Abstract

X-ray diffraction tomography (XDT) probes the spatially variant x-ray diffraction (XRD) profile within volumetric objects. Here, we demonstrate a tabletop XDT setup with coded cone-beam illumination that accelerates the acquisition process of three-dimensional (3D) objects. Compared to the attenuation-based x-ray computed tomography (CT), XDT images display high contrast and specificity among materials with similar absorption coefficients. However, due to the weak signal level of diffraction and the low efficiency in source utilization and detection, conventional XDT systems require high-brilliance synchrotron sources to manage the acquisition time. In this paper, we propose a coded-illumination XDT system that utilizes the cone-beam from a tabletop x-ray tube and eliminates the detector-side collimation. The multiplexed measurement promotes parallelization in the data acquisition and enables simple implementation of compressive measurements, addressing the need of tabletop XDT systems in industrial nondestructive testing and medical imaging applications. We have demonstrated 1 order of magnitude reduction in XDT acquisition time, making high-contrast 3D x-ray imaging accessible to various research and application areas.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Pencil beam coded aperture x-ray scatter imaging

Kenneth MacCabe, Kalyani Krishnamurthy, Amarpreet Chawla, Daniel Marks, Ehsan Samei, and David Brady
Opt. Express 20(15) 16310-16320 (2012)

Complementary coded apertures for 4-dimensional x-ray coherent scatter imaging

Shuo Pang, Mehadi Hassan, Joel Greenberg, Andrew Holmgren, Kalyani Krishnamurthy, and David Brady
Opt. Express 22(19) 22925-22936 (2014)

Snapshot fan beam coded aperture coherent scatter tomography

Mehadi Hassan, Joel A. Greenberg, Ikenna Odinaka, and David J. Brady
Opt. Express 24(16) 18277-18289 (2016)

References

  • View by:
  • |
  • |
  • |

  1. J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
    [Crossref]
  2. W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
    [Crossref]
  3. P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
    [Crossref]
  4. F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
    [Crossref]
  5. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
    [Crossref]
  6. I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
    [Crossref]
  7. P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
    [Crossref]
  8. S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
    [Crossref]
  9. Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
    [Crossref]
  10. U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
    [Crossref]
  11. H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
    [Crossref]
  12. G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem. 71, 869–881 (2004).
    [Crossref]
  13. C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
    [Crossref]
  14. C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
    [Crossref]
  15. P. Evans, K. Rogers, A. Dicken, S. Godber, and D. Prokopiou, “X-ray diffraction tomography employing an annular beam,” Opt. Express 22, 11930–11944 (2014).
    [Crossref]
  16. A. J. Dicken, J. P. O. Evans, K. D. Rogers, D. Prokopiou, S. X. Godber, and M. Wilson, “Depth resolved snapshot energy-dispersive X-ray diffraction using a conical shell beam,” Opt. Express 25, 21321–21328 (2017).
    [Crossref]
  17. 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]
  18. 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]
  19. G. Harding, J. Kosanetzky, and U. Neitzel, “X-ray-diffraction computed-tomography,” Med. Phys. 14, 515–525 (1987).
    [Crossref]
  20. M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
    [Crossref]
  21. G. N. Hounsfield, “Computerized transverse axial scanning (tomography): Part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
    [Crossref]
  22. A. C. Miracle and S. K. Mukherji, “Conebeam CT of the head and neck, Part 1: physical principles,” Am. J. Neuroradiol. 30, 1088–1095 (2009).
    [Crossref]
  23. A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
    [Crossref]
  24. 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, 256–265 (2003).
    [Crossref]
  25. G. Harding, “X-ray diffraction imaging—a multi-generational perspective,” Appl. Radiat. Isot. 67, 287–295 (2009).
    [Crossref]
  26. K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
    [Crossref]
  27. S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
    [Crossref]
  28. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).
  29. G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
    [Crossref]
  30. U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
    [Crossref]
  31. N. Ratner and Y. Y. Schechner, “Illumination multiplexing within fundamental limits,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
  32. 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]

2018 (1)

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

2017 (1)

2016 (1)

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
[Crossref]

2015 (2)

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

2014 (2)

2013 (2)

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]

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

2012 (2)

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[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]

2011 (1)

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

2009 (4)

I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[Crossref]

A. C. Miracle and S. K. Mukherji, “Conebeam CT of the head and neck, Part 1: physical principles,” Am. J. Neuroradiol. 30, 1088–1095 (2009).
[Crossref]

