Abstract

Small-angle x-ray scattering computed tomography (SAXS-CT) is a nondestructive method for the nanostructure analysis of heterogeneous materials. However, the limits of a long data acquisition time and vast amounts of data prevent SAXS-CT from becoming a routine experimental method in the applications of synchrotron radiation. In this study, the ordered subsets expectation maximization (OSEM) algorithm is introduced to improve the efficiency of SAXS-CT. To demonstrate the practicability of this method, a systematic simulation and experiments were carried out. The simulation results on a numerical phantom show that the OSEM-based SAXS-CT can effectively eliminate streaking artifacts and improve the efficiency of data acquisition by at least 3 times compared with the filter backprojection algorithm. By compromising the reconstruction speed and image quality, the optimal reconstruction parameters are also given for the image reconstruction in the OSEM-based SAXS-CT experiments. An experiment on a bamboo sample verified the validity of the proposed method with limited projection data. A further experiment on polyethylene demonstrated that the OSEM-based SAXS-CT is able to reveal the local nanoscale information about the crystalline structure and distributional difference inside the sample. In conclusion, the OSEM-based SAXS-CT can significantly improve experimental efficiency, which may promote SAXS-CT becoming a conventional method.

© 2017 Optical Society of America

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References

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  1. P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
    [Crossref]
  2. C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
    [Crossref]
  3. A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
    [Crossref]
  4. S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
    [Crossref]
  5. T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
    [Crossref]
  6. T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
    [Crossref]
  7. S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
    [Crossref]
  8. 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]
  9. E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray Sci. Technol. 14, 119–139 (2006).
  10. 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]
  11. H. M. Hudson and R. S. Larkin, “Accelerated image-reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
    [Crossref]
  12. H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 2835–2851 (1999).
    [Crossref]
  13. Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
    [Crossref]
  14. J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
    [Crossref]
  15. 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]
  16. R. L. Siddon, “Fast calculation of the exact radiological path for a three-dimensional CT array,” Med. Phys. 12, 252–255 (1985).
    [Crossref]
  17. S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
    [Crossref]
  18. Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
    [Crossref]
  19. G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
    [Crossref]
  20. Z. Ma, L. Balzano, and G. W. M. Peters, “Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution,” Macromolecules 49, 2724–2730 (2016).
    [Crossref]
  21. S. Rober, P. Bosecke, and H. G. Zachmann, “Small-angle x-ray-scattering pole figures of semicrystalline polymers obtained by synchrotron radiation,” Makromol. Chem. Macromol. Symp. 15, 295–310 (1988).
    [Crossref]

2016 (1)

Z. Ma, L. Balzano, and G. W. M. Peters, “Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution,” Macromolecules 49, 2724–2730 (2016).
[Crossref]

2015 (2)

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]

2014 (1)

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

2013 (1)

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

2012 (2)

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

2011 (3)

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

2009 (1)

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

2008 (1)

S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
[Crossref]

2007 (1)

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

2006 (2)

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]

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray Sci. Technol. 14, 119–139 (2006).

1999 (2)

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 2835–2851 (1999).
[Crossref]

1997 (1)

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

1994 (1)

H. M. Hudson and R. S. Larkin, “Accelerated image-reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref]

1988 (1)

S. Rober, P. Bosecke, and H. G. Zachmann, “Small-angle x-ray-scattering pole figures of semicrystalline polymers obtained by synchrotron radiation,” Makromol. Chem. Macromol. Symp. 15, 295–310 (1988).
[Crossref]

1985 (1)

R. L. Siddon, “Fast calculation of the exact radiological path for a three-dimensional CT array,” Med. Phys. 12, 252–255 (1985).
[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]

Almer, J. D.

S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
[Crossref]

Altamura, D.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Andersson, S.

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Balzano, L.

