Dark-field X-ray imaging of unsaturated water transport in porous
materials
Supplementary Materials
F. Yang,1,2,a) F. Prade,3 M. Griffa,1,a I. Jerjen,1 C. Di Bella,1,2 J. Herzen,3
A. Sarapata,3 F. Pfeiffer,3 P. Lura1,2
1Empa,
Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, 8600, Switzerland
2Institute
for Building Materials (IfB), ETH Zurich, Zürich, 8093, Switzerland
3Physik-Department
& Institut für Medizintechnik, Technische Universität München, Garching, Germany
1. Mortar samples: mix design
The mortar samples were cast in the laboratory according to the following mix design
parameters: 0.585 water-to-cement ratio (w/c), by mass; 61% of sand (average size 0.3 - 0.4
mm and maximum 1 mm), 11% of cement (CEM I 52.5 N, mass volumetric density of 3.13 g
 cm-3 and Blaine fineness of 3440 cm2  g-1) and 14% of inert quartz filler (Sibelco C400,
volumetric mass density of 2.65 g  cm-3 and average grain size, D50, equal to 15 m), the
fractions being expressed in respect to the total mass of the mix.
2. Description of the Talbot-Lau interferometer used for multi-contrast X-ray
radiography during the water capillary uptake experiment
Figure S1: schematic representation of the X-ray imaging setup equipped with a Talbot-Lau
interferometer, composed of the three aligned gratings, G0 (source grating), G1 (phase grating) and
G2 (analyzer grating).
_____________________________
a) Authors to whom correspondence should be addressed. Electronic mail: [email protected], [email protected].
1
In this Section we describe the Talbot-Lau interferometer used in our measurements and we
summarize the basic physical principles of Talbot-Lau interferometry for multi-contrast X-ray
radiography. A recap list of the interferometer and measurement parameters is presented at
the end of the Section, in the form of a table (Table S-I), for the readers having already
knowledge about multi-contrast X-ray imaging with a Talbot-Lau interferometer.
During the capillary uptake experiment, we acquired successively X-ray radiographs with the
instrument schematically depicted in Fig. S1, consisting in a high-power X-ray source of type
COMET XRS-160 (1 mm focal spot size), a 2D Varian Paxscan 2520D flat panel X-ray
detector (1920  1536 pixels, 127  127 m2 pixel area) and a Talbot-Lau X-ray
interferometer positioned in between the source and the detector.
The Talbot-Lau interferometer is the X-ray optics instrument used, in conjunction with the
phase stepping protocol, for retrieving from a series of X-ray radiographs the three
radiographs with different contrast, due to X-ray attenuation, refraction and (U-)SAXS,
respectively.
The basic physical principle through which the three types of radiographs are retrieved is the
following.
In Fig. S1, G0, G1 and G2 are the basic components of the Talbot-Lau interferometer. These
are X-ray optics gratings realized by microworks GmbH. G0, the source grating, is in our case
made of gold, with thickness T0  160 ÷ 170 m and period p0 = 10 m, with transmitting
apertures used to convert the spatially incoherent X-ray source into a periodic array of line
sources, mutually incoherent but creating a beam of quasi-coherent radiation (Lau effect). The
X-rays impinge upon another grating, G1, called the phase grating or beam splitter. Its
function is the production of a downstream, periodic interference pattern with period p
(Talbot self-imaging effect1). G1 consists of an array of apertures, with period p1, and of a
substrate made of a partially opaque material with a selected thickness T1 such that the
cumulative X-ray phase shift through the material itself has a predefined value  at a central
energy E. In our specific case, the material is nickel, T1 = 8 m, E = 45 keV,  = /2 and p1 =
5 m. Depending upon the  value, the interference pattern achieves periodicity p of the same
order of magnitude of p1, at very specific distances, called Talbot fractional distances, dT,F.
This periodic interference pattern and its changes produced by the object are measured on a
plane positioned at one of the Talbot fractional distances. The interference pattern is measured
first in the absence of the object, then in its presence.