G. Harding, “X-ray diffraction imaging—a multi-generational perspective,” Appl. Radiat. Isot. 67, 287–295 (2009).
[Crossref]

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

2008 (1)

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

2007 (1)

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

2006 (2)

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

2004 (1)

G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem. 71, 869–881 (2004).
[Crossref]

2003 (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, 256–265 (2003).
[Crossref]

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[Crossref]

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

2002 (1)

A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
[Crossref]

1998 (1)

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

1994 (1)

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

1987 (1)

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

1985 (1)

G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref]

1973 (1)

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): Part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[Crossref]

Almendarez-Camarillo, A.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Altamura, D.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Baruchel, J.

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

Baruffaldi, F.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Batenburg, K. J.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Bech, M.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Beraudi, A.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Bleuet, P.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Bomsdorf, H.

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Brady, D.

Brady, D. J.

Budai, J. D.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Bunk, O.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Chawla, A.

Choi, K.

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

Chung, J.-S.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Cong, W.

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
[Crossref]

Dicken, A.

Dicken, A. J.

Dooryhée, E.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Evans, J. P. O.

Evans, P.

Gehrke, R.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Georgiadis, M.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Giannini, C.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Godber, S.

Godber, S. X.

Grass, M.

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[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, 256–265 (2003).
[Crossref]

Greenberg, J.

Greenberg, J. A.

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

Guilhem, Y.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Guizar-Sicairos, M.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Hämäläinen, K.

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Harder, R.

I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[Crossref]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[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, 256–265 (2003).
[Crossref]

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[Crossref]

A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
[Crossref]

Harding, G.

G. Harding, “X-ray diffraction imaging—a multi-generational perspective,” Appl. Radiat. Isot. 67, 287–295 (2009).
[Crossref]

G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem. 71, 869–881 (2004).
[Crossref]

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

G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref]

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, 256–265 (2003).
[Crossref]

A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
[Crossref]

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Harwit, M.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Hassan, M.

Hodeau, J.-L.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Holmgren, A.

Holmgren, A. D.

Hounsfield, G. N.

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): Part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[Crossref]

Huotari, S.

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Ice, G. E.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Jud, C.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Kanzenbach, J.

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Kapadia, A. J.

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

Katsevich, A.

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

King, A.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Kleuker, U.

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

Kohlbrecher, J.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Kosanetzky, J.

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

G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref]

Krishnamurthy, K.

Kuhlmann, M.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Ladisa, M.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Larson, B. C.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Lauridsen, E. M.

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

Lengeler, B.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Liebi, M.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Linde, R.

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Ludwig, W.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

MacCabe, K.

MacCabe, K. P.

Marks, D.

Martens, G.

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Menzel, A.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Miracle, A. C.

A. C. Miracle and S. K. Mukherji, “Conebeam CT of the head and neck, Part 1: physical principles,” Am. J. Neuroradiol. 30, 1088–1095 (2009).
[Crossref]

Monaco, G.

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Mukherji, S. K.

A. C. Miracle and S. K. Mukherji, “Conebeam CT of the head and neck, Part 1: physical principles,” Am. J. Neuroradiol. 30, 1088–1095 (2009).
[Crossref]

Neitzel, U.

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

Nervo, L.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Norton, D. P.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Palenstijn, W. J.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Pang, S.

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (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]

Park, C.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Pfeifer, M. A.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Pfeiffer, F.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Poulsen, H. F.

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

Preuss, M.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Prokopiou, D.

Pylkkänen, T.

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Ratner, N.

N. Ratner and Y. Y. Schechner, “Illumination multiplexing within fundamental limits,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Reischig, P.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Robinson, I.

I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[Crossref]

Robinson, I. K.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Rogers, K.

Rogers, K. D.

Roth, S. V.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Samei, E.

Schaff, F.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Schechner, Y. Y.

N. Ratner and Y. Y. Schechner, “Illumination multiplexing within fundamental limits,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Schlomka, J. P.

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[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, 256–265 (2003).
[Crossref]

A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
[Crossref]

Schmidt, S.

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

Schneider, P.

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Schroer, C. G.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Siliqi, D.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Sloane, N. J. A.

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Spanne, P.

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

Stea, S.

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Strecker, H.

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Stribeck, N.

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Suortti, P.

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

Susini, J.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Tamura, N.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Tischler, J. Z.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Tornai, M. P.

van Stevendaal, U.