Z. Ma, L. Balzano, and G. W. M. Peters, “Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution,” Macromolecules 49, 2724–2730 (2016).
[Crossref]

Barre, S. F.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

Baruffaldi, F.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[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]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Beraudi, A.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Bosecke, P.

S. Rober, P. Bosecke, and H. G. Zachmann, “Small-angle x-ray-scattering pole figures of semicrystalline polymers obtained by synchrotron radiation,” Makromol. Chem. Macromol. Symp. 15, 295–310 (1988).
[Crossref]

Bouchet, A.

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Bubnova, R. S.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[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, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Burghammer, M.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Chen, R.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

De Carlo, F.

S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
[Crossref]

De Caro, L.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Deng, B.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Diaz, A.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Du, G.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Erdogan, H.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 2835–2851 (1999).
[Crossref]

Fei, B.

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Feidenhans’l, R.

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Feldkamp, J. M.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

Fessler, J. A.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 2835–2851 (1999).
[Crossref]

Filatov, S. K.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

Fischer, S.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Forster, S.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Fratzl, P.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

Gehrke, R.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[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]

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, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Gourrier, A.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[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]

Gupta, H. S.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Hudson, H. M.

H. M. Hudson and R. S. Larkin, “Accelerated image-reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref]

Jakob, H. F.

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

Jensen, T. H.

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[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]

Kao, C. M.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray Sci. Technol. 14, 119–139 (2006).

Klaushofer, K.

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[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]

Kuhlmann, M.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[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]

Ladisa, M.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Lammie, D.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Larkin, R. S.

H. M. Hudson and R. S. Larkin, “Accelerated image-reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref]

Le Duc, G.

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[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]

Leppänen, K.

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[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]

Lindner, P.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Lovric, G.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

Lv, W.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Ma, Z.

Z. Ma, L. Balzano, and G. W. M. Peters, “Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution,” Macromolecules 49, 2724–2730 (2016).
[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]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Mokso, R.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

Nader, A.

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

Pan, X. H.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray Sci. Technol. 14, 119–139 (2006).

Paris, O.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Paufler, P.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

Perlich, J.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Peters, G. W. M.

Z. Ma, L. Balzano, and G. W. M. Peters, “Dissolution and re-emergence of flow-induced shish in polyethylene with a broad molecular weight distribution,” Macromolecules 49, 2724–2730 (2016).
[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]

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Molecular X-ray computed tomography of myelin in a rat brain,” NeuroImage 57, 124–129 (2011).
[Crossref]

Ren, H.

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Riekel, C.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Rinnerthaler, S.

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

Rober, S.

S. Rober, P. Bosecke, and H. G. Zachmann, “Small-angle x-ray-scattering pole figures of semicrystalline polymers obtained by synchrotron radiation,” Makromol. Chem. Macromol. Symp. 15, 295–310 (1988).
[Crossref]

Roschger, P.

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

Roth, S. V.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[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]

Roth-Kleiner, M.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

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]

Schellbach, C.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Schittny, J. C.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[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.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[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]

Serimaa, R.

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Shakhverdova, I.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

Shen, F.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Sibillano, T.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Siddon, R. L.

R. L. Siddon, “Fast calculation of the exact radiological path for a three-dimensional CT array,” Med. Phys. 12, 252–255 (1985).
[Crossref]

Sidky, E. Y.

E. Y. Sidky, C. M. Kao, and X. H. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray Sci. Technol. 14, 119–139 (2006).

Siliqi, D.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Stampanoni, M.

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

Stea, S.

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

Stock, S. R.

S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
[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]

Sztucki, M.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Thomsen, M.

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. Le Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phy. Med. Biol. 56, 1717–1726 (2011).
[Crossref]

Timmann, A.

