Abstract

We use coherently scattered X-rays to measure the molecular composition of an object throughout its volume. We image a planar slice of the object in a single snapshot by illuminating it with a fan beam and placing a coded aperture between the object and the detectors. We characterize the system and demonstrate a resolution of 13 mm in range and 2 mm in cross-range and a fractional momentum transfer resolution of 15%. In addition, we show that this technique allows a 100x speedup compared to previously-studied pencil beam systems using the same components. Finally, by scanning an object through the beam, we image the full 4-dimensional data cube (3 spatial and 1 material dimension) for complete volumetric molecular imaging.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. G. Harding, “X-ray diffraction imaging, a multi-generational perspective,” Applied Radiation and Isotopes 67, 287–295 (2009).
    [Crossref]
  2. B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
    [Crossref]
  3. J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
    [Crossref]
  4. M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
    [Crossref]
  5. G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
    [Crossref]
  6. G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
    [Crossref] [PubMed]
  7. O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
    [Crossref] [PubMed]
  8. K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express 20, 16310–16320 (2012).
    [Crossref]
  9. J. A. Greenberg, K. Krishnamurthy, and D. Brady, “Snapshot molecular imaging using coded energy-sensitive detection,” Opt. Express 21, 25480–25491 (2013).
    [Crossref] [PubMed]
  10. J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic x-ray diffraction imaging,” Analyst 139, 709–713 (2014).
    [Crossref]
  11. S. Pang, M. Hassan, J. Greenberg, A. Holmgren, K. Krishnamurthy, and D. Brady, “Complementary coded apertures for 4-dimensional x-ray coherent scatter imaging,” Opt. Express 22, 22925–22936 (2014).
    [Crossref] [PubMed]
  12. D. J. Brady, A. Mrozack, K. MacCabe, and P. Llull, “Compressive tomography,” Adv. Opt. Photon. 7, 756–813 (2015).
    [Crossref]
  13. J. A. Greenberg and D. J. Brady, “Snapshot full-volume coded aperture x-ray diffraction tomography,” Proc. SPIE 9847, 984706 (2016).
    [Crossref]
  14. K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2d tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).
    [Crossref] [PubMed]
  15. J. Greenberg, K. Krishnamurthy, and D. Brady, “Compressive single-pixel snapshot x-ray diffraction imaging,” Opt. Lett. 39, 111–114 (2014).
    [Crossref]
  16. B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
    [Crossref] [PubMed]
  17. D. J. Brady, D. L. Marks, K. P. MacCabe, and J. A. O’ Sullivan, “Coded apertures for x-ray scatter imaging,” Appl. Opt. 52, 7745–7754 (2013).
    [Crossref] [PubMed]
  18. E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Appl. Opt. 17, 337–347 (1978).
    [Crossref] [PubMed]
  19. K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2d tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).
    [Crossref] [PubMed]
  20. I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
    [Crossref]
  21. J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
    [Crossref]
  22. I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).
  23. H. Erdogan and J. Fessler, “Monotonic algorithms for transmission tomography,” Medical Imaging, IEEE Transactions on 18, 801–814 (1999).
    [Crossref]
  24. A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).
  25. J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
    [Crossref]

2016 (3)

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

J. A. Greenberg and D. J. Brady, “Snapshot full-volume coded aperture x-ray diffraction tomography,” Proc. SPIE 9847, 984706 (2016).
[Crossref]

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

2015 (2)

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

D. J. Brady, A. Mrozack, K. MacCabe, and P. Llull, “Compressive tomography,” Adv. Opt. Photon. 7, 756–813 (2015).
[Crossref]

2014 (3)

2013 (4)

2012 (1)

2011 (1)

B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
[Crossref] [PubMed]

2010 (1)

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

2009 (2)

G. Harding, “X-ray diffraction imaging, a multi-generational perspective,” Applied Radiation and Isotopes 67, 287–295 (2009).
[Crossref]

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

1999 (1)

H. Erdogan and J. Fessler, “Monotonic algorithms for transmission tomography,” Medical Imaging, IEEE Transactions on 18, 801–814 (1999).
[Crossref]

1990 (1)

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
[Crossref]

1987 (1)

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

1978 (1)

1975 (1)

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Barnes, P.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

Brady, D.

