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

Published online by Cambridge University Press:  14 March 2019

Zachary H. Levine ,
Adele P. Peskin ,
Edward J. Garboczi  and
Andrew D. Holmgren
Zachary H. Levine
Affiliation:
Sensor Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8441, USA
Adele P. Peskin*
Affiliation:
Software and Systems Division, National Institute of Standards and Technology, Boulder, Colorado 80305-3337, USA
Edward J. Garboczi
Affiliation:
Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
Andrew D. Holmgren
Affiliation:
Holmgren Professional Research Experience Program, University of Colorado, Boulder, Colorado 80309, USA Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305, USA
*
*Author for correspondence: Adele P. Peskin, E-mail: [email protected]
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Abstract

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.

Keywords

computed tomographymulti-energyspatial averagingimage processing
Type
Materials Science Applications
Information
Microscopy and Microanalysis , Volume 25 , Issue 1 , February 2019 , pp. 70 - 76
Copyright
Copyright © Microscopy Society of America 2019 

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Footnotes

This contribution of NIST, an agency of the US government, is not subject to copyright.

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