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.

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    [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]
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  5. D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A21, 1140–1147, (2004).
    [CrossRef]
  6. P. Potuluri, U. Gopinathan, J. Adleman, and D. Brady, “Lensless sensor system using a reference structure,” Opt. Express11, 965–974 (2003).
    [CrossRef] [PubMed]
  7. P. Potuluri, M. Xu, and D. Brady, “Imaging with random 3d reference structures,” Opt. Express11, 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. Express15, 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).
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    [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,” SPIE5030, 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 Interface5, 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,” SPIE7079, 707915-1–707915-11, (2008).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [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. B140, 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,” Analyst134, 1802–1807, (2009).
    [CrossRef] [PubMed]
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    [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 Statistics32, 500–527, (2004).
    [CrossRef]

2010

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. A623, 1050 – 1060, (2010).
[CrossRef]

2009

O. Lazzari, S. Jacques, T. Sochi, and P. Barnes, “Reconstructive color x-ray diffraction imaging - a novel TEDDI imaging method,” Analyst134, 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]

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).

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

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 Interface5, 477–481 (2008).
[CrossRef]

R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” SPIE7079, 707915-1–707915-11, (2008).

2007

M. Gehm, R. John, D. Brady, R. Willett, and T. Schulz, “Single-shot compressive spectral imaging with a dual-disperser architecture,” Opt. Express15, 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 Graphics26, 69-1–69-12 (2007).

2006

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 Record5, 3170 –3173, (2006).
[CrossRef]

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

2005

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

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

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics32, 500–527, (2004).
[CrossRef]

D. J. Brady, N. P. Pitsianis, and X. Sun, “Reference structure tomography,” J. Opt. Soc. Am. A21, 1140–1147, (2004).
[CrossRef]

2003

2002

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

1999

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

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. B140, 253 – 257 (1998).
[CrossRef]

1997

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

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

1989

1985

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

1983

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

1972

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 Graphics26, 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,” Analyst134, 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. B140, 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. A21, 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 Interface5, 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 Record5, 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. B140, 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. B140, 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. A623, 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. A623, 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,” SPIE5030, 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. B140, 253 – 257 (1998).
[CrossRef]

Hansson, C.

R. J. Cernik, K. H. Khor, and C. Hansson, “X-ray colour imaging,” Journal of the Royal Society Interface5, 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,” SPIE5030, 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,” SPIE5030, 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. B140, 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,” Analyst134, 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. B140, 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. B140, 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. A623, 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 Interface5, 477–481 (2008).
[CrossRef]

Kolaczyk, E.

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” The Annals of Statistics32, 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. B140, 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,” Analyst134, 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,” SPIE7079, 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,” SPIE7079, 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 Graphics26, 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 Statistics32, 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. A623, 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 Graphics26, 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 Record5, 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,” SPIE5030, 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,” SPIE7079, 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,” Analyst134, 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. A623, 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,” SPIE7079, 707915-1–707915-11, (2008).

Sun, X.

Tumblin, J.

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Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems

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).

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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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