4. Summary and Discussion

X-ray absorption measurements are becoming more common in tracking moisture content and movement in materials such as cement pastes, mortars, and wood. However, no published data describing in detail the uncertainty and accuracy in the measurements due to various machine settings and different specimen materials were found. In this paper, the results of several experiments that were conducted to elucidate the uncertainty of measurements from an x-ray absorption machine and to determine the proper averaging procedures to reduce random noise in the data were presented.

X-ray absorption measurements are often thought of as a Poisson process in which the uncertainty of the measurements is the square root of the number of x-ray counts at a given point [6, 7]. Based on the tests performed within, this estimate of uncertainty is most accurate in magnitude and trend when considering one point or several points of a uniform specimen like water. Experiments with water showed the uncertainty as indicated by the normalized root mean square error (NRMSE) to be within 25 % to 60 % of the Poisson estimate. The Poisson estimates and the NRMSEs agreed that when the number of counts increases, the uncertainty decreases, whether the increase in counts is due to increasing the x-ray intensity, the collimator size, or the integration time.

For those cases in which random noise was averaged out, such as when the same vertical profile is measured several times, averaging up to four profiles together at each point can reduce the uncertainty by up to a factor of two. In this situation, the Poisson estimate may be considered the maximum uncertainty. When averaging several profiles from different locations in a specimen, some microstructural features may be added to or averaged out of the mean profile. The Poisson estimate in this case is no longer reliable in predicting the magnitude of the uncertainty, but may provide a good estimate of the change in uncertainty due to different averaging procedure. The NRMSEs for a paste specimen for which several vertical profiles of counts at different horizontal locations were averaged together were generally less than the Poisson estimate by as much as a factor of two. For a mortar specimen, some NRMSEs were higher by up to a factor of five and some were lower by up to a factor of four.

Such spatial averaging should only be performed in cases where it is conclusively known that the boundaries are not altering the microstructure in the direction being averaged. For example, averaging several points in a horizontal line to get one point of a vertical profile is only valid when the boundaries at either end of the horizontal line do not induce an effect on density or composition along that line.

The NRMSE was less than 2 % for a vertical profile of a uniform water specimen and was about 1 % when the same point was sampled continuously for counts exceeding 17 000. The expected uncertainty in approximating the mean profile of a cement paste specimen may range from less than 1 % to almost 5 % depending on the horizontal resolution and the number of scans that are averaged. For a mortar specimen, this range may be from less than 1 % to almost 10 %. To keep the NRMSEs below 2 % for the mortar specimen examined here, it was necessary to scan a sample at a horizontal resolution of 2 mm or less with counts of 4000 or higher. For the paste specimen studied here, a horizontal resolution of 10 mm was sufficient to obtain a NRMSE of 2 % or less with counts of 1500 or higher. For the paste and mortar specimens, when counts were above 5000, one scan of the specimen at a given horizontal resolution provided data within one percentage point of the average of up to four scans. With counts per second of greater than 1000, an integration time of 5 s produced uncertainties of 2 % or less.

Because the uncertainties change depending on the settings that are chosen and depending on the composition and structure of the specimen being scanned, it is impossible to determine ideal settings and averaging procedures that will be valid in every circumstance. The values summarized above are intended as a guide. For more specific information about scans of a given specimen, it is recommended first that the degree of accuracy or uncertainty that is desired be determined. Next, a specimen of a uniform material such as aluminum or water of the same size as the actual specimen to be scanned should be used with various machine settings to get an idea of the base uncertainty for a specimen this size with these possible settings. After this, at least one specimen should be scanned at a very high horizontal and vertical resolution to determine the true structure of the specimen. Then, lower resolution scans can be checked against the more detailed one to see how well they match. By repeating this procedure, the uncertainties of the measurements and the proper machine settings and averaging procedures can be determined.

Finally, the process of x-ray absorption is not only dependent on the density and thickness of specimen but also on its composition. This work showed that while a mortar specimen was about 20 % denser than a paste specimen, the mortar counts were twice as large as those for the pastes. This fact must be remembered when comparing counts from two specimens of differing composition.