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[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, 256–265 (2003).
[Crossref]

Vartanyants, I. A.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Verbeni, R.

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Viganó, N.

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Walter, P.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Wang, G.

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
[Crossref]

Welcomme, E.

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

Weyrich, W.

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

Williams, G. J.

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

Wilson, M.

Yang, W.

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

Zaslansky, P.

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

Zhu, Z.

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
[Crossref]

Am. J. Neuroradiol. (1)

A. C. Miracle and S. K. Mukherji, “Conebeam CT of the head and neck, Part 1: physical principles,” Am. J. Neuroradiol. 30, 1088–1095 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. G. Schroer, M. Kuhlmann, S. V. Roth, R. Gehrke, N. Stribeck, A. Almendarez-Camarillo, and B. Lengeler, “Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering,” Appl. Phys. Lett. 88, 164102 (2006).
[Crossref]

Appl. Radiat. Isot. (1)

G. Harding, “X-ray diffraction imaging—a multi-generational perspective,” Appl. Radiat. Isot. 67, 287–295 (2009).
[Crossref]

Br. J. Radiol. (1)

G. N. Hounsfield, “Computerized transverse axial scanning (tomography): Part I. Description of system,” Br. J. Radiol. 46, 1016–1022 (1973).
[Crossref]

J. Appl. Crystallogr. (2)

W. Ludwig, E. M. Lauridsen, S. Schmidt, H. F. Poulsen, and J. Baruchel, “High-resolution three-dimensional mapping of individual grains in polycrystals by topotomography,” J. Appl. Crystallogr. 40, 905–911 (2007).
[Crossref]

P. Reischig, A. King, L. Nervo, N. Viganó, Y. Guilhem, W. J. Palenstijn, K. J. Batenburg, M. Preuss, and W. Ludwig, “Advances in X-ray diffraction contrast tomography: flexibility in the setup geometry and application to multiphase materials,” J. Appl. Crystallogr. 46, 297–311 (2013).
[Crossref]

Med. Phys. (2)

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

U. van Stevendaal, J. P. Schlomka, A. Harding, and M. Grass, “A reconstruction algorithm for coherent scatter computed tomography based on filtered back-projection,” Med. Phys. 30, 2465–2474 (2003).
[Crossref]

Nat. Mater. (4)

J. D. Budai, W. Yang, N. Tamura, J.-S. Chung, J. Z. Tischler, B. C. Larson, G. E. Ice, C. Park, and D. P. Norton, “X-ray microdiffraction study of growth modes and crystallographic tilts in oxide films on metal substrates,” Nat. Mater. 2, 487–492 (2003).
[Crossref]

I. Robinson and R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[Crossref]

P. Bleuet, E. Welcomme, E. Dooryhée, J. Susini, J.-L. Hodeau, and P. Walter, “Probing the structure of heterogeneous diluted materials by diffraction tomography,” Nat. Mater. 7, 468–472 (2008).
[Crossref]

S. Huotari, T. Pylkkänen, R. Verbeni, G. Monaco, and K. Hämäläinen, “Direct tomography with chemical-bond contrast,” Nat. Mater. 10, 489–493 (2011).
[Crossref]

Nature (3)

F. Schaff, M. Bech, P. Zaslansky, C. Jud, M. Liebi, M. Guizar-Sicairos, and F. Pfeiffer, “Six-dimensional real and reciprocal space small-angle X-ray scattering tomography,” Nature 527, 353–356 (2015).
[Crossref]

M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[Crossref]

M. Liebi, M. Georgiadis, A. Menzel, P. Schneider, J. Kohlbrecher, O. Bunk, and M. Guizar-Sicairos, “Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography,” Nature 527, 349–352 (2015).
[Crossref]

Opt. Express (4)

Phys. Med. Biol. (3)

U. Kleuker, P. Suortti, W. Weyrich, and P. Spanne, “Feasibility study of x-ray diffraction computed tomography for medical imaging,” Phys. Med. Biol. 43, 2911–2923 (1998).
[Crossref]

G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
[Crossref]

S. Pang, Z. Zhu, G. Wang, and W. Cong, “Small-angle scatter tomography with a photon-counting detector array,” Phys. Med. Biol. 61, 3734–3748 (2016).
[Crossref]

Proc. SPIE (4)

K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[Crossref]