J. M. Feldkamp, M. Kuhlmann, S. V. Roth, A. Timmann, R. Gehrke, I. Shakhverdova, P. Paufler, S. K. Filatov, R. S. Bubnova, and C. G. Schroer, “Recent developments in tomographic small-angle X-ray scattering,” Phys. Status Solidi A 206, 1723–1726 (2009).
[Crossref]

Wagermaier, W.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Wang, Y.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Y. Wang, K. Leppänen, S. Andersson, R. Serimaa, H. Ren, and B. Fei, “Studies on the nanostructure of the cell wall of bamboo using X-ray scattering,” Wood Sci. Technol. 46, 317–332 (2012).
[Crossref]

Wess, T. J.

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

Xiao, T.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Xu, H.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Yan, F.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Yang, Q.

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
[Crossref]

Zachmann, H. G.

S. Rober, P. Bosecke, and H. G. Zachmann, “Small-angle x-ray-scattering pole figures of semicrystalline polymers obtained by synchrotron radiation,” Makromol. Chem. Macromol. Symp. 15, 295–310 (1988).
[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]

Zielske, K.

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

Adv. Colloid Interface Sci. (1)

S. Forster, S. Fischer, K. Zielske, C. Schellbach, M. Sztucki, P. Lindner, and J. Perlich, “Calculation of scattering-patterns of ordered nano- and mesoscale materials,” Adv. Colloid Interface Sci. 163, 53–83 (2011).
[Crossref]

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]

Calcif. Tissue Int. (1)

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle X-ray scattering analysis of human bone sections,” Calcif. Tissue Int. 64, 422–429 (1999).
[Crossref]

IEEE Trans. Med. Imaging (1)

H. M. Hudson and R. S. Larkin, “Accelerated image-reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref]

J. Appl. Crystallogr. (4)

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle X-ray scattering of complex biological materials,” J. Appl. Crystallogr. 30, 765–769 (1997).
[Crossref]

C. Giannini, D. Siliqi, M. Ladisa, D. Altamura, A. Diaz, A. Beraudi, T. Sibillano, L. De Caro, S. Stea, F. Baruffaldi, and O. Bunk, “Scanning SAXS-WAXS microscopy on osteoarthritis-affected bone–an age-related study,” J. Appl. Crystallogr. 47, 110–117 (2014).
[Crossref]

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning X-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr. 40, S78–S82 (2007).
[Crossref]

G. Lovric, S. F. Barre, J. C. Schittny, M. Roth-Kleiner, M. Stampanoni, and R. Mokso, “Dose optimization approach to fast X-ray microtomography of the lung alveoli,” J. Appl. Crystallogr. 46, 856–860 (2013).
[Crossref]

J. Struct. Biol. (1)

S. R. Stock, F. De Carlo, and J. D. Almer, “High energy X-ray scattering tomography applied to bone,” J. Struct. Biol. 161, 144–150 (2008).
[Crossref]

J. Synchrotron Radiat. (1)

Q. Yang, B. Deng, W. Lv, F. Shen, R. Chen, Y. Wang, G. Du, F. Yan, T. Xiao, and H. Xu, “Fast and accurate X-ray fluorescence computed tomography imaging with the ordered-subsets expectation maximization algorithm,” J. Synchrotron Radiat. 19, 210–215 (2012).
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J. X-ray Sci. Technol. (1)

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Figures (13)

Fig. 1.
Fig. 1.

(a) Side view of the schematic diagram of SAXS-CT. The scattering pattern from a pencil beam is recorded using a 2D detector; (b) scanning strategy for the data acquisition, where d represents the intersection length of the ray with the pixel; (c) data-processing procedure for SAXS-CT.

Fig. 2.
Fig. 2.

(a) Numerical phantom with 512  pixels×512  pixels; (b)–(d) calculated 1D scattering curves of model I, model II and model III.

Fig. 3.
Fig. 3.

Tomographic slices for a specific scattering vector (q=0.51  nm1) reconstructed using OSEM [(a)–(g)] and FBP [(h)–(n)].

Fig. 4.
Fig. 4.

