Abstract

This paper describes a fan beam coded aperture x-ray scatter imaging system that acquires a tomographic image from each snapshot. This technique exploits the cylindrical symmetry of the scattering cross section to avoid the scanning motion typically required by projection tomography. We use a coded aperture with a harmonic dependence to determine range and a shift code to determine cross range. Here we use a forward-scatter configuration to image 2D objects and use serial exposures to acquire tomographic video of motion within a plane. Our reconstruction algorithm also estimates the angular dependence of the scattered radiance, a step toward materials imaging and identification.

© 2013 Optical Society of America

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  1. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  2. P. G. Lale, “The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography,” Phys. Med. Biol. 4, 159–167 (1959).
    [CrossRef]
  3. G. Harding and J. Kosanetzky, “Scattered x-ray beam nondestructive testing,” Nucl. Instrum. Methods Phys. Res. Sect. A 280, 517–528 (1989).
    [CrossRef]
  4. K. MacCabe, K. Krishnamurthy, A. Chawla, D. Marks, E. Samei, and D. Brady, “Pencil beam coded aperture x-ray scatter imaging,” Opt. Express 20, 16310–16320 (2012).
    [CrossRef]
  5. G. Harding and J. Kosanetzky, “Elastic scatter computed tomography,” Phys. Med. Biol. 30, 183–186 (1985).
    [CrossRef]
  6. G. Harding, “X-ray scatter tomography for explosives detection,” Rad. Phys. Chem. 71, 869–881 (2004).
    [CrossRef]
  7. R. W. Madden, J. Mahdavieh, R. C. Smith, and R. Subramanian, “An explosives detection system for airline security using coherent x-ray scattering technology,” Proc. SPIE 7079, 707915 (2008).
    [CrossRef]
  8. J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
    [CrossRef]
  9. M. T. 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, 3907–3925 (2005).
    [CrossRef]
  10. E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
    [CrossRef]
  11. V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
    [CrossRef]
  12. J. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Australia 1, 172173 (1968).
  13. R. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
    [CrossRef]
  14. D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
  15. M. T. E. Golay, “Multi-slit spectrometry,” J. Opt. Soc. Am. 39, 437–444 (1949).
    [CrossRef]
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  17. S. Mende, E. Claflin, R. Rairden, and G. Swenson, “Hadamard spectroscopy with a two-dimensional detecting array,” Appl. Opt. 32, 7095–7105 (1993).
    [CrossRef]
  18. A. Mrozack, D. L. Marks, and D. J. Brady, “Coded aperture spectroscopy with denoising through sparsity,” Opt. Express 20, 2297–2309 (2012).
    [CrossRef]
  19. 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]
  20. A. Wagadarikar, R. John, R. Willett, and D. J. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
    [CrossRef]
  21. D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51, 071403 (2012).
    [CrossRef]
  22. K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
    [CrossRef]
  23. S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
    [CrossRef]
  24. N. V. Arendtsz and E. M. Hussein, “Energy-spectral compton scatter imaging. I. Theory and mathematics,” IEEE Trans. Nucl. Sci. 42, 2155–2165 (1995).
    [CrossRef]
  25. F. Farmer and M. Collins, “A new approach to the determination of anatomical cross-sections of the body by compton scattering of gamma-rays,” Phys. Med. Biol. 16, 577–586 (1971).
    [CrossRef]
  26. C. A. Carlsson, “Imaging modalities in x-ray computerized tomography and in selected volume tomography,” Phys. Med. Biol. 44, R23–R56 (1999).
    [CrossRef]
  27. D. L. Batchelar and I. A. Cunningham, “Material-specific analysis using coherent-scatter imaging,” Med. Phys. 29, 1651–1660 (2002).
    [CrossRef]
  28. K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr. 8, 306–316 (1984).
  29. D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
    [CrossRef]
  30. Clock animation, http://www.disp.duke.edu/images/clock-animation-labeled.gif .

2012 (3)

2011 (1)

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
[CrossRef]

2009 (1)

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

2008 (2)

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

2007 (3)

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]

E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
[CrossRef]

2005 (1)

M. T. 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, 3907–3925 (2005).
[CrossRef]

2004 (1)

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

2002 (1)

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

1999 (1)

C. A. Carlsson, “Imaging modalities in x-ray computerized tomography and in selected volume tomography,” Phys. Med. Biol. 44, R23–R56 (1999).
[CrossRef]

1995 (1)

N. V. Arendtsz and E. M. Hussein, “Energy-spectral compton scatter imaging. I. Theory and mathematics,” IEEE Trans. Nucl. Sci. 42, 2155–2165 (1995).
[CrossRef]

1993 (1)

1989 (2)

G. Harding and J. Kosanetzky, “Scattered x-ray beam nondestructive testing,” Nucl. Instrum. Methods Phys. Res. Sect. A 280, 517–528 (1989).
[CrossRef]

S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
[CrossRef]

1985 (1)

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

1984 (1)

K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr. 8, 306–316 (1984).

