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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  1. M. E. Davis, “Ordered porous materials for emerging applications,” Nature417(6891), 813–821 (2002).
    [CrossRef] [PubMed]
  2. H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature386(6623), 379–382 (1997).
    [CrossRef]
  3. C. N. Davies, Aerosol Science, First ed. (Academic Press, 1966).
  4. 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]
  5. B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science237(4821), 1439–1444 (1987).
    [CrossRef] [PubMed]
  6. T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A467–468, 1005–1009 (2001).
    [CrossRef]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
    [CrossRef]
  12. 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]
  13. M. D. Alaimo, D. Magatti, F. Ferri, and M. A. C. Potenza, “Heterodyne speckle velocimetry,” Appl. Phys. Lett.88(19), 191101 (2006).
    [CrossRef]
  14. 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]
  15. A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids47(4-5), 569–577 (2009).
    [CrossRef]
  16. 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]
  17. C. V. Nguyen, J. Carberry, and A. Fouras, “Volumetric-correlation PIV to measure particle concentration and velocity of microflows,” Exp. Fluids (in-press).
  18. 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]
  19. A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University Press, 2010).
  20. M. Nieto-Vesperinas, Scattering And Diffraction in Physical Optics, 2nd ed. (World Scientific Pub Co Inc, 2006).
  21. 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]
  22. E. L. Crow and K. Shimizu, Lognormal Distributions: Theory and Applications (M. Dekker, 1988).
  23. 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. A467–468, 682–685 (2001).
    [CrossRef]
  24. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

2010

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

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids47(4-5), 569–577 (2009).
[CrossRef]

2008

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

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

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

2004

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

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

M. E. Davis, “Ordered porous materials for emerging applications,” Nature417(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

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. A467–468, 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. A467–468, 1005–1009 (2001).
[CrossRef]

1997

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature386(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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

1995

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

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

1963

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. A467–468, 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. A467–468, 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,” Science237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Davis, M. E.

M. E. Davis, “Ordered porous materials for emerging applications,” Nature417(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,” Science237(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. A467–468, 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,” Science237(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. Fluids47(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,” Nature384(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. A467–468, 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,” Nature384(6607), 335–338 (1996).
[CrossRef]

Havlin, S.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature386(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. Fluids47(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. A467–468, 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. A467–468, 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. A467–468, 682–685 (2001).
[CrossRef]

King, P. R.

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature386(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. Fluids47(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,” Nature386(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. A467–468, 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. A467–468, 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. Fluids47(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. A467–468, 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,” Nature384(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,” Science237(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,” Nature386(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,” Nature384(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. A467–468, 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. A467–468, 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. A467–468, 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,” Nature384(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. A467–468, 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. A467–468, 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. A467–468, 682–685 (2001).
[CrossRef]

AIAA J.

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.

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

A. Fouras, D. Lo Jacono, C. V. Nguyen, and K. Hourigan, “Volumetric correlation PIV: a new technique for 3D velocity vector field measurement,” Exp. Fluids47(4-5), 569–577 (2009).
[CrossRef]

J. Appl. Phys.

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.

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.

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.

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.

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

M. E. Davis, “Ordered porous materials for emerging applications,” Nature417(6891), 813–821 (2002).
[CrossRef] [PubMed]

H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature386(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,” Nature384(6607), 335–338 (1996).
[CrossRef]

Nucl. Instrum. Meth. A

T. Narayanan, O. Diat, and P. Bösecke, “SAXS and USAXS on the high brilliance beamline at the ESRF,” Nucl. Instrum. Meth. A467–468, 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. A467–468, 682–685 (2001).
[CrossRef]

Phys. Med. Biol.

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.

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

B. P. Flannery, H. W. Deckman, W. G. Roberge, and K. L. D’Amico, “Three-Dimensional X-ray Microtomography,” Science237(4821), 1439–1444 (1987).
[CrossRef] [PubMed]

Other

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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Figures (5)

Fig. 1
Fig. 1

Schematic of propagation-based phase contrast X-ray imaging setup and image processing steps. The sample and detector are in-line and z is the propagation distance for phase contrast imaging. A region of a typical X-ray image has been magnified to highlight the speckled appearance produced by particles. A spatial autocorrelation is performed; which is azimuthally averaged to produce the final one-dimensional autocorrelation function.

Fig. 2
Fig. 2

The autocorrelation function produced by an equal mixture of two particle sizes is equal to the weighted sum of the autocorrelation functions of particles of each size. SAF69 and SAF116 are equally weighted autocorrelation functions of single particles with diameters of 69 μm and 116 μm respectively. SAF69,116 is the autocorrelation of an equal mixture (by number) of particles. All SAFs in this figure were averaged over 256 windows.

Fig. 3
Fig. 3

Calculated distribution of particle diameters from simulated data. Each point represents the fraction of particles of that diameter.

Fig. 4
Fig. 4

Experimentally obtained volume fraction of one particle size from nine bimodal mixtures averaged over 460 windows. True solutions lie on the solid line.

Fig. 5
Fig. 5

Calculated volume fraction of one particle size in a mixture of two particles from simulated data; illustrating the reduction in error by averaging over 256 windows (b) versus 4 windows (a). Ideal solutions lie on the solid line. (c) Root mean square error as a function of the number of windows averaged over.

Equations (7)

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

I(x,y)= I (x,y) I in (x,y) 1μT( x,y ),
I m (x,y)= r= R min R max { n=1 N r [ δ(x x n )δ(y y n ) ] I m r (x,y) } ,
PSD{ I m (x,y) }= | r= R min R max { n=1 N r { δ(x x n )δ(y y n ) } { I m r (x,y) } } | 2
SAF{ I m ( x,y ) }= 1 { | r= R min R max [ n=1 N r { δ(x x n )δ(y y n ) } { I m r (x,y) } ] | 2 }.
SAF{ I m ( x,y ) } r= R min R max 1 { n=1 N r | { δ(x x n )δ(y y n ) } | 2 | { I m r (x,y) } | 2 } .
SAF{ I m (x,y) }= r= R min R max N r SAF{ I m r (x,y) } .
SAF{ i(x,y) }=f SAF 69 +(1f) SAF 116

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