OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 8 — Sep. 4, 2013

Snapshot 2D tomography via coded aperture x-ray scatter imaging

Kenneth P. MacCabe, Andrew D. Holmgren, Martin P. Tornai, and David J. Brady  »View Author Affiliations

Applied Optics, Vol. 52, Issue 19, pp. 4582-4589 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (624 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(340.7430) X-ray optics : X-ray coded apertures
(110.1758) Imaging systems : Computational imaging
(110.3200) Imaging systems : Inverse scattering

ToC Category:
X-ray Optics

Original Manuscript: February 11, 2013
Manuscript Accepted: April 5, 2013
Published: June 26, 2013

Virtual Issues
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics

Kenneth P. MacCabe, Andrew D. Holmgren, Martin P. Tornai, and David J. Brady, "Snapshot 2D tomography via coded aperture x-ray scatter imaging," Appl. Opt. 52, 4582-4589 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


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

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material

» Media 1: AVI (70 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited