Abstract

We use coded aperture x-ray scatter imaging to interrogate scattering targets with a pencil beam. Observations from a single x-ray exposure of a flat-panel scintillation detector are used to simultaneously determine the along-beam positions and momentum transfer profiles of two crystalline powders (NaCl and Al). The system operates with a 3 cm range resolution and a momentum transfer resolution of 0.1 nm−1. These results demonstrate that a single snapshot can be used to estimate scattering properties along an x-ray beam, and serve as a foundation for volumetric imaging of scattering objects.

© 2012 OSA

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  1. D. J. Brady, Optical Imaging and Spectroscopy (Wiley-OSA, 2009).
    [CrossRef]
  2. S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
    [CrossRef] [PubMed]
  3. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (Academic Press, 1979).
  4. A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).
  5. D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147, (2004).
    [CrossRef]
  6. P. Potuluri, U. Gopinathan, J. Adleman, and D. Brady, “Lensless sensor system using a reference structure,” Opt. Express 11, 965–974 (2003).
    [CrossRef] [PubMed]
  7. P. Potuluri, M. Xu, and D. Brady, “Imaging with random 3d reference structures,” Opt. Express 11, 2134–2141, (2003).
    [CrossRef] [PubMed]
  8. M. Gehm, R. John, D. Brady, R. Willett, and T. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027, (2007).
    [CrossRef] [PubMed]
  9. A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [CrossRef] [PubMed]
  10. K. Choi and D. J. Brady, “Coded aperture computed tomography,” in “Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems,” SPIE  7468, 74680B-1–74680B-10, (2009).
  11. D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660, (2002).
    [CrossRef] [PubMed]
  12. J.-P. Schlomka, A. Harding, U. van Stevendaal, M. Grass, and G. L. Harding, “Coherent scatter computed tomography: a novel medical imaging technique,” SPIE 5030, 256–265, (2003).
    [CrossRef]
  13. M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
    [CrossRef] [PubMed]
  14. R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
    [CrossRef]
  15. G. Harding and B. Schreiber, “Coherent x-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem. 56, 229–245, (1999).
    [CrossRef]
  16. G. Harding, “X-ray scatter tomography for explosives detection,” Radiat. Phys. Chem. 71, 869–881 (2004).
    [CrossRef]
  17. R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).
  18. C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
    [CrossRef]
  19. G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186, (1985).
    [CrossRef] [PubMed]
  20. J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett. 88, 243506 (2006).
    [CrossRef]
  21. G. Harding, M. Newton, and J. Kosanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33 (1990).
    [CrossRef]
  22. C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
    [CrossRef]
  23. O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive color x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst 134, 1802–1807, (2009).
    [CrossRef] [PubMed]
  24. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59, (1972).
    [CrossRef]
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    [CrossRef]
  26. A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
    [CrossRef]
  27. J. M. Boone and J. A. Seibert, “An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kv,” Med. Phys. 24, 1661–1670, (1997).
    [CrossRef] [PubMed]
  28. S. R. Beath and I. A. Cunningham, “Pseudomonoenergetic x-ray diffraction measurements using balanced filters for coherent-scatter computed tomography,” Med. Phys. 36, 1839–1847, (2009).
    [CrossRef] [PubMed]
  29. C. Dodge and M. Flynn, “Advanced integral method for the simulation of diagnostic x-ray spectra,” Med. Phys. 33, 1983 (2006).
  30. E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics 32, 500–527, (2004).
    [CrossRef]

2010 (1)

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

2009 (4)

K. Choi and D. J. Brady, “Coded aperture computed tomography,” in “Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems,” SPIE  7468, 74680B-1–74680B-10, (2009).