2
There are three types of changes produced by the object 𝑛(𝑥, 𝑦, 𝑧): X-ray attenuation
decreases the average value of the periodic (intensity) interference pattern; X-ray refraction
laterally shifts the pattern, along the x-axis; (U-)SAXS decreases the amplitude of the pattern.
If a detector with pixel size much smaller than p is positioned at the chosen Talbot distance
from G1, the periodic intensity pattern, for example, with a sinusoidal shape along the y-axis if
the gratings are periodic in that direction, can be directly measured before and after the
insertion of the object within the beam. In most applications, including the present study, the
detector has pixels with size much larger than p. In those cases, a third grating, G2, is used,
also called analyzer or absorption grating. It consists in a similar grating as G1 but with the
apertures filled in with a X-ray highly absorbing material, in our case gold, with thickness T2
= 150 m. The G2 grating has similar design as the G0 one. The periodicity of G2, p2, is equal
to p. Figure S1 shows the geometrical arrangement of the Talbot-Lau interferometer, source,
detector and sample position used in our experiment. The source-to-detector distance, dS,D,
was 2010 mm while the source-to-sample distance, dS,s, was 1235 mm, leading to a
magnification factor M for the overall imaging system equal to 1.6 and an effective pixel size
in the radiographs of 78 m. The distance between the source and G0 was dS,G0 = 80 mm,
while the distance between G0 and G1, dG0,G1, was fixed equal to dG1,G2 = dT,F = 910 mm,
corresponding to approximately the 1st fractional Talbot distance of the overall interferometer.
With such geometrical configuration and with the chosen E,  and p1, it is obtained that p = p2
= 10 m.
Moving either G2 or equivalently G1 along the direction of the gratings’ periodicity (x-axis in
our case), with displacement steps being a small fraction of p and in order to cover a distance
equal to a few times p, it is possible to resolve and reconstruct the periodic interference
pattern at each pixel of the detector by recording a radiograph in correspondence of each
displacement step. This protocol of radiograph acquisition is called phase stepping. If
performed both in the absence and in the presence of the object, it leads to two sets of
radiographs, out of which three types of radiographs of the object are retrieved.
The three types of retrieved radiographs, as functions of the pixel position on the detector
plane, (𝑥, 𝑦), are defined as
𝑃𝜇 (𝑥, 𝑦) ≡ ∫Γ(𝑥,𝑦) 𝜇(𝑥, 𝑦, 𝑧)𝑑𝛾
𝜕𝑃𝛿
𝜕𝑥
(𝑥, 𝑦) ≡
𝜕
𝜕𝑥
(S1)
(∫Γ(𝑥,𝑦) 𝛿(𝑥, 𝑦, 𝑧)𝑑𝛾 )
(S2)
3
𝑃𝜉 (𝑥, 𝑦) ≡ ∫Γ(𝑥,𝑦) 𝜉(𝑥, 𝑦, 𝑧)𝑑𝛾
(S3)
where Γ(𝑥, 𝑦) indicates a rectilinear path (``ray´´) from the center of the X-ray source to the
pixel of position (𝑥, 𝑦), 𝑑𝛾 indicates an increment of the running coordinate along the path Γ,
∫Γ(𝑥,𝑦)∙ indicates the linear projection (path integral) of a certain function of (𝑥, 𝑦, 𝑧),
𝜇(𝑥, 𝑦, 𝑧) is the X-ray linear attenuation coefficient of the investigated object, related with the
imaginary part 𝛽(𝑥, 𝑦, 𝑧) of the X-ray refractive index, 𝑛(𝑥, 𝑦, 𝑧) = 1 − 𝛿(𝑥, 𝑦, 𝑧) + 𝑖 ⋅
𝛽(𝑥, 𝑦, 𝑧), 𝜇(𝑥, 𝑦, 𝑧) = 2𝑘𝛽(𝑥, 𝑦, 𝑧), where 𝑘 is the X-ray wave number, 𝛿(𝑥, 𝑦, 𝑧) is the
decrement of the (real part of) the refractive index and 𝜉(𝑥, 𝑦, 𝑧) is the X-ray scattering
coefficient. For the physical interpretation of 𝜉(𝑥, 𝑦, 𝑧), we refer to the theoretical model
proposed by Wang et al.2 and Bech et al.3, according to which 𝜉 is the variance of the (U)SAXS angle Gaussian distribution, per unit of thickness of the object along the beam
direction.
