At a given x-ray source intensity, the number of counts changes proportionally with the change in collimator size (see "Water" data in Table 2). For vertical scans of the water specimen discussed above, at a constant x-ray source intensity, the NRMSEs of the measurements from all of the collimators referenced to collimator #2 (the largest opening area) increased as the collimator size decreased ("Water I" in Fig. 4a). This dependence on collimator size is directly related to the number of counts measured for each collimator. To demonstrate this fact, the NRMSEs from scans for each collimator at a constant intensity (Water I) were compared with those from scans in which the counts were held relatively constant ("Water II" in Fig. 4a). As the collimator opening gets smaller, the counts in Water I decreased and the NRMSEs increased, as mentioned above. When the x-ray counts for each collimator are kept at ≈17 000 counts per point by adjusting the x-ray source intensity for each collimator (Water II), the trend in NRMSEs seen in Water I is no longer present. Therefore, for a specimen that is uniform in composition and density, increasing the collimator size reduces the uncertainty because the number of counts is increased for a given integration time.
Fig. 4. Normalized Root Mean Square Errors (NRMSE) for each collimator (experiment CVP). (a) Water. (b) Paste. (c) Mortar. See Table 1 for more details about experiment CVP and see Table 2 for more information about the collimators. The "I" in the legend label refers to scans in which the x-ray source intensity was kept constant (allowing counts to vary by collimator size) while "II" refers to scans in which the counts were held constant. For Water II, the average counts were within ±0.6 % of 17 170 counts. For Paste II, the average counts were within ±1.8 % of 17 192 counts. For Mortar II, the average counts were within ±2 % of 17 637 counts.