1)

D. 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. Phys. D Appl. Phys. (1)

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys. 36(10A), A107–A112 (2003).
[CrossRef]

J. Synchrotron Radiat. (1)

H. Suhonen, M. Fernández, A. Bravin, J. Keyriläinen, and P. Suortti, “Refraction and scattering of X-rays in analyzer-based imaging,” J. Synchrotron Radiat. 14(6), 512–521 (2007).
[CrossRef] [PubMed]

Nat. Phys. (1)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4(3), 238–243 (2008).
[CrossRef]

Nature (3)

M. E. Davis, “Ordered porous materials for emerging applications,” Nature 417(6891), 813–821 (2002).
[CrossRef] [PubMed]

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature 386(6623), 379–382 (1997).
[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]

Nucl. Instrum. Meth. A (2)

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A 467–468, 1005–1009 (2001).
[CrossRef]

S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215-m-long beamline at SPring-8,” Nucl. Instrum. Meth. A 467–468, 682–685 (2001).
[CrossRef]

Phys. Med. Biol. (1)

M. J. Kitchen, D. 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]

Rev. Sci. Instrum. (2)

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,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997).
[CrossRef]

Science (1)

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science 237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Other (6)

C. N. Davies, Aerosol Science, First ed. (Academic Press, 1966).

C. V. Nguyen, J. Carberry, and A. Fouras, “Volumetric-correlation PIV to measure particle concentration and velocity of microflows,” Exp. Fluids (in-press).

E. L. Crow and K. Shimizu, Lognormal Distributions: Theory and Applications (M. Dekker, 1988).

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University Press, 2010).

M. Nieto-Vesperinas, Scattering And Diffraction in Physical Optics, 2nd ed. (World Scientific Pub Co Inc, 2006).

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

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