Abstract

We demonstrate a technique for measuring the range-resolved coherent scatter form factors of different objects from a single snapshot. By illuminating the object with an x-ray pencil beam and placing a coded aperture in front of a linear array of energy-sensitive detector elements, we record the coherently scattered x-rays. This approach yields lateral, range, and momentum transfer resolutions of 1 mm, 5 mm, and 0.2 nm−1, respectively, which is sufficient for the distinguishing a variety of solids and liquids. These results indicate a path toward real-time volumetric molecular imaging for non-destructive examination in a variety of applications, including medical diagnostics, quality inspection, and security detection.

© 2013 OSA

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  1. 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). URL + http://dx.doi.org/10.1117/12.479949 .
    [CrossRef]
  2. G. Harding and B. Schreiber, “Coherent X-ray scatter imaging and its applications in biomedical science and industry,” Radiation Phys. Chem.56(12), 229–245 (1999). URL http://www.sciencedirect.com/science/article/pii/S0969806X99002832 .
    [CrossRef]
  3. 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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
    [CrossRef]
  4. D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
    [CrossRef]
  5. A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
    [CrossRef]
  6. J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).
  7. S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
    [CrossRef]
  8. H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
    [CrossRef] [PubMed]
  9. G. Harding and J. Kosanetzky, “Status and outlook of coherent-x-ray scatter imaging,” J. Opt. Soc. Am. A4(5), 933–944 (1987). URL http://josaa.osa.org/abstract.cfm?URI=josaa-4-5-933 .
    [CrossRef] [PubMed]
  10. B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
    [CrossRef] [PubMed]
  11. J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett.88(24), 243506–243508 (2006). URL http://link.aip.org/link/?APL/88/243506/1 .
    [CrossRef]
  12. G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
    [CrossRef]
  13. A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
    [CrossRef] [PubMed]
  14. K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express20(15), 16310–16320 (2012). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-20-15-16310 .
    [CrossRef]
  15. 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(19), 4582–4589 (2013). URL http://ao.osa.org/abstract.cfm?URI=ao-52-19-4582 .
    [CrossRef] [PubMed]
  16. R. D. Speller, J. A. Horrocks, and R. J. Lacey, “X-ray scattering signatures for material identification,” Proc. SPIE 2092, Substance Detection Systems pp. 366–377 (1994). URL + http://dx.doi.org/10.1117/12.171256 .
    [CrossRef]
  17. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena60(1), 259–268 (1992).
    [CrossRef]
  18. P. Getreuer, “Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman,” Image Processing On Line10(2012).
  19. S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
    [CrossRef]
  20. B. W. King and P. C. Johns, “Measurement of coherent scattering form factors using an image plate,” Phys. Med. Biol.54(20), 6437 (2009). URL http://stacks.iop.org/0031-9155/54/i=20/a=C01 .
    [CrossRef]
  21. J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
    [CrossRef]
  22. P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

2013

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (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(19), 4582–4589 (2013). URL http://ao.osa.org/abstract.cfm?URI=ao-52-19-4582 .
[CrossRef] [PubMed]

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

2012

2011

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
[CrossRef] [PubMed]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

2010

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

2009

B. W. King and P. C. Johns, “Measurement of coherent scattering form factors using an image plate,” Phys. Med. Biol.54(20), 6437 (2009). URL http://stacks.iop.org/0031-9155/54/i=20/a=C01 .
[CrossRef]

2006

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett.88(24), 243506–243508 (2006). URL http://link.aip.org/link/?APL/88/243506/1 .
[CrossRef]

2003

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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

1999

G. Harding and B. Schreiber, “Coherent X-ray scatter imaging and its applications in biomedical science and industry,” Radiation Phys. Chem.56(12), 229–245 (1999). URL http://www.sciencedirect.com/science/article/pii/S0969806X99002832 .
[CrossRef]

1994

R. D. Speller, J. A. Horrocks, and R. J. Lacey, “X-ray scattering signatures for material identification,” Proc. SPIE 2092, Substance Detection Systems pp. 366–377 (1994). URL + http://dx.doi.org/10.1117/12.171256 .
[CrossRef]

1992

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena60(1), 259–268 (1992).
[CrossRef]

1991

J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).

1990

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
[CrossRef]

1987

Bednarzik, M.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Bell, S.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Brady, D.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express20(15), 16310–16320 (2012). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-20-15-16310 .
[CrossRef]

Brady, D. J.

Brner, M.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Cernik, R. J.