Brady, D. J.

J. A. Greenberg and D. J. Brady, “Snapshot full-volume coded aperture x-ray diffraction tomography,” Proc. SPIE 9847, 984706 (2016).
[Crossref]

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

D. J. Brady, A. Mrozack, K. MacCabe, and P. Llull, “Compressive tomography,” Adv. Opt. Photon. 7, 756–813 (2015).
[Crossref]

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2d tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).
[Crossref] [PubMed]

D. J. Brady, D. L. Marks, K. P. MacCabe, and J. A. O’ Sullivan, “Coded apertures for x-ray scatter imaging,” Appl. Opt. 52, 7745–7754 (2013).
[Crossref] [PubMed]

K. P. MacCabe, A. D. Holmgren, M. P. Tornai, and D. J. Brady, “Snapshot 2d tomography via coded aperture x-ray scatter imaging,” Appl. Opt. 52, 4582–4589 (2013).
[Crossref] [PubMed]

A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).

Brady, L.

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Briggs, E. A.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Brown, R. T.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Cannon, T. M.

Carin, D.

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Carin, L.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

Chawla, A.

Cromer, D. T.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Erdogan, H.

H. Erdogan and J. Fessler, “Monotonic algorithms for transmission tomography,” Medical Imaging, IEEE Transactions on 18, 801–814 (1999).
[Crossref]

Fenimore, E. E.

Fessler, J.

H. Erdogan and J. Fessler, “Monotonic algorithms for transmission tomography,” Medical Imaging, IEEE Transactions on 18, 801–814 (1999).
[Crossref]

Grass, M.

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Greenberg, J.

S. Pang, M. Hassan, J. Greenberg, A. Holmgren, K. Krishnamurthy, and D. Brady, “Complementary coded apertures for 4-dimensional x-ray coherent scatter imaging,” Opt. Express 22, 22925–22936 (2014).
[Crossref] [PubMed]

J. Greenberg, K. Krishnamurthy, and D. Brady, “Compressive single-pixel snapshot x-ray diffraction imaging,” Opt. Lett. 39, 111–114 (2014).
[Crossref]

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Greenberg, J. A.

J. A. Greenberg and D. J. Brady, “Snapshot full-volume coded aperture x-ray diffraction tomography,” Proc. SPIE 9847, 984706 (2016).
[Crossref]

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic x-ray diffraction imaging,” Analyst 139, 709–713 (2014).
[Crossref]

J. A. Greenberg, K. Krishnamurthy, and D. Brady, “Snapshot molecular imaging using coded energy-sensitive detection,” Opt. Express 21, 25480–25491 (2013).
[Crossref] [PubMed]

A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).

Harding, A.

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Harding, G.

G. Harding, “X-ray diffraction imaging, a multi-generational perspective,” Applied Radiation and Isotopes 67, 287–295 (2009).
[Crossref]

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
[Crossref]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

Harding, G. L.

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Hassan, M.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic x-ray diffraction imaging,” Analyst 139, 709–713 (2014).
[Crossref]

S. Pang, M. Hassan, J. Greenberg, A. Holmgren, K. Krishnamurthy, and D. Brady, “Complementary coded apertures for 4-dimensional x-ray coherent scatter imaging,” Opt. Express 22, 22925–22936 (2014).
[Crossref] [PubMed]

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Holmgren, A.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

S. Pang, M. Hassan, J. Greenberg, A. Holmgren, K. Krishnamurthy, and D. Brady, “Complementary coded apertures for 4-dimensional x-ray coherent scatter imaging,” Opt. Express 22, 22925–22936 (2014).
[Crossref] [PubMed]

Holmgren, A. D.

Howerton, R. J.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Hubbell, J. H.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Jacques, S.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

Johns, P.

B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
[Crossref] [PubMed]

Kaganovsky, Y.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Kang, N.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Kapadia, A. J.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).

King, B.

B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
[Crossref] [PubMed]

Kosanetzky, J.

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
[Crossref]

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

Krishnamurthy, K.

Lakshmanan, M. N.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).

Landheer, K.