A. Harding, J.-P. Schlomka, and G. L. Harding, “Simulations and experimental feasibility study of fan-beam coherent-scatter CT,” Proc. SPIE 4786, 202–209 (2002).
[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, 256–265 (2003).
[Crossref]

H. Strecker, G. L. Harding, H. Bomsdorf, J. Kanzenbach, R. Linde, and G. Martens, “Detection of explosives in airport baggage using coherent x-ray scatter,” Proc. SPIE 2092, 399–410 (1994).
[Crossref]

Radiat. Phys. Chem. (1)

G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem. 71, 869–881 (2004).
[Crossref]

Sci. Rep. (2)

C. Giannini, D. Siliqi, O. Bunk, A. Beraudi, M. Ladisa, D. Altamura, S. Stea, and F. Baruffaldi, “Correlative light and scanning X-ray scattering microscopy of healthy and pathologic human bone sections,” Sci. Rep. 2, 435 (2012).
[Crossref]

Z. Zhu, A. Katsevich, A. J. Kapadia, J. A. Greenberg, and S. Pang, “X-ray diffraction tomography with limited projection information,” Sci. Rep. 8, 522 (2018).
[Crossref]

Other (2)

M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

N. Ratner and Y. Y. Schechner, “Illumination multiplexing within fundamental limits,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Supplementary Material (2)

NameDescription
» Supplement 1       Supplemental document
» Visualization 1       3D rendering of X-ray diffraction tomography reconstruction of the sample under different momentum transfer values.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1. Comparison between CT and XDT systems. (a) Fan-beam CT; (b) cone-beam CT, which opens up fan-beam to cone-beam illumination and uses a panel detector to capture 2D radiographies; (c) fan-beam XDT (or CSCT). Detector-side collimators are required to localize the scattering volume. (d) Opening up fan-beam to cone-beam cannot further parallelize the XDT measurement, because the scattering signal from different layers will overlap on the detector. (e) Our proposed cone-beam setup with illumination coding allows volumetric imaging with high collection efficiency. The scattering signal from each beam can be retrieved by changing the illumination pattern.
Fig. 2.
Fig. 2. Pencil-beam and multiplexed XDT geometry. (a) Pencil-beam XDT. The red dot above each scattering pattern indicates which pinhole along the row (y direction) and column (s direction) generates this diffraction image. (b) XDT with illumination coding. The illumination pattern is changed by shifting the mask vertically. The individual scattering pattern generated by each pencil beam can be retrieved from these measurements.
Fig. 3.
Fig. 3. Binary Hadamard mask designed (a1) and manufactured (a2) according to S35. Designed (a3) and manufactured (a4) Hadamard mask for compression according to S35. (b1)–(b4) System matrix corresponding to each mask. The red, dashed rectangle marks the size of the shaped beam on the mask.
Fig. 4.
Fig. 4. CT and XDT reconstruction of the sample. (a) CT image of the layer marked by the red, dashed line in (c). (b) XDT reconstruction at q=0.06, 0.09, and 0.12 Å, respectively. (c) 3D rendering of the attenuation map of the sample. (d) 3D rendering of XDT reconstruction on all sample layers at q=0.06, 0.09, and 0.12 Å (Visualization 1). All scale bars represent 5 mm.
Fig. 5.
Fig. 5. Material identification based on the XDT reconstruction. (a) Reconstructed form factor of the acrylic and nylon from two representative pixels marked in (b) compared with references. (b) Material map of the layer marked by the white, dashed line in (c). Acrylic and nylon are rendered in red and green, respectively. (c) 3D rendering of the material map from different perspectives. All scale bars represent 5 mm.
Fig. 6.
Fig. 6. Reconstruction comparison of the Hadamard multiplexing scheme, Hadamard multiplexing with compression scheme, and pencil-beam XDT (layer located at 5.6 mm from the sample top). (a) Reconstruction from Hadamard mask with compressive tomography at q=0.06, 0.09, and 0.12  Å1, respectively. The scale bar represents 5 mm. (b) Reconstruction from the full projection data measured using a normal Hadamard mask at the same q values; (c) reconstruction from the pencil-beam XDT scan; (d), (e) comparison between the reconstructed form factors with the reference profile for the pixels marked by red (acrylic region) and green (nylon region), respectively.

Equations (3)

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

dI=I0re22(1+cos2θ)f(r,q)dΩdVdq,
q=Ehcsin(θ2)=Ehcw2(Lt),
Gi(xd,yd)=jSijIj(xd,yd),

Metrics