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Chan, J. W.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

Chawla, A.

Chiu, W. K. S.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

Christodoulou, C.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Chu, Y. S.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

David, C.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Delfs, J.

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett.88(24), 243506–243508 (2006). URL http://link.aip.org/link/?APL/88/243506/1 .
[CrossRef]

Desai, H.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Dicken, A.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

Egan, C. K.

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Evans, P.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena60(1), 259–268 (1992).
[CrossRef]

Gaskin, J. A.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Getreuer, P.

P. Getreuer, “Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman,” Image Processing On Line10(2012).

Godber, S.

Gonsalves, R.

J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).

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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

Greenberg, J. A.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

Harding, G.

G. Harding and B. Schreiber, “Coherent X-ray scatter imaging and its applications in biomedical science and industry,” Radiation Phys. Chem.56(12), 229–245 (1999). URL http://www.sciencedirect.com/science/article/pii/S0969806X99002832 .
[CrossRef]

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
[CrossRef]

G. Harding and J. Kosanetzky, “Status and outlook of coherent-x-ray scatter imaging,” J. Opt. Soc. Am. A4(5), 933–944 (1987). URL http://josaa.osa.org/abstract.cfm?URI=josaa-4-5-933 .
[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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

Hills, D.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Hogan, J.

J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).

Holmgren, A. D.

Horrocks, J. A.

R. D. Speller, J. A. Horrocks, and R. J. Lacey, “X-ray scattering signatures for material identification,” Proc. SPIE 2092, Substance Detection Systems pp. 366–377 (1994). URL + http://dx.doi.org/10.1117/12.171256 .
[CrossRef]

Jacques, S.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Jacques, S. D. M.

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

Johns, P. C.

B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
[CrossRef] [PubMed]

B. W. King and P. C. Johns, “Measurement of coherent scattering form factors using an image plate,” Phys. Med. Biol.54(20), 6437 (2009). URL http://stacks.iop.org/0031-9155/54/i=20/a=C01 .
[CrossRef]

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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

Kapadia, A.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

Kim, J.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

King, B. W.

B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
[CrossRef] [PubMed]

B. W. King and P. C. Johns, “Measurement of coherent scattering form factors using an image plate,” Phys. Med. Biol.54(20), 6437 (2009). URL http://stacks.iop.org/0031-9155/54/i=20/a=C01 .
[CrossRef]

Kosanetzky, J.

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
[CrossRef]

G. Harding and J. Kosanetzky, “Status and outlook of coherent-x-ray scatter imaging,” J. Opt. Soc. Am. A4(5), 933–944 (1987). URL http://josaa.osa.org/abstract.cfm?URI=josaa-4-5-933 .
[CrossRef] [PubMed]

Krieger, A.

J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).

Krishnamurthy, K.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express20(15), 16310–16320 (2012). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-20-15-16310 .
[CrossRef]

Lacey, R. J.

R. D. Speller, J. A. Horrocks, and R. J. Lacey, “X-ray scattering signatures for material identification,” Proc. SPIE 2092, Substance Detection Systems pp. 366–377 (1994). URL + http://dx.doi.org/10.1117/12.171256 .
[CrossRef]

Lakshmanan, M.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

Landheer, K. A.

B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
[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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

Lombardo, J. J.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

MacCabe, K.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express20(15), 16310–16320 (2012). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-20-15-16310 .
[CrossRef]

MacCabe, K. P.

Marks, D.

Maser, J.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

Mohr, J.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Nazaretski, E.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

Newton, M.

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
[CrossRef]

O’Flynn, D.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena60(1), 259–268 (1992).
[CrossRef]

Pani, S.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Ramsey, B. D.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Reid, C.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Reid, C. B.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Rogers, J.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

Rogers, K.

A. Dicken, K. Rogers, P. Evans, J. W. Chan, J. Rogers, and S. Godber, “Combined X-ray diffraction and kinetic depth effect imaging,” Opt. Express19(7), 6406–6413 (2011). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-19-7-6406 .
[CrossRef] [PubMed]

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena60(1), 259–268 (1992).
[CrossRef]

Rutishauser, S.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Samei, E.

Schlomka, J.-P.

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett.88(24), 243506–243508 (2006). URL http://link.aip.org/link/?APL/88/243506/1 .
[CrossRef]

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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

Schreiber, B.

