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.

Measurements of strain and strain rate, obtained by tissue Doppler might provide new parameters for assessing cardiac function in neonates. The noise-to-signal ratio is high. We investigated the effect of the frequency of the probe used, and the settings for tissue Doppler frame rate, on the noise in the analyses in three series of tissue Doppler images. In the first series, we used the 5S probe, with a frequency of 2.4 MHz, and the default frame rate. We used the10S probe, with a frequency of 8.0 MHz, in the other two series, one with a low and one with the default frame rate. The noise was lower using the 5S rather than the 10S probe, and lower when using the low frame rate rather than the default rate with the 10S probe. Using the settings eligible for two segment analyses with the lowest noise for each series, the noise was from 36 to 42% higher when using the 10S probe at default frame rate, and from 13 to 14% higher when using the 10S probe at low frame rate compared to the 5S probe at default frame rate. There were no differences in peak systolic strain or strain rate between the series. We found, therefore, that use of the 5S probe with the default setting for frame rate, along with a length of 1 mm and width of 2 mm for the region of interest, and a strain length of 10 mm, provided the optimal settings for two-segment analyses in this study.