1982 (1)

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

1971 (1)

F. Farmer and M. Collins, “A new approach to the determination of anatomical cross-sections of the body by compton scattering of gamma-rays,” Phys. Med. Biol. 16, 577–586 (1971).
[CrossRef]

1968 (2)

J. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Australia 1, 172173 (1968).

R. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[CrossRef]

1959 (1)

P. G. Lale, “The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography,” Phys. Med. Biol. 4, 159–167 (1959).
[CrossRef]

1949 (1)

Ables, J.

J. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Australia 1, 172173 (1968).

Alvar, K.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Arendtsz, N. V.

N. V. Arendtsz and E. M. Hussein, “Energy-spectral compton scatter imaging. I. Theory and mathematics,” IEEE Trans. Nucl. Sci. 42, 2155–2165 (1995).
[CrossRef]

Batchelar, D. L.

M. T. 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, 3907–3925 (2005).
[CrossRef]

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

Brady, D.

Brady, D. J.

A. Mrozack, D. L. Marks, and D. J. Brady, “Coded aperture spectroscopy with denoising through sparsity,” Opt. Express 20, 2297–2309 (2012).
[CrossRef]

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51, 071403 (2012).
[CrossRef]

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

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

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).

Carlsson, C. A.

C. A. Carlsson, “Imaging modalities in x-ray computerized tomography and in selected volume tomography,” Phys. Med. Biol. 44, R23–R56 (1999).
[CrossRef]

Carson, R.

K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr. 8, 306–316 (1984).

Chawla, A.

Choi, K.

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

Claflin, E.

Collins, M.

F. Farmer and M. Collins, “A new approach to the determination of anatomical cross-sections of the body by compton scattering of gamma-rays,” Phys. Med. Biol. 16, 577–586 (1971).
[CrossRef]

Corey, R.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Costello, D.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Crotty, D. J.

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
[CrossRef]

Cunningham, I. A.

M. T. 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, 3907–3925 (2005).
[CrossRef]

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

Davidson, M. T.

M. T. 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, 3907–3925 (2005).
[CrossRef]

Denstedt, J. D.

M. T. 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, 3907–3925 (2005).
[CrossRef]

Dicke, R.

R. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[CrossRef]

Farmer, F.

F. Farmer and M. Collins, “A new approach to the determination of anatomical cross-sections of the body by compton scattering of gamma-rays,” Phys. Med. Biol. 16, 577–586 (1971).
[CrossRef]

Fenimore, E. E.

Gehm, M.

Golay, M. T. E.

Gordon, R.

E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
[CrossRef]

Gottesman, S. R.

Grubsky, V.

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
[CrossRef]

Harding, G.

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

G. Harding and J. Kosanetzky, “Scattered x-ray beam nondestructive testing,” Nucl. Instrum. Methods Phys. Res. Sect. A 280, 517–528 (1989).
[CrossRef]

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

Harwit, M.

M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979), Vol. 1.

Hussein, E. M.

N. V. Arendtsz and E. M. Hussein, “Energy-spectral compton scatter imaging. I. Theory and mathematics,” IEEE Trans. Nucl. Sci. 42, 2155–2165 (1995).
[CrossRef]

Jannson, T.

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
[CrossRef]

John, J.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

John, R.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kittle, D. S.

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51, 071403 (2012).
[CrossRef]

Kocimski, S.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Kosanetzky, J.

G. Harding and J. Kosanetzky, “Scattered x-ray beam nondestructive testing,” Nucl. Instrum. Methods Phys. Res. Sect. A 280, 517–528 (1989).
[CrossRef]

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

Krishnamurthy, K.

Lale, P. G.

P. G. Lale, “The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography,” Phys. Med. Biol. 4, 159–167 (1959).
[CrossRef]

Lange, K.

K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr. 8, 306–316 (1984).

Lurie, N.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

MacCabe, K.

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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

Marks, D.

Marks, D. L.

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51, 071403 (2012).
[CrossRef]

A. Mrozack, D. L. Marks, and D. J. Brady, “Coded aperture spectroscopy with denoising through sparsity,” Opt. Express 20, 2297–2309 (2012).
[CrossRef]

McKinley, R. L.

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
[CrossRef]

Mende, S.

Mrozack, A.

Patton, N.

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
[CrossRef]

Pistorius, S.

E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
[CrossRef]

Rairden, R.

Romanov, V.

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
[CrossRef]

Samei, E.

Schulz, T.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Sloane, N. J.

M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979), Vol. 1.

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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

Stokes, J.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

Swenson, G.

Thayer, D.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Tornai, M. P.

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
[CrossRef]

Trippe, A.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Van Uytven, E.

E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
[CrossRef]

Velupillai, S.

M. T. 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, 3907–3925 (2005).
[CrossRef]

Wagadarikar, A.

Willett, R.

Young, J.

