Coded Aperture X-ray Imaging (CAXI)

Introduction to coded aperture x-ray imaging (CAXI)

Since their discovery, x-rays have played a vital role in the fields of medical, industrial, and security imaging. The utility of x-ray imaging stems from its capacity to investigate non-destructively the internal structure of an object. The first step in any such imaging scheme necessarily involves illuminating the object with incident x-rays, which either interact (i.e. , are scattered or absorbed) or do not interact (i.e. , are transmitted) with the object. While most conventional x-ray imaging schemes rely on measuring the transmitted signal only, this approach can result in insufficient information for a particular task (e.g. detecting the presence of cancer or explosives). Scatter imaging, in contrast, has garnered substantial interest in the last two decades due to its ability to capture molecular information. By combining ideas from compressive sensing and reference structure/coded aperture imaging, DISP is currently developing novel approaches to transmission and scatter tomography that allow for faster, more sensitive x-ray imaging architectures for application in a variety of areas.

Compressive x-ray computed tomography

Building on earlier work on reference structure tomography and compressive measurement, DISP is developing high measurement efficiency x-ray tomography systems that allow one to acquire measurements in parallel (rather than sequentially) [1,2]. The key to this approach is the use of a coded aperture, which acts as a reference structure to disambiguate these superposed projections. By using decompressive inference, the number of images required for a 3D reconstruction is reduced. This approach enables snapshot operation, which opens possibilities for video-rate x-ray tomography as well as potentially drastically reducing the imaging dose.

X-ray scatter imaging

Transmission-based imaging systems measure the transmission of x-rays through an object, where the rays are assumed to travel in a straight path from the source to detector. While this scheme has the advantage that the x-ray signal is typically bright and highly-focused, it has several drawbacks. For example, the requirement that one make many measurements to estimate a single voxel renders imaging dynamic scenes challenging. In addition, this leads to unnecessarily high object exposure, which is important for the case of medical imaging. Finally, the contrast of this method may be insufficient for certain applications (such as cancer detection). In general, these dose- and speed-related issues stem from the fact that transmission-based imaging ignores all of the photons that actually interact with the object.

Scatter tomography, wherein one measures the x-rays scattered (or deflected) by the object, mitigates many of the issues inherent in transmission tomography. The signal becomes more information rich, for example, because each photon carries a wave vector, polarization, and energy associated with the location and type of scatter. These extra dimensions of information provide additional contrast mechanisms, which can lead to novel diagnostic capabilities (in the case of medical imaging) or present new, material-specific information (for security and industrial screening). In addition, the fact that scattered x-rays propagate in a direction that is distinct from that of the incident beam lifts the degeneracy inherent in transmission imaging. This allows one to perform snapshot tomography – in other words, a single measurement with scatter can reveal the same structural details as multi-exposure transmission imaging.

Two important scattering mechanisms are Compton scattering and coherent scattering. Compton scattering occurs over a broad angular range, which has led to the development of Compton backscatter imaging where the source and detector are nearly coincident. Compton imaging has been used to detect landmines as well as inspect cargo and passengers in transit systems. These systems usually operate by raster-scanning a pencil beam over the target and measuring the scattered irradiance on a detector to assemble a 2D image. Metals tend to produce less backscatter than lighter atoms, which makes backscatter imaging useful for peering into metal containers and examining their organic contents. DISP is currently exploring volumetric Compton scatter imaging using coded apertures with structured illumination [3,4].

Coherent scattering can produce structured diffraction patterns through interference between neighboring atoms. This structure reveals the sample's interatomic spacings, useful for identifying chemical targets in medical and security systems. In addition to transmission and Compton scatter imaging, DISP is researching coherent scatter imaging using coded apertures. Coherent scatter imaging simultaneously determines the positions and diffraction properties (or molecular signatures) of scatterers in a volume. This concept is demonstrated in Refs [5,6,7,8] below. While these works involve the use of different source geometries (including pencil, fan, and cone beams), coded aperture parameters (e.g., code structure and placement), and detector types (single pixels, linear and planar arrays with and without energy sensitivity), they all demonstrate the capacity to perform efficient, highly-parallel material-specific imaging.


  1. D. J. Brady, N. P. Pitsianis, and X. Sun, "Reference structure tomography," J. Opt. Soc. Am. A 21, 1140-1147 (2004).
  2. K. Choi and D. J. Brady, "Coded aperture computed tomography," Proc. SPIE 7468, 74680B (2009).
  3. K. MacCabe, A. Holmgren, M. Tornai, and D. Brady, "Snapshot 2D tomography via coded aperture x-ray scatter imaging," Appl. Opt. 52, 4582-4589 (2013).
  4. D. Brady, D. Marks, K. MacCabe, and J. O'Sullivan, "Coded apertures for x-ray scatter imaging," Appl. Opt. 52, 7745-7754 (2013).
  5. 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).
  6. K. MacCabe, A. Holmgren, J. Greenberg, and D. Brady, "Coding for x-ray scatter imaging," in Imaging and Applied Optics, OSA Technical Digest (online) (Optical Society of America, 2013), paper CM4C.2.
  7. J. Greenberg, K. Krishnamurthy, and D. Brady, "Snapshot molecular imaging using coded energy-sensitive detection," Opt. Express 21, 25480-25491 (2013).
  8. Joel A. Greenberg ; Kalyani Krishnamurthy ; Manu Lakshmanan ; Kenneth MacCabe ; Scott Wolter ; Anuj Kapadia ; David Brady; Coding and sampling for compressive x-ray diffraction tomography. Proc. SPIE 8858, Wavelets and Sparsity XV, 885813 (September 26, 2013).
  9. J. A. Greenberg, K. Krishnamurthy, D. J. Brady, "Compressive single-pixel snapshot X-ray diraction imaging", Opt. Lett. Vol. 39, Issue 1, pp. 111-114 (2014)
  10. J. A. Greenberg, M. Hassan, K. Krishnamurthy, D. J. Brady, "Structured illumination for tomographic X-ray diffraction imaging" Analyst DOI: 10.1039/C3AN01641B (2014)

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