B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
[Crossref] [PubMed]

Lazzari, O.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

Li, M.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Liu, J.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Llull, P.

Lu, W.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

MacCabe, K.

MacCabe, K. P.

Marks, D.

Marks, D. L.

Mrozack, A.

Neitzel, U.

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

Newton, M.

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
[Crossref]

O’ Sullivan, J. A.

O’Sullivan, J.

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

O’Sullivan, J. A.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

Odinaka, I.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Pang, S.

Politte, D.

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

Politte, D. G.

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

Samei, E.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express 20, 16310–16320 (2012).
[Crossref]

Schlomka, J.-P.

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Sochi, T.

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

Sun, B.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Tornai, M. P.

van Stevendaal, U.

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Veigele, W. J.

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Zhang, F.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Zhong, Y.

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Adv. Opt. Photon. (1)

Analyst (2)

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive colour x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807 (2009).
[Crossref] [PubMed]

J. A. Greenberg, M. Hassan, K. Krishnamurthy, and D. Brady, “Structured illumination for tomographic x-ray diffraction imaging,” Analyst 139, 709–713 (2014).
[Crossref]

Appl. Opt. (4)

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G. Harding, “X-ray diffraction imaging, a multi-generational perspective,” Applied Radiation and Isotopes 67, 287–295 (2009).
[Crossref]

J. Med. Imag. (1)

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imag. 3, 013505 (2016).
[Crossref]

Journal of Physical and Chemical Reference Data (1)

J. H. Hubbell, W. J. Veigele, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, “Atomic form factors, incoherent scattering functions, and photon scattering cross sections,” Journal of Physical and Chemical Reference Data 4471 (1975).
[Crossref]

Med. Phys. (1)

G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

Medical Imaging, IEEE Transactions on (1)

H. Erdogan and J. Fessler, “Monotonic algorithms for transmission tomography,” Medical Imaging, IEEE Transactions on 18, 801–814 (1999).
[Crossref]

Microchem. J. (1)

B. Sun, M. Li, F. Zhang, Y. Zhong, N. Kang, W. Lu, and J. Liu, “The performance of a fast testing system for illicit materials detection based on energy-dispersive x-ray diffraction technique,” Microchem. J. 95, 293–297 (2010).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Med. Biol. (2)

B. King, K. Landheer, and P. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol. 56, 4377 (2011).
[Crossref] [PubMed]

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
[Crossref]

Proc. SPIE (3)

J. A. Greenberg and D. J. Brady, “Snapshot full-volume coded aperture x-ray diffraction tomography,” Proc. SPIE 9847, 984706 (2016).
[Crossref]

I. Odinaka, J. A. Greenberg, Y. Kaganovsky, A. Holmgren, M. Hassan, D. G. Politte, J. A. O’Sullivan, L. Carin, and D. J. Brady, “Coded aperture x-ray diffraction imaging with transmission computed tomography side-information,” Proc. SPIE 9783, 978323 (2016).
[Crossref]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).
[Crossref]

Other (3)

A. D. Holmgren, M. N. Lakshmanan, A. J. Kapadia, J. A. Greenberg, and D. J. Brady, “Background scatter reduction for structured illumination x-ray systems,” submitted to Nuclear Inst. and Methods in Physics Research, B (2015).

I. Odinaka, Y. Kaganovsky, J. Greenberg, M. Hassan, D. Politte, J. O’Sullivan, D. Carin, and L. Brady, “Spectrally grouped edge-preserving reconstruction for scatter imaging using admm,” Accepted to the Proceedings of the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (2015).

J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging pp. 256–265 (2003).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: AVI (1329 KB)      3D visualization of Fig. 6 (movie)

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Figures (7)

Fig. 1
Fig. 1

Schematic of the fan beam CACSSI setup showing the placement of the source, collimator, object, coded aperture and detector pixels, as well as indicating several key lengths. For our experimental setup, we use zm = 925.35 mm, zd = 1137 mm, xd = 248 mm, and yd = 120 mm.

Fig. 2
Fig. 2

(a) Schematic of the uncertainties in object location determined by the coded aperture and imperfect knowledge of the ray (blue line) connecting the source (blue star) and object (red circle). (b) and (c) show the experimental (black dots) and theoretical (red line, using Eq. (14) values of the total scatter intensity for a point object along a line of fixed z and y, respectively.