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

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

S. R. Beath and I. A. Cunningham, “Pseudomonoenergetic x-ray diffraction measurements using balanced filters for coherent-scatter computed tomography,” Med. Phys. 36, 1839–1847, (2009).
[CrossRef] [PubMed]

2008 (3)

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[CrossRef] [PubMed]

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
[CrossRef]

2007 (2)

M. Gehm, R. John, D. Brady, R. Willett, and T. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express 15, 14013–14027, (2007).
[CrossRef] [PubMed]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

2006 (2)

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

A. Chawla and E. Samei, “Geometrical repeatability and motion blur analysis of a new multi-projection x-ray imaging system,” IEEE Nuclear Science Symposium Conference Record 5, 3170 –3173, (2006).
[CrossRef]

2005 (1)

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

2004 (3)

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

D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147, (2004).
[CrossRef]

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics 32, 500–527, (2004).
[CrossRef]

2003 (3)

2002 (1)

D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660, (2002).
[CrossRef] [PubMed]

1999 (1)

G. Harding and B. Schreiber, “Coherent x-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem. 56, 229–245, (1999).
[CrossRef]

1998 (1)

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

1997 (1)

J. M. Boone and J. A. Seibert, “An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kv,” Med. Phys. 24, 1661–1670, (1997).
[CrossRef] [PubMed]

1990 (1)

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

1989 (1)

1985 (1)

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

1983 (1)

C. Dodge and M. Flynn, “Advanced integral method for the simulation of diagnostic x-ray spectra,” Med. Phys. 33, 1983 (2006).

1972 (1)

Adleman, J.

Agrawal, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

Barnes, P.

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

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Batchelar, D. L.

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660, (2002).
[CrossRef] [PubMed]

Beath, S. R.

S. R. Beath and I. A. Cunningham, “Pseudomonoenergetic x-ray diffraction measurements using balanced filters for coherent-scatter computed tomography,” Med. Phys. 36, 1839–1847, (2009).
[CrossRef] [PubMed]

Boone, J. M.

J. M. Boone and J. A. Seibert, “An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kv,” Med. Phys. 24, 1661–1670, (1997).
[CrossRef] [PubMed]

Boyce, S.

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

Brady, D.

Brady, D. J.

K. Choi and D. J. Brady, “Coded aperture computed tomography,” in “Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems,” SPIE  7468, 74680B-1–74680B-10, (2009).

D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A 21, 1140–1147, (2004).
[CrossRef]

D. J. Brady, Optical Imaging and Spectroscopy (Wiley-OSA, 2009).
[CrossRef]

Cernik, R. J.

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
[CrossRef]

Chawla, A.

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

A. Chawla and E. Samei, “Geometrical repeatability and motion blur analysis of a new multi-projection x-ray imaging system,” IEEE Nuclear Science Symposium Conference Record 5, 3170 –3173, (2006).
[CrossRef]

Choi, K.

K. Choi and D. J. Brady, “Coded aperture computed tomography,” in “Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems,” SPIE  7468, 74680B-1–74680B-10, (2009).

Cockcroft, J.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Colston, S.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Crespy, C.

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Cunningham, I. A.

S. R. Beath and I. A. Cunningham, “Pseudomonoenergetic x-ray diffraction measurements using balanced filters for coherent-scatter computed tomography,” Med. Phys. 36, 1839–1847, (2009).
[CrossRef] [PubMed]

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660, (2002).
[CrossRef] [PubMed]

Davidson, M. T. M.

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

Delfs, J.

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

Denstedt, J. D.

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

Dodge, C.

C. Dodge and M. Flynn, “Advanced integral method for the simulation of diagnostic x-ray spectra,” Med. Phys. 33, 1983 (2006).

Duvauchelle, P.

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Fenimore, E. E.

Flynn, M.

C. Dodge and M. Flynn, “Advanced integral method for the simulation of diagnostic x-ray spectra,” Med. Phys. 33, 1983 (2006).

Gehm, M.

Gopinathan, U.

Gottesman, S. R.

Grass, M.

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

Hall, C.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Hansson, C.

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
[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,” SPIE 5030, 256–265, (2003).
[CrossRef]

Harding, G.

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

G. Harding and B. Schreiber, “Coherent x-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem. 56, 229–245, (1999).
[CrossRef]

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

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

Harding, G. L.