𝜕𝑃𝛿
𝜕𝑥
(𝑥, 𝑦) is identical to the X-ray refraction angle along the x-direction, 𝛼𝑥 (𝑥, 𝑦),
and is proportional to
∂Φ
𝜕𝑥
(𝑥, 𝑦), where Φ(𝑥, 𝑦) is the cumulative phase shift between the X-
rays propagating in empty space and those passing through the object. Thus,
𝜕𝑃𝛿
𝜕𝑥
(𝑥, 𝑦) is also
called differential phase contrast radiograph.
The three types radiographs are retrieved starting by the raw radiographs (raw X-ray intensity
map) by the following image processing steps.
The X-ray intensity I recorded at any pixel (𝑥, 𝑦) varies periodically, with period p, as a
function of the relative position ∆𝐺 between G1 and G2 along the scanning (x-)axis. Being a
periodic function, it can be represented by its Fourier trigonometric series,
2𝜋
𝑠,𝑟
𝑠,𝑟
𝐼(𝑥, 𝑦, ∆𝐺) = 𝑎0 𝑠,𝑟 (𝑥, 𝑦) + ∑+∞
𝑚=1 𝑎𝑚 (𝑥, 𝑦) 𝑐𝑜𝑠 ( 𝑝 𝑚∆𝐺 + 𝜙𝑚 (𝑥, 𝑦))
2
(S4),
where the suffixes s and r refer to the phase stepping protocol performed in the presence and in
the absence of the sample, respectively.
If the interference pattern is approximately sinusoidal, the Fourier trigonometric series can be
truncated at the 1st order and its parameters, 𝑎0 𝑠,𝑟 (𝑥, 𝑦), 𝑎1 𝑠,𝑟 (𝑥, 𝑦) and 𝜙1 𝑠,𝑟 (𝑥, 𝑦), can be
obtained with best fitting methods. Once these parameters are retrieved for any pixel of
4
coordinates (𝑥, 𝑦), the three radiographs can be retrieved according to the following
formulas4-7:
𝑎 𝑠 (𝑥,𝑦)
𝑃𝜇 (𝑥, 𝑦) = −𝑙𝑛 (𝑎0𝑟 (𝑥,𝑦))
(S5)
0
𝜕𝑃𝛿
𝜕𝑥
(𝑥, 𝑦) = −
𝑃𝜉 (𝑥, 𝑦) = −
𝑝2
2𝜋𝑑𝑇,𝐹
(𝜙1 𝑠 (𝑥, 𝑦) − 𝜙1 𝑟 (𝑥, 𝑦))
(𝑝2 )2
2𝜋 2 (𝑑𝑇,𝐹 )
(S6)
𝑉𝑠
2
𝑙𝑛 (𝑉 𝑟 )
(S7)
where 𝑙𝑛(∙) indicates the natural logarithm and
𝑎 𝑠,𝑟
𝑉 𝑠,𝑟 ≡ 𝑎1 𝑠,𝑟
(S8)
0
is called the visibility of the interference pattern (the lower the visibility, the larger the (U)SAXS).
In our measurements, the method used for estimating 𝑎0 𝑠,𝑟 (𝑥, 𝑦), 𝑎1 𝑠,𝑟 (𝑥, 𝑦) and 𝜙1 𝑠,𝑟 (𝑥, 𝑦)
was based upon the 1D Fourier transform implemented via a standard FFT algorithm
available in MatlabTM.
The phase stepping protocol consisted in 8 steps over 1 period of the interference pattern (p =
10 m). The detector exposure time in correspondence of each step of the phase stepping
protocol was 0.5 s. Each phase stepping protocol execution lasted in total about 11 s (4.5 s +
integration time + delay due to the repositioning of the piezo-electric motor moving the G1
grating). During the first hour of the experiment, the phase stepping protocol was run
continuously. After the first hour, a time gap of 2 min was introduced between two successive
phase step protocols.