Fig. 3
Fig. 3

Photo of the coded aperture used in the experiment. The MURA pattern that is repeated is 01001 (where 0 and 1 represent complete and no attenuation, respectively).

Fig. 4
Fig. 4

(a) Raw scatter data (in energy-position space) for a 4 × 2 mm sheet of HDPE placed at zo=583 mm and yo=12 mm. (b) The associated estimated scatter intensity through the object space (note that the axes are scaled to aid visual inspection). (c) The estimated coherent scatter form factor (frec, red line) at the true object location and the reference form factor (fref, blue line) obtained via a non-imaging X-ray diffractometer.

Fig. 5
Fig. 5

(a) Scatter intensity for two small pieces of HDPE separated by sy = 10 mm. (b) Cross section of the scatter intensity at fixed z location (associated with the red dashed line in (a). Here P and V indicated the maximum and minimum intra-object scatter intensities, respectively, which are used for determining the c(sy,z). (c) and (d) show experimental (black dots) and theoretical (blue solid line given by Eq. (16)) values for the contrast as a function of y and z, respectively. The point at which the contrast becomes non-zero corresponds to the spatial resolution of the system.

Fig. 6
Fig. 6

(a) Schematic of the phantom consisting of the letter ‘D’ (white, composed of HDPE) and ‘U’ (red, composed of teflon). Each snapshot measures the material distribution along the yz plane (as illustrated by the dashed rectangle) and the object is translated along the x direction to image the full object. (b) 3-dimensional pseudorendered classification map of the phantom obtained via experiment (see Visualization 1 for additional perspectives).

Fig. 7
Fig. 7

(a1) and (b1) Classification maps for the letters ‘D’ (HDPE, white) and ‘U’ (teflon, red), respectively, where color represents the material. Here black indicates a voxel in which either no material present or the form factor has no significant correlation with a member of the library (using a minimum correlation threshold of 0.85), and the blue dashed line indicates the true location and shape of each letter. (a2) and (b2) Representative estimated (red line) and ground truth (blue line) scatter form factors for HDPE and teflon, respectively.

Equations (16)

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q = 1 2 d = E h c sin ( θ 2 ) ,
d σ ( E ) d Ω = d σ coh ( E ) d Ω + d σ inc ( E ) d Ω
= d σ 0 d Ω [ f ( q ) + f K N ( E , θ ) f inc ( q ) ] ,
g coh ( E , r d ) = d r o d q Φ ( E ) d σ coh ( E ) d Ω Δ Ω T ( E , r o , r d ) t ( r d , r o , r m ) δ ( E h c q sin ( θ / 2 ) )
g inc ( E , r d ) = d r o d q Φ ( E ) d σ inc ( E ) d Ω Δ Ω T ( E , r o , r d ) t ( r d , r o , r m ) .
r ( r d , r o , r m ) = t m [ x o ( 1 α ) + α x d , y o ( 1 α ) + α y d ] ,
t m ( x , y ) = n = 1 i = 1 5 A i Π ( y in ) ,
d σ inc ( E ) d Ω σ inc ( E ) 4 π ,
g = Hf .
Δ z m = ( z d z o ) 2 u ( z d z m ) L ,
Δ y m = v ( z d z o ) ( z d z m ) ,
Δ y ( z o + Δ z m / 2 ) tan ( θ o + Δ θ o / 2 ) ( z o Δ z m / 2 ) tan ( θ o Δ θ o / 2 ) ,
Δ q q = ( Δ E E ) 2 + ( Δ θ θ ) 2 ,
f est ( y ) = N y ( 0 , σ y ) * Π ( y y c w y ) = π 2 σ y [ erf ( 2 y c + w y + 2 y 2 2 σ y ) + erf ( 2 y c + w y 2 y 2 2 σ ) ] ,
f est ( 2 ) ( y ) = f est ( y ) | y c s y / 2 + f est ( y ) | y c s y / 2 .
c ( s y ) = P V P = f est ( 2 ) ( s y / 2 ) f est ( 2 ) ( 0 ) f est ( 2 ) ( s / 2 ) ,

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