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

Harwit, M.

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

Husermann, D.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Jacques, S.

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

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

John, R.

Jupe, A.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Kaftandjian, V.

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Khor, K. H.

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
[CrossRef]

Kolaczyk, E.

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics 32, 500–527, (2004).
[CrossRef]

Kosanetzky, J.

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

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

Kunz, M.

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Lazzari, O.

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

Madden, R. W.

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

Mahdavieh, J.

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

McAdams, H.

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

Mohan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

Newton, M.

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

Nowak, R.

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics 32, 500–527, (2004).
[CrossRef]

Pitsianis, N. P.

Ponard, P.

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Potuluri, P.

Raskar, R.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

Richardson, W. H.

Samei, E.

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

A. Chawla and E. Samei, “Geometrical repeatability and motion blur analysis of a new multi-projection x-ray imaging system,” IEEE Nuclear Science Symposium Conference Record 5, 3170 –3173, (2006).
[CrossRef]

Schlomka, J.-P.

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

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

Schreiber, B.

G. Harding and B. Schreiber, “Coherent x-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem. 56, 229–245, (1999).
[CrossRef]

Schulz, T.

Seibert, J. A.

J. M. Boone and J. A. Seibert, “An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kv,” Med. Phys. 24, 1661–1670, (1997).
[CrossRef] [PubMed]

Sloane, N. J. A.

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

Smith, R. C.

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

Sochi, T.

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

Soulez, F.

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Subramanian, R.

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

Sun, X.

Tumblin, J.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

van Stevendaal, U.

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

Veeraraghavan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

Velupillai, S.

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

Wagadarikar, A.

Washington, L.

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

Willett, R.

Xu, M.

ACM Transactions on Graphics (1)

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics 26, 69-1–69-12 (2007).

Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems (1)

K. Choi and D. J. Brady, “Coded aperture computed tomography,” in “Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems,” SPIE  7468, 74680B-1–74680B-10, (2009).

Analyst (1)

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

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. Delfs and J.-P. Schlomka, “Energy-dispersive coherent scatter computed tomography,” Appl. Phys. Lett. 88, 243506 (2006).
[CrossRef]

IEEE Nuclear Science Symposium Conference Record (1)

A. Chawla and E. Samei, “Geometrical repeatability and motion blur analysis of a new multi-projection x-ray imaging system,” IEEE Nuclear Science Symposium Conference Record 5, 3170 –3173, (2006).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

A. Chawla, S. Boyce, L. Washington, H. McAdams, and E. Samei, “Design and development of a new multi-projection x-ray system for chest imaging,” IEEE Trans. Nucl. Sci. 56, 36–45, (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Journal of the Royal Society Interface (1)

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface 5, 477–481 (2008).
[CrossRef]

Med. Phys. (4)

D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660, (2002).
[CrossRef] [PubMed]

J. M. Boone and J. A. Seibert, “An accurate method for computer-generating tungsten anode x-ray spectra from 30 to 140 kv,” Med. Phys. 24, 1661–1670, (1997).
[CrossRef] [PubMed]

S. R. Beath and I. A. Cunningham, “Pseudomonoenergetic x-ray diffraction measurements using balanced filters for coherent-scatter computed tomography,” Med. Phys. 36, 1839–1847, (2009).
[CrossRef] [PubMed]

C. Dodge and M. Flynn, “Advanced integral method for the simulation of diagnostic x-ray spectra,” Med. Phys. 33, 1983 (2006).