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

R. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

N. V. Arendtsz and E. M. Hussein, “Energy-spectral compton scatter imaging. I. Theory and mathematics,” IEEE Trans. Nucl. Sci. 42, 2155–2165 (1995).
[CrossRef]

J. Comput. Assist. Tomogr. (1)

K. Lange and R. Carson, “EM reconstruction algorithms for emission and transmission tomography,” J. Comput. Assist. Tomogr. 8, 306–316 (1984).

J. Opt. Soc. Am. (1)

Med. Phys. (2)

E. Van Uytven, S. Pistorius, and R. Gordon, “An iterative three-dimensional electron density imaging algorithm using uncollimated Compton scattered x rays from a polyenergetic primary pencil beam,” Med. Phys. 34, 256–265 (2007).
[CrossRef]

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

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

J. Stokes, K. Alvar, R. Corey, D. Costello, J. John, S. Kocimski, N. Lurie, D. Thayer, A. Trippe, and J. Young, “Some new applications of collimated photon scattering for nondestructive examination,” Nucl. Instrum. Methods Phys. Res. 193, 261–267 (1982).
[CrossRef]

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

G. Harding and J. Kosanetzky, “Scattered x-ray beam nondestructive testing,” Nucl. Instrum. Methods Phys. Res. Sect. A 280, 517–528 (1989).
[CrossRef]

Opt. Eng. (1)

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51, 071403 (2012).
[CrossRef]

Opt. Express (3)

Phys. Med. Biol. (6)

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

M. T. 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, 3907–3925 (2005).
[CrossRef]

P. G. Lale, “The examination of internal tissues, using gamma-ray scatter with a possible extension to megavoltage radiography,” Phys. Med. Biol. 4, 159–167 (1959).
[CrossRef]

F. Farmer and M. Collins, “A new approach to the determination of anatomical cross-sections of the body by compton scattering of gamma-rays,” Phys. Med. Biol. 16, 577–586 (1971).
[CrossRef]

C. A. Carlsson, “Imaging modalities in x-ray computerized tomography and in selected volume tomography,” Phys. Med. Biol. 44, R23–R56 (1999).
[CrossRef]

D. J. Crotty, R. L. McKinley, and M. P. Tornai, “Experimental spectral measurements of heavy K-edge filtered beams for x-ray computed mammotomography,” Phys. Med. Biol. 52, 603–616 (2007).
[CrossRef]

Proc. Astron. Soc. Australia (1)

J. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Australia 1, 172173 (1968).

Proc. SPIE (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,” Proc. SPIE 7079, 707915 (2008).
[CrossRef]

V. Grubsky, V. Romanov, N. Patton, and T. Jannson, “Compton imaging tomography technique for NDE of large nonuniform structures,” Proc. SPIE 8144, 81440G (2011).
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K. Choi and D. J. Brady, “Coded aperture computed tomography,” Proc. SPIE 7468, 74680B (2009).
[CrossRef]

Rad. Phys. Chem. (1)

G. Harding, “X-ray scatter tomography for explosives detection,” Rad. Phys. Chem. 71, 869–881 (2004).
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Other (4)

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Clock animation, http://www.disp.duke.edu/images/clock-animation-labeled.gif .

Supplementary Material (1)

» Media 1: AVI (70 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Coordinate system diagram showing a single scattering event.

Fig. 2.
Fig. 2.

Diagram of the experimental system.

Fig. 3.
Fig. 3.

Photos of (a) plastic DUKE letters and (b) the clock in position for the experiments.

Fig. 4.
Fig. 4.

Cropped and binned scatter image for the plastic DUKE letters, corresponding to a 4.9cm×4.5cm detection area.

Fig. 5.
Fig. 5.

Reconstructed images for DUKE letters. (a) Density image f(x,z), with x=vertical and z=horizontal. (b) Reconstructed scatter radiance b(θ).

Fig. 6.
Fig. 6.

Reconstructions of the clock’s second hand. (a) Reconstructed density images f(x,z,t), with x=horizontal and z=vertical. Each frame is labeled with the timestamp. (b) Reconstructed scatter radiance b(θ). See Media 1.

Equations (14)

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T(x,y)=(1+iAiΠ(uxi)j(1)jΠ(2νyj)2),
gj(r)=rVd3rT(r+(rr)dz)|rr|2fj(r)b(θ),
gij=gj(ri).
fj(r)=kδ(xxk)δ(zzk)fkj,
gij=kT(ri+(rkri)dzk)|rirk|2b(θik)fkj,
g=(G·*B)f,
b(θ)=lblΠ(θθlΔθl),
yPoisson(g+g0).
ijgijxyijgij+g0ijijgijx=1x,
xn+1=xn·*ijgijxyijgij+g0ijijgijx,
fn+1=fn·*(G·*B)T(y·/(g+g0))·/(G·*B)T1g,
bn+1=bn·*(ijkΠikGikfkjyijgij+g0ij)·/(ijkΠikGikfkj),
Δz=z2Yvd.
Δx=zud,

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