Multi-Energy X-Ray Tomography of an Optical Fiber: The Role of Spatial Averaging

Using a commercial X-ray tomography instrument, we have obtained reconstructions of a graded-index optical fiber with voxels of edge length 1.05 µm at 12 tube voltages. The fiber manufacturer created a graded index in the central region by varying the germanium concentration from a peak value in the center of the core to a very small value at the core-cladding boundary. Operating on 12 tube voltages, we show by a singular value decomposition that there are only two singular vectors with significant weight. Physically, this means scans beyond two tube voltages contain largely redundant information. We concentrate on an analysis of the images associated with these two singular vectors. The first singular vector is dominant and images of the coefficients of the first singular vector at each voxel look are similar to any of the single-energy reconstructions. Images of the coefficients of the second singular vector by itself appear to be noise. However, by averaging the reconstructed voxels in each of several narrow bands of radii, we can obtain values of the second singular vector at each radius. In the core region, where we expect the germanium doping to go from a peak value at the fiber center to zero at the core-cladding boundary, we find that a plot of the two coefficients of the singular vectors forms a line in the two-dimensional space consistent with the dopant decreasing linearly with radial distance from the core center. The coating, made of a polymer rather than silica, is not on this line indicating that the two-dimensional results are sensitive not only to the density but also to the elemental composition.