NMSEs of the tomographic slices reconstructed using FBP and OSEM with different PAIs.

Fig. 5.
Fig. 5.

For two selected PAIs, the 1D scattering curves of three particle distribution models reconstructed using OSEM (upper row) and FBP (lower row). (a) Model I; (b) model II; (c) model III.

Fig. 6.
Fig. 6.

NMSE as a function of iteration number for different PAIs. (a) PAI, Δϕ=1°; (b) PAI, Δϕ=2°; (c) PAI, Δϕ=3°; (d) PAI, Δϕ=6°.

Fig. 7.
Fig. 7.

Rotational invariance verified for the bamboo sample. 1, stray light; 2: beamstop.

Fig. 8.
Fig. 8.

SAXS-CT results for the bamboo sample. (a) X-ray absorption micro-CT slice of the bamboo sample; (b) 2D SAXS pattern of the bamboo sample; (c) integral scattering tomographic slice reconstructed via OSEM using the azimuthal range of 80°<η<100° and the q-range of q[0.150.40]  nm1 [ROI I of (b)]; (d) image fusion of (c) and (a); (e) integral scattering tomographic slice reconstructed using OSEM in the azimuthal range of 10°<η<10° and the q-range of q[0.381.95]  nm1 [ROI II of (b)]; (f) image fusion of (e) and (a); (g) reconstructed 2D SAXS patterns for three locations in the bamboo sample, indicated by the red, blue, and yellow squares.

Fig. 9.
Fig. 9.

Integral scattering tomographic slices of the bamboo sample for ROI I and ROI II indicated in Fig. 8(b) reconstructed using OSEM (top) and FBP (bottom) with PAI of 6°(a) and 12°(b), respectively.

Fig. 10.
Fig. 10.

Rotational invariance verified for the hollow polyethylene rod. 1, area between detector modules; 2, stray light; 3, beamstop.

Fig. 11.
Fig. 11.

SAXS-CT results for polyethylene. (a) X-ray micro-CT absorption slice of the hollow polyethylene rod; (b) 2D SAXS pattern of the sample; (c) integral scattering tomographic slice reconstructed via OSEM using the azimuthal range of 10°<η<10° and the q-range of q[0.350.71]  nm1 [ROI I of (b)]; (d) integral scattering tomographic slice reconstructed via OSEM using the azimuthal range of 100°<η<80° and the q-range of q[0.350.71]  nm1 [ROI II of (b)]; (e)–(h) reconstructed 2D SAXS patterns for the four different locations marked by arrows in (c).

Fig. 12.
Fig. 12.

Integral scattering tomographic slices at different PAIs, reconstructed using the OSEM [(a)–(d)] and FBP [(e)–(h)] algorithms, respectively, for ROI I and ROI II, as indicated in Fig. 11(b).

Fig. 13.
Fig. 13.

CNRs of integral scattering tomographic slices for ROI I (a) and ROI II (b), as a function of PAI.

Tables (1)

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Table 1. Parameters of Three Particle Distribution Models

Equations (10)

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I=I1f(s,u,q)Ω(s,u,q)ds,
Inorm(q)=I(q)I1(ionization)Ibac(q)Ibac(ionization).
pl(m,n,q)=i,jA(i,i,m,n)Sl(i,j,q),
Sl(i,j,q)=Sl(i,j,q)(m,n)ClA(i,j,m,n)(m,n)ClA(i,j,m,n)I(m,n,q)pl(m,n,q),
A(i,j,m,n)=Δd(i,j,m,n)Ω(i,j,q).
NMSE=i,j(Si,jS˜i,j)2i,jSi,j2,
CNR=2|xc1xc2|σ1+σ2,
Iϕ(qx,qz)=u=1NuIϕ,u(qx,qz,u).
RSD=σ(Iϕ(qx,qz))Iϕ(qx,qz).
I˜=qminqmaxη1η2I(q,η)dqdη,

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