20 phase stepping protocols before starting the liquid uptake and 20 after it were performed in
the absence of the samples (flat field correction procedure).
5
Table S-I. List of the Talbot-Lau interferometer parameters used in the experiment.
Parameter definition
Symbol
Value
source-to-source grating distance
source grating-to-phase grating distance
phase grating-to-analyzer grating distance
source-to-detector distance
source-to-sample distance
optical magnification factor of the system
period of the source grating
thickness of the source grating
duty cycle source grating
period of the phase grating
thickness of the phase grating
duty cycle of the phase grating
design energy of the phase grating
cumulative phase shift at the design energy by the phase grating
period of the interference pattern
period of the analyzer grating
thickness of the analyzer grating
duty cycle of the analyzer grating
mean energy of the X-ray beam
acceleration voltage for the X-ray source (max value)
X-ray source current
X-ray source size
detector physical pixel size
number of pixels (horizontal  vertical)
effective pixel size (considering the optical magnification)
exposure time for each raw radiograph
total number of phase stepping protocol steps
dS,G0
80 mm
910 mm
910 mm
2010 mm
1235 mm
 1.63
10 m
 160-170 m
0.5
5 m
8 m
0.5
45 keV
/2
10 m
10 m
150 m
0.5
39 keV
60 kV
30 mA
 1 mm
127 m
1920  1536
78 m
0.5 s
8
dG0,G1
dG1,G2
dS,D
dS,s
M
p0
T0
d0
p1
T1
d1
E

p
p2 = p
T2
d2
<E>
Vp
I
f
P
NX  NY
Pe
te
Ns
3. Time-series of the attenuation and dark-field radiographs acquired during
the experiment. Description of the movie file.
The movie file of the time series of the attenuation and dark field radiographs is in MOV
format, compressed with M-JPEG codec for QuickTimeTM. It can be viewed either by
QuickTimeTM or by VLC Player.
The movie can be downloaded from the same Web page where these text Supplementary
Materials are available or by clicking on Fig. S2, that shows its initial frame, or directly from
the following URL
(http://www.calcolodistr.altervista.org/en/work/sunto/Suppl_Mats_Movie_CapillaryUptake.m
ov). The file has size of about 12.5 MBytes. A corresponding version in animated GIF format,
thus visible with any Web browser, can be also downloaded from the following URL
6
(http://www.calcolodistr.altervista.org/en/work/sunto/Suppl_Mats_Movie_CapillaryUptake.gi
f). Attention: the GIF file is 310 MBytes large.
The bright or dark line towards the bottom of each inset is due to a not completely efficient
flat field correction caused by the temporal evolution of the water surface position caused by
evaporation during the experiment.
Figure S2: first snapshot of the movie file containing the time series of the attenuation (top row) and
dark-field (bottom row) radiographs retrieved with the Talbot-Lau interferometer-based radiography
instrument during the water capillary uptake experiment. The experiment time is indicated at the
bottom left of each frame. Time 0.000 min corresponds to the beginning of the radiographic
acquisition. The frame rate is 10 frames/seconds. The experimental time gap between two frames is
about 10.98 s during the first 60 minutes, then 130.98 s till the end of the experiment (about 13
hours). The samples are C_U, C_120D and C_200D, respectively from left to right. For each type of
radiograph, the dynamic range is fixed constant at any time, as described for Fig. 1 in the article.
4. Qualitative tracking of the wetting front. Image processing approach.
In this Section, we describe the image processing approach used for determining the wetting
front position at different time instants during the experiments, as plotted in Fig. 2 of the
article.
7
We used the differential dark-field radiographs for tracing the wetting front during the
experiment. The differential dark-field radiograph at time t is obtained by subtracting the dark
field radiograph at time t0 (beginning of the experiment) from the one at time t.
The (x; y) coordinate system consists of the horizontal direction (left-right) and vertical
direction (top-bottom), respectively, of the images in Fig. 1 and Fig. S2. See also the
Cartesian coordinate system in Fig. S1.