Nucl. Instrum. Methods Phys. Res. A (1)

C. Crespy, P. Duvauchelle, V. Kaftandjian, F. Soulez, and P. Ponard, “Energy dispersive x-ray diffraction to identify explosive substances: Spectra analysis procedure optimization,” Nucl. Instrum. Methods Phys. Res. A 623, 1050 – 1060, (2010).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (1)

C. Hall, P. Barnes, J. Cockcroft, S. Colston, D. Husermann, S. Jacques, A. Jupe, and M. Kunz, “Synchrotron energy-dispersive x-ray diffraction tomography,” Nucl. Instrum. Methods Phys. Res. B 140, 253 – 257 (1998).
[CrossRef]

Opt. Express (3)

Phys. Med. Biol. (3)

M. T. M. Davidson, D. L. Batchelar, S. Velupillai, J. D. Denstedt, and I. A. Cunningham, “Laboratory coherent-scatter analysis of intact urinary stones with crystalline composition: a tomographic approach,” Phys. Med. Biol. 50, 3907 (2005).
[CrossRef] [PubMed]

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

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

Radiat. Phys. Chem. (2)

G. Harding and B. Schreiber, “Coherent x-ray scatter imaging and its applications in biomedical science and industry,” Radiat. Phys. Chem. 56, 229–245, (1999).
[CrossRef]

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

SPIE (2)

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE 7079, 707915-1–707915-11, (2008).

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

The Annals of Statistics (1)

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics 32, 500–527, (2004).
[CrossRef]

Other (2)

D. J. Brady, Optical Imaging and Spectroscopy (Wiley-OSA, 2009).
[CrossRef]

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

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Figures (7)

Fig. 1
Fig. 1

Basic pencil beam coded aperture X-ray tomography system

Fig. 2
Fig. 2

XSPECT model for the source spectral number density N(ν) at the object.

Fig. 3
Fig. 3

X-ray projection of the 29.7 cm×29.4 cm secondary aperture (full detector image). The aperture is cropped slightly in the horizontal direction

Fig. 4
Fig. 4

Diffraction images acquired with (a) NaCl, (b) Al, and (c) a combination of NaCl and Al placed in the beam.

Fig. 5
Fig. 5

Reconstruction results when a single sample (NaCl or Al) is placed along the beam. The along-beam distance z is measured in negative values from the detector. (a) Spatial scattering profile f (z) for NaCl. (b) Spatial scattering profile f (z) for Al. (c) Momentum transfer profile f (q) for NaCl. (d) Momentum transfer profile f (q) for Al.

Fig. 6
Fig. 6

Reconstruction results with both samples in the beam. (a) Spatial scattering profile f (z) with both samples in the beam. (b) Momentum transfer profile f (q) for NaCl at z = −59.3 cm. (c) Momentum transfer profile f (q) for Al at z = −52 cm.

Fig. 7
Fig. 7

Polar plots of (a) the combined NaCl and Al diffraction pattern and (b) the modeled diffraction pattern Hf̂ based on the corresponding object estimate f̂.

Equations (10)

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g ( ρ , ϕ ) = d z ( 1 z 2 + ρ 2 ) t ( ρ [ 1 d z ] , ϕ ) d q f ( z , q ) P ( ν = z q ρ ) .
t ( ρ , ϕ ) = 1 + sign ( sin ( u x ) ) 2 ,
f ( z , q ) = j f j rect ( z z j Δ z ) rect ( q q j Δ q ) ,
g i = ρ d ρ rect ( ρ ρ i Δ ρ ) d ϕ rect ( ϕ ϕ i Δ ϕ ) g ( ρ , ϕ ) ,
g = Hf ,
H i j = ρ i Δ ρ 2 ρ i + Δ ρ 2 ρ d ρ ϕ i Δ ϕ 2 ϕ i + Δ ϕ 2 d ϕ z j Δ z 2 z j + Δ z 2 d z ( 1 z 2 + ρ 2 ) × t ( ρ [ 1 d z ] , ϕ ) q j Δ q 2 q j + Δ q 2 d q P ( z q ρ ) ,
y ~ Poisson ( Hf + μ b )
μ ^ b arg min g Γ ( log ( b | g ) + τ pen ( g ) )
( b | g ) = i ( b i | g i ) = i exp ( g i ) g i b i b i ! ,
f ^ arg min f ˜ ( log ( y | H , μ ^ b , f ˜ ) ) .

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