The water, paste, and mortar experiments discussed above showed that the uncertainty decreases as the number of counts increase, whether that increase in counts is due to increased intensity, increased integration time, or increased collimator size. These findings are consistent with those from a Poisson process. The results of the paste and mortar collimator experiments, however, suggest that the physical structure of the specimen may invalidate the use of the Poisson estimate of uncertainty for some specimens since the NRMSEs did not scale in the same way with the number of counts (Fig. 4).
The vertical profile results presented thus far were for vertical profiles at one horizontal location. In this section, the discussion focuses on how averaging over larger specimen domains influences the uncertainty of the estimated mean vertical structure of the specimen. Two different averaging procedures were examined: 1) averaging together vertical profiles at different horizontal locations (different horizontal resolutions; experiment XVP in Table 1) and 2) averaging a number of scanning repetitions (experiment RVP in Table 1). For these experiments, the data from the scans with a horizontal and vertical resolution of 1 mm (Fig. 1), averaged over four scans, at x-ray intensity settings of 43 kV and 700 µA (intensity C) was used as the true mean vertical count profile of the specimens. Three intensities were used (Table 1).
The paste specimen at intensity C has a NSD of roughly 7.1 %, while that for the mortar sample is about 2.9 %. The reason that the paste (Fig. 7) has a higher overall vertical variability than the mortar (Fig. 8) is that the paste counts show a distinct vertical trend with higher counts near the top of the specimen and fewer counts near the bottom. This trend is the result of more efficient compaction and possible subsequent bleeding of the paste specimen, induced by the vibrating table, than of the mortar specimen due to the smaller average particle size in the paste. The result is better packing and higher densities near the bottom of the specimen and lower density near the top, as observed previously for w/b = 0.75 pastes [1, 2].
Fig. 7. Normalized counts from the vertical scans of a paste specimen in experiment IVP for three different intensities (A, B, and C). See Table 1 for more details. The profiles were determined by averaging the points at each level from 20 scans.
Fig. 8. Normalized counts from the vertical scans of a mortar specimen in experiment IVP for three different intensities (A, B, and C). See Table 1 for more details. The profiles were determined by averaging the points at each level from 20 scans.