For each of the three samples, the same procedure detailed below is carried out:
1. Select a region of interest (ROI) for each sample, including the overall sample.
Crop each time-lapsed radiograph to that ROI. For a given sample, the ROI is the
same at any time and for any type of retrieved radiograph.
2. Transform each cropped differential dark-field radiograph into an 8-bit binary
image by selecting a pixel value threshold and defining each pixel of the new
image with value 0 if its original value is below that threshold and 255 if above.
Pixels with value 0 correspond to the progressing wetting region between time t0
and time t. Pixels with value 255 correspond to regions with no significant
change due to wetting. The main boundary between the dark (pixel value 0) and
the bright (pixel value 255) regions is thus defined as the wetting front. The
remaining noise, shown as large dark dots or clusters in the bright region, is
removed by a median filter with selective parameters, consisting in redefining a
pixel value as the median pixel value calculated within a neighborhood centered
in the pixel itself, if the original pixel value deviates more than a certain threshold
value from such median value. This filter is implemented as a built-in function in
ImageJ (“Remove Outliers”)7-8.
3. For each x-coordinate in the image, the first pixel with 0 value, in direction from
top to bottom, is searched for. Its y-coordinate corresponds to the vertical position
of the wetting front at that x-coordinate. In case of no pixels with 0 value, the ycoordinate is set to the maximum, pointing to the bottom of the image. In this
way, a M  N (rows  columns) matrix, called A, is generated. M is the total
number of time steps during the experiment. N is total number of pixels along the
x-axis. Each element of such matrix is the y-coordinate of the found wetting front,
at the given time and for the given x-position within the image.
8
4. Smoothing of the wetting front at each time-step.
4.1) For each row of the matrix A, define a range of central columns where
the wetting front is smoother, using the MATLABTM in-built function
smooth(...) (9-pixel span moving window averaging algorithm).
4.2) Using the matrix elements within the smoothed region, perform a 1D
extrapolation by polynomial fitting with an approach similar to the least
squares method (in house developed MATLABTM function).
5. Removing the sampling points on the wetting front that are outside the sample
boundary.
5.1) Following the same procedures in step 1 and 2, get the sample boundary
profile within the ROI but using the attenuation radiograph at time t = t0.
5.2) Extract the coordinates of each point along the left and right boundary,
(𝑥𝑘𝑙𝑏 , 𝑦𝑘𝑙𝑏 ) and (𝑥𝑘𝑟𝑏 , 𝑦𝑘𝑟𝑏 ), 𝑘 ∈ [1, total number of rows in the ROI].
5.3) For each element in the matrix generated in step 4, search for the points
on the left and on the right boundary with the same y-coordinate. If the xcoordinate is outside the range [𝑥𝑘𝑙𝑏 𝑥𝑘𝑟𝑏 ], set that element value (ycoordinate) to NaN (not-a-number).
6. Further smoothing of the wetting front by a 1D interpolation (MATLABTM builtin function interp1(…), methods spline) for the matrix elements within
the central smoothed region, as defined in step 4.1), in order to remove NaN
values and outliers.
At each time step, i.e., along each row of the matrix A, the wetting front’s coordinates of the
left and right boundaries are defined as the first and last elements of A with non-NaN value.
The binarization of the differential dark-field radiographs at each time instant (step 2) was
suggested by the pixel value histogram at any time instant, which suggests the existence of
two pixel populations (those in a wetted region and those in a completely dry one). Figure S3
shows such histograms at three different time instants, ta < tb < tc (insets (a), (b) and (c)
respectively) for the differential dark-field radiograph of the C_200D sample. The
corresponding histograms for the two other samples exhibit similar features as the one
reported in Fig. S3. It can be observed in Fig. S3 that the population of pixels with lower
values increases with time, as a consequence of the capillary uptake.