G. Harding and B. Schreiber, “Coherent X-ray scatter imaging and its applications in biomedical science and industry,” Radiation Phys. Chem.56(12), 229–245 (1999). URL http://www.sciencedirect.com/science/article/pii/S0969806X99002832 .
[CrossRef]

Scuffham, J. W.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Seller, P.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Sellin, P. J.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Speller, R.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Speller, R. D.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

R. D. Speller, J. A. Horrocks, and R. J. Lacey, “X-ray scattering signatures for material identification,” Proc. SPIE 2092, Substance Detection Systems pp. 366–377 (1994). URL + http://dx.doi.org/10.1117/12.171256 .
[CrossRef]

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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[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). URL + http://dx.doi.org/10.1117/12.479949 .
[CrossRef]

Veale, M. C.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Weitkamp, T.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Wilson, M. D.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

Wolter, S.

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
[CrossRef]

Wong, B.

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

Yan, H.

H. Yan, Y. S. Chu, J. Maser, E. Nazaretski, J. Kim, J. J. Lombardo, and W. K. S. Chiu, “Quantitative x-ray phase imaging at the nanoscale by multilayer Laue lenses,” Sci. Rep.3, 1307 (2013).
[CrossRef] [PubMed]

Zanette, I.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

Analyst

S. D. M. Jacques, C. K. Egan, M. D. Wilson, M. C. Veale, P. Seller, and R. J. Cernik, “A laboratory system for element specific hyperspectral X-ray imaging,” Analyst138, 755–759 (2013). URL http://dx.doi.org/10.1039/C2AN36157D .
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett.88(24), 243506–243508 (2006). URL http://link.aip.org/link/?APL/88/243506/1 .
[CrossRef]

Appl. Radia. Isotopes

A. Dicken, K. Rogers, P. Evans, J. Rogers, and J. W. Chan, “The separation of X-ray diffraction patterns for threat detection,” Appl. Radia. Isotopes68(3), 439–443 (2010). URL http://www.sciencedirect.com/science/article/pii/S0969804309007611 .
[CrossRef]

IEEE Trans. Nuclear Sci.

J. Hogan, R. Gonsalves, and A. Krieger, “Fluorescent computer tomography: a model for correction of X-ray absorption,” IEEE Trans. Nuclear Sci.38(6), 1721–1727 (1991).

Image Processing On Line

P. Getreuer, “Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman,” Image Processing On Line10(2012).

J. Instrumen.

P. Seller, S. Bell, R. J. Cernik, C. Christodoulou, C. K. Egan, J. A. Gaskin, S. Jacques, S. Pani, B. D. Ramsey, C. Reid, P. J. Sellin, J. W. Scuffham, R. D. Speller, M. D. Wilson, and M. C. Veale, “Pixellated Cd(Zn)Te high-energy X-ray instrument,” J. Instrumen.6(12), C12,009 (2011). URL http://stacks.iop.org/1748-0221/6/i=12/a=C12009 .

D. O’Flynn, C. B. Reid, C. Christodoulou, M. D. Wilson, M. C. Veale, P. Seller, D. Hills, H. Desai, B. Wong, and R. Speller, “Explosive detection using pixellated X-ray diffraction (PixD),” J. Instrumen.8(03), P03007 (2013). URL http://stacks.iop.org/1748-0221/8/i=03/a=P03007 .
[CrossRef]

J. Opt. Soc. Am. A

Microchem. 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(2), 293–297 (2010). URL http://www.sciencedirect.com/science/article/pii/S0026265X10000056 .
[CrossRef]

Microelectron. Eng.

S. Rutishauser, M. Bednarzik, I. Zanette, T. Weitkamp, M. Brner, J. Mohr, and C. David, “Fabrication of two-dimensional hard X-ray diffraction gratings,” Microelectron. Eng.101(0), 12–16 (2013). URL http://www.sciencedirect.com/science/article/pii/S0167931712004935 .
[CrossRef]

Opt. Express

Phys. Med. Biol.

