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Opportunity at National Institute of Standards and Technology (NIST)

Novel Mathematical Techniques for Reconstruction of Computed Tomography Applied to Three-Dimensional Imaging of Advanced Materials


Material Measurement Laboratory, Applied Chemicals and Materials Division

RO# Location
50.64.72.B8382 Boulder, CO

Please note: This Agency only participates in the February and August reviews.


Name E-mail Phone
Fekete, James R 303.497.5204
Garboczi, Edward Joseph 303.497.7032
Tewary, Vinod K. 303.497.5753


Computed tomography (CT) is a powerful technique for imaging the “inside” of objects by using x rays, neutrons, ultrasonic waves, and electrical conductivity, among other probes. Modern CT, evolved over the last several decades, has revolutionized diagnostic medicine with its ability to produce three-dimensional images of biological objects. This technique has also been applied to non-medical imaging with considerable success. Currently, there is a strong interest in the use of CT for three-dimensional characterization of advanced materials, particularly at the mesoscopic scales. Such characterizations are important for predictive and interpretative mathematical modeling of physical and mechanical characteristics of advanced materials that are needed for their technological applications. In addition to the experimental difficulties associated with high-resolution measurement techniques, interpretation and inversion of CT data is a challenging mathematical problem, especially for applications beyond simple local density descriptions. The objective of this project is to develop a computationally efficient algorithm for CT reconstruction of local vector and tensor data. One possible approach is to use a Green’s function based technique—especially with Radon transform representation. This technique, developed at NIST over the last several years for calculation of the elastic Green’s functions, has been found to be convenient for inversion of data on elastic wave propagation. Another advantage of this technique is that it provides a power series expansion of the Green’s function that can be used for multiscale modeling of materials. The power series can seamlessly link the atomistic and the macroscopic scales in solids, and can probably be extended to mesoscopic scales for CT application. NIST is also interested in the experimental tomographic techniques that are needed to measure local vector and tensor data. A focus on the development of such techniques could also be a focus of this post-doctoral opportunity.


Advanced materials; Computed tomography; Reconstruction; Green’s function; Mathematical modeling; Radon transform; Three-dimensional imaging;


Citizenship:  Open to U.S. citizens
Level:  Open to Postdoctoral applicants
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