9
The choice of the threshold for dividing the pixel population into two sub-populations was
based upon three different methods: (a) manual choice based upon the pixel value histogram
of the overall time series of differential radiographs, choosing the value in correspondence of
the crossing point of the two Gaussian-like profiles; (b) automatic choice based upon the
Ridler-Calvard binarization algorithm9 run for each differential radiograph independently; (c)
automatic choice based upon the Ridler-Calvard binarization algorithm run for the entire time
series of differential radiographs. The three different approaches led to minor variations in the
final results for the wetting front tracking. Figure S4 shows the wetting front lines obtained
with the three different methods (insets (a), (b) and (c) respectively) at the same time instants
as defined for Fig. 2 within the article and for the C_200D sample. As for Fig. 2 in the article,
the wetting fronts are superimposed to the last attenuation radiograph of the sample. It can be
seen that qualitative differences among the retrieved wetting fronts exist but mainly at a
limited number of time instants, while most of the time the difference is very subtle. The
manual choice and the automatic one for each single radiograph led to very similar results
(insets (a) and (b) in Fig. S4), while the automatic choice based upon the overall time series
led to more differences. Thus, we chose to present in Fig. 2 within the article the results
obtained with the manual choice.
Figure S3: pixel value histogram of the differential dark-field radiograph of sample C_200D at three
time instants ta < tb < tc (insets (a), (b) and (c) respectively) during the capillary uptake. ta is 1 hour
since the beginning of the uptake, when a small part of the sample gets wet. tb is about 7 hours, when
the wetting front has reached approximately the mid height of the sample. tc is close to the end of the
experiment, when more than three quarters of the sample height is invaded by water. At any time
instant, the histogram is bi-disperse with two overlapped Gaussian-like profiles corresponding to two
pixel sub-populations (wet and dry). During the capillary uptake, the number of pixels corresponding
to wetted regions increases. As a consequence, there is a net transfer of pixels from the right subpopulation (“dry pixels”) to the left one (“wet pixels”).
10
Figure S4: wetting front positions (red lines, color online) overlaid on top of a central region of
interest of the last attenuation radiograph of the C_200D sample. Different insets correspond to
different methods for the segmentation (by choice of a pixel value threshold) of the two pixel
populations for the differential dark-field radiographs (Fig. S3). (a): manual choice of the pixel value
threshold based upon the histogram of the overall time series of differential dark-field radiographs.
(b): automatic choice of the threshold by the Ridler-Calvard algorithm9 applied independently to each
differential dark-field radiograph. (c): automatic choice of the threshold by the Ridler-Calvard
algorithm9 applied to the overall time series of differential dark-field radiographs.
5. Contrast-to-noise ratio analysis
We report in this Section the results of the contrast-to-noise ratio (CNR) analysis, according
to its definition in Eq. 1 within the article. Figure S5 shows the locations of the two regions of
interest (ROIs) used to calculate the CNR for each sample. These ROIs are the red rectangles
overlaid on the samples in each radiograph type, each of which is shown at three time
instants: at the beginning of the experiment, t0 (insets (a) and (d)), after about 1 hour since the
beginning, t1 (insets (b) and (e)) and at the end, t2 (insets (c) and (f)).
The CNR values at the corresponding times and for each sample are reported in Table S-II
and S-III, respectively for attenuation and dark-field radiographs.
Figure S6 is analogous to Fig. S5 except that different ROIs have been chosen for each
sample. In this case the ROIs overlap more with large, spherical pores, called air voids and
with equivalent diameter much larger than the spatial resolution of the radiography system (80
– 150 m), thus clearly distinguishable in every type of radiograph. The CNR values
calculated in correspondence of these ROIs at the same time instants t0, t1 and t2 are reported
in Table S-IV and S-V, respectively for attenuation and dark-field radiographs.
11
The comparison of the tables shows that the CNR values have a dependence upon the choice
of the ROI, mainly for the attenuation radiographs. However, the CNR temporal evolution
with the capillary uptake process follows the same trend both in the case of Fig. S5 and of S6:
the CNR slightly decrease for the attenuation radiographs while it increases dramatically for
the dark-field ones.
