Qualitative Characterization of Granular Materials and Moisture Measurements - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 91

TDR measurements were performed through a 15 cm-long commercial three-rod
probe (CS630, Campbell Scientific).
Before proceeding with the detailed discussion on the proposed experimental and
metrological approaches, let us briefly summarize the key-points of the procedure.
After a specific probe calibration (as reported in subsection 3.6.1), for each of the
pre-established moisture levels ( θ ref ) at which the samples were moistened, the cor-

responding app value was evaluated. This way, the functional relationships between

the apparent dielectric constant and the corresponding moisture level were identified
through an appropriate fitting of the data. The overall uncertainty of

ε

app was evalu-
ated so as to draw a preliminary comparison between the different performances of
the used TDR instruments and to understand to which extent results depend either
on the instrument or on other experimental conditions.
Successively, the fitted data were used to extrapolate specific calibration curves,
for each considered material and for each instrument. Simultaneously, an evaluation
of the overall uncertainty in the estimation of

ε

from the calibration curves was
done through the non-linear regression method. This was done to provide a compre-
hensive panorama of the measurement system as a whole and to validate a general
method which, in turn, can be applied also for other types of materials.
As reported in [3] and according to the calibration procedure described in Sect.
3.6.1, a ten-measurement set was preliminarily carried out with the three-rod probe-
footnotemark immersed first in air and then in demineralized water.

θ

5.3.2 Uncertainty Evaluation for Apparent Dielectric Permittivity

Measurement and Individuation of the Calibration Curves

The evaluation of the apparent dielectric constant from TDR measurements relies
on (3.5), which is reported here for convenience:

L app
L

2

ε app = (5.5)

where L app is the apparent probe length in the MUT and L is the length of the probe
in air. To take into account the uncertainty sources, a ten-measurement set of the
apparent length L app was acquired for each sample. For each set of measurements,
both the mean apparent length L app and the standard deviation σ L app were calcu-

lated 4 , then the expanded uncertainty U L app was evaluated through the t -Student dis-
tribution, according to the relation:

U L app = 2 . 26 σ L app (5.6)

3

A coaxial geometry for the probe would guarantee a reliable matched transmission line.
Nevertheless, three-rod probes are definitely more practically usable when investigating
granular materials, thanks to the easier insertion in the MUT.

4

σ L app is the standard deviation corresponding to the Gaussian distribution, which was ver-
ified through the χ -square test.