B. W. King, K. A. Landheer, and P. C. Johns, “X-ray coherent scattering form factors of tissues, water and plastics using energy dispersion,” Phys. Med. Biol.56(14), 4377 (2011). URL http://stacks.iop.org/0031-9155/56/i=14/a=010 .
[CrossRef] [PubMed]

G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive X-ray diffraction tomography,” Phys. Med. Biol.35(1), 33 (1990). URL http://stacks.iop.org/0031-9155/35/i=1/a=004 .
[CrossRef]

B. W. King and P. C. Johns, “Measurement of coherent scattering form factors using an image plate,” Phys. Med. Biol.54(20), 6437 (2009). URL http://stacks.iop.org/0031-9155/54/i=20/a=C01 .
[CrossRef]

Physica D: Nonlinear Phenomena

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Proc. SPIE

J. A. Greenberg, K. Krishnamurthy, M. Lakshmanan, K. MacCabe, S. Wolter, A. Kapadia, and D. Brady, “Coding and sampling for compressive x-ray diffraction tomography,” Proc. SPIE8858, 885813 (2013). URL http://dx.doi.org/10.1117/12.2027128 .
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Figures (6)

Fig. 1
Fig. 1

(a) Schematic and (b) photograph of the CACSSI setup, including the x-ray source, collimators, coded aperture, object space, and detector. (c) X-ray transmission image of the coded aperture.

Fig. 2
Fig. 2

Expected (a) momentum transfer and (b) spatial resolution as a function of q for different values of z (as determined by Eqs. (6) and (7) for u = 1/2 mm−1, ΔE=4 keV, [Emin, Emax]=[20, 125] keV, δx=1 mm and zm=135 mm.

Fig. 3
Fig. 3

(a) Raw scatter data and (b) the full 2-dimensional reconstruction of the object in q–z space for a 10 mm thick sheet of HDPE placed at z=252 mm. (c) Correlation r as a function of position. (d) Form factors obtained via XRD (blue corresponds to fine q sampling and green corresponds to interpolation at the estimated object’s q sampling) and CACSSI (red). The data was acquired using 500 mAs.

Fig. 4
Fig. 4

Momentum transfer spectra for a 10 mm diameter vial containing (a) a mixture of MeOH and H2O at various concentrations and (b) H2O and H2O2 (measured one at a time). The data was acquired using 500 mAs for the vial placed at z = 267 mm.

Fig. 5
Fig. 5

Object reconstruction results for a 10 mm diameter vial of graphite and Al powder placed at z=242 and z=267 mm, respectively. (a) Correlation along the range dimension and thresholded at 0.75 (red and blue correspond to Al and graphite, respectively). Form factors of (b) graphite and (c) Al obtained via XRD (blue corresponds to fine q sampling and green corresponds to interpolation at the estimated object’s q sampling) and CACSSI (red). The data was acquired using 500 mAs.

Fig. 6
Fig. 6

Form factors for a 10 mm diameter vial of (a) H2O at z=226 mm, (b) Teflon at z=242 mm and (c) Al powder at z=267 mm obtained XRD (blue corresponds to fine q sampling and green corresponds to interpolation at the estimated object’s q sampling) and CACSSI (red). The data was acquired using 500 mAs.

Equations (13)

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q 1 2 d = E h c sin ( θ / 2 ) ,
d σ coh ( E ) d Ω = r e 2 2 [ 1 + cos ( θ ) 2 ] f ( q ) .
y ( E , x ) = d q d z Φ ( E ) d σ coh ( E ) d Ω Δ Ω T ( E , x , z ) t [ x ( 1 z m z ) ] δ ( E 2 h c q z x ) .
h ( E , x ; q o , z o ) z o ( x 2 + z o 2 ) 3 / 2 T o ( E ) f o Φ ( E = 2 h c q o z o x ) t [ x ( 1 z m z o ) ] .
H i j d E d x h ( E , x ; q j , z j ) exp [ log ( 2 ) ( E E i Δ E ) 2 ] rect ( x x i Δ x ) ,
Δ z z = E max E min 2 h c q u z m ( E max E min )
Δ q 2 = [ ( Δ E E ) 2 + ( δ θ θ ) 2 ] 1 / 2 = [ ( Δ z z ) 2 + Δ E δ x c h q z ] 1 / 2
f ^ = argmin f ˜ ( log p ( y | H f ˜ + μ b ) + τ f ˜ TV )
log p ( y | H f ˜ + μ b ) = k [ ( j H k , j f ˜ j + μ b k ) + y k log ( j H k , j f ˜ j + μ b k ) log y k ! ]
μ ^ b = argmin μ ˜ b [ log p ( b | μ ˜ b ) + λ μ ˜ b TV ] ,
E-step : z ( p ) = f ^ ( p 1 ) × H T ( y H f ^ ( p 1 ) + μ ^ b ) H T 1 N × 1
M-step : f ^ ( p ) = argmin f ˜ [ log p ( z ( p ) | f ˜ ) + τ f ˜ TV ]
r ( z ) = f ^ ( , z ) , f ( , z ) f ^ ( , z ) , f ( , z )

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