The CNR is less dependent upon the choice of the ROI in the case of the dark-field
radiographs because their pixel values are more strongly dependent upon the microstructural
features, especially the local porosity, at a length scale below the spatial resolution of the
imaging system, i.e., below 80 – 150 m. The majority of the pores in the mortar samples
have equivalent diameter much below the spatial resolution and are more homogeneously
distributed in the samples than the larger pores, e.g., those which are clearly visible in both
types of radiographs. This fact is confirmed by the measurement of the cumulative pore size
distribution by Mercury Intrusion Porosimetry (MIP)11, whose data are reported in Fig. S7 for
two different samples produced with the same mix design and curing conditions as for the
samples used for the capillary uptake/radiography measurements. The MIP measurements
show that the majority of the pores have equivalent diameter much below the spatial
resolution of the radiography system.
Table S-II. Contrast-to-noise ratio (CNR) of the attenuation radiographs, calculated via Eq. 1
in the article and the two regions of interest in Fig. S5, for each sample and at the
radiographic sampling times t0 (start of the experiment), t1 (after 1 hour) and t2 (end of the
experiment).
t0
t1
t2
C_U
0.523
0.440
0.244
C_120D
0.430
0.481
0.265
C_200D
1.447
1.157
1.033
12
Table S-III. Contrast-to-noise ratio (CNR) of the dark field radiographs, calculated via Eq. 1
in the article and the two regions of interest in Fig. S5, for each sample and at the
radiographic sampling times t0 (start of the experiment), t1 (after 1 hour) and t2 (end of the
experiment).
t0
t1
t2
C_U
0
0.034
2.864
C_120D
0.473
0.658
2.777
C_200D
0.399
3.318
5.260
Figure S5: dark-field ((a), (b) and (c)) and attenuation ((d), (e) and (f)) radiographs at three different
time instants, t0 (beginning of the experiment, (a) and (d)), t1 (after one hour since the begin, (b) and
(e)) and t2 (end of the experiment, (c) and (f)), with superimposed onto them the regions of interest
(ROIs) used for calculating the contrast-to-noise ratio. For each sample, the ROIs are two, one in a
region remaining non-wetted during the overall duration of the experiment and one that becomes
wetted during the experiment. For each sample, the ROIs are the same at any time and in any type of
radiograph.
13
Table S-IV. Contrast-to-noise ratio (CNR) of the attenuation radiographs, calculated via Eq. 1
in the article and the two regions of interest in Fig. S6, for each sample and at the
radiographic sampling times t0 (start of the experiment), t1 (after 1 hour) and t2 (end of the
experiment).
t0
t1
t2
C_U
0.596
0.48
0.422
C_120D
0.232
0.282
0.141
C_200D
0.169
0.163
0.027
Table S-V. Contrast-to-noise ratio (CNR) of the dark field radiographs, calculated via Eq. 1 in
the article and the two regions of interest in Fig. S6, for each sample and at the radiographic
sampling times t0 (start of the experiment), t1 (after 1 hour) and t2 (end of the experiment).
t0
t1
t2
C_U
0.321
0.407
1.958
C_120D
0.338
0.499
2.295
C_200D
0.129
0.127
3.471
14
Figure S6: dark-field ((a), (b) and (c)) and attenuation ((d), (e) and (f)) radiographs at three different
time instants, t0 (beginning of the experiment, (a) and (d)), t1 (after one hour since the begin, (b) and
(e)) and t2 (end of the experiment, (c) and (f)), with superimposed onto them the regions of interest
(ROIs) used for calculating the contrast-to-noise ratio. For each sample, the ROIs are two, one in a
region remaining non-wetted during the overall duration of the experiment and one that becomes
wetted during the experiment. For each sample, the ROIs are the same at any time and in any type of
radiograph.
Figure S7: cumulative pore size distribution measured by a Thermoelectron Pascal 140/440 setup for
Mercury Intrusion Porosimetry (MIP)11. Two different mortar samples were measured. They were
prepared with the same mix design and curing conditions of the samples used for the capillary uptake
and radiography measurements but they were not subjected to the thermal pre-conditioning (see
Section 1). These measurements show that the majority of the pores have equivalent radius below the
spatial resolution of the radiography setup (80 - 150 m).
15
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16