Application of Macro X-ray Fluorescence Fast Mapping to Thickness Estimation of Layered Pigments

Abstract

Even though X-ray fluorescence (XRF) is strictly an atomic method, this technique has been developed mostly at research centers for nuclear physics. One of its most valuable variations is the mapping mode that allows it to shift XRF from a punctual to an image technique. Macro X-ray Fluorescence (MA-XRF) is a widespread analytical technique applied in cultural heritage for characterizing the elemental composition of pigments with a non-destructive, rapid and green approach. When dealing with cultural heritage materials, the sustainability of the applied techniques is directly linked to the limited impact on the work of art. MA-XRF can reveal hidden sub-surface layers or restorations, but, nonetheless, it is hardly adopted for estimating the thickness of layers without resorting to complex Monte Carlo simulations or without combining information from other techniques. Exploiting the recurrent presence of lead white under pictorial layers in historical artworks, we perform a calibration on stand-alone layers produced ad hoc for the relative absorption of Pb L fluorescence lines, and then, their ratio is successfully used to estimate the thickness of azurite and ultramarine blue layers over lead white. The final result is rendered as a heatmap, easy to present to non-technical personnel frequently involved in the cultural heritage field. The new proposed procedure for calculating layer thickness extends the concept of non-invasive applications, paving the way to the possibility of performing stratigraphy without sampling.

Full text

Citation: Zito, R.; Bonizzoni, L.;
Ludwig, N. Application of Macro
X-ray Fluorescence Fast Mapping to
Thickness Estimation of Layered
Pigments. Sustainability 2024,16, 2467.
https://doi.org/10.3390/su16062467
Academic Editors: Mariateresa
Lettieri and Monia Vadrucci
Received: 18 December 2023
Revised: 7 March 2024
Accepted: 7 March 2024
Published: 15 March 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sustainability
Article
Application of Macro X-ray Fluorescence Fast Mapping to
Thickness Estimation of Layered Pigments
Riccardo Zito 1, Letizia Bonizzoni 2, * and Nicola Ludwig 2
1XGLAB—Bruker Nano Analytics, Via Conte Rosso 23, 20134 Milano, Italy
2Department of Physics A. Pontremoli, State University of Milano Italy, Via Celoria 16, 20133 Milano, Italy;
nicola.ludwig@unimi.it
*Correspondence: letizia.bonizzoni@unimi.it
Abstract: Even though X-ray fluorescence (XRF) is strictly an atomic method, this technique has
been developed mostly at research centers for nuclear physics. One of its most valuable variations
is the mapping mode that allows it to shift XRF from a punctual to an image technique. Macro
X-ray Fluorescence (MA-XRF) is a widespread analytical technique applied in cultural heritage
for characterizing the elemental composition of pigments with a non-destructive, rapid and green
approach. When dealing with cultural heritage materials, the sustainability of the applied techniques
is directly linked to the limited impact on the work of art. MA-XRF can reveal hidden sub-surface
layers or restorations, but, nonetheless, it is hardly adopted for estimating the thickness of layers
without resorting to complex Monte Carlo simulations or without combining information from
other techniques. Exploiting the recurrent presence of lead white under pictorial layers in historical
artworks, we perform a calibration on stand-alone layers produced ad hoc for the relative absorption
of Pb L fluorescence lines, and then, their ratio is successfully used to estimate the thickness of azurite
and ultramarine blue layers over lead white. The final result is rendered as a heatmap, easy to present
to non-technical personnel frequently involved in the cultural heritage field. The new proposed
procedure for calculating layer thickness extends the concept of non-invasive applications, paving
the way to the possibility of performing stratigraphy without sampling.
Keywords: MA-XRF; pigment layers; thickness determination; XRF; cultural heritage application
1. Introduction
Analyses based on the detection of characteristic X-ray fluorescence are among the
most used for application to the study of cultural heritage, encompassing PIXE (particle-
induced X-ray emission) [
1
–
3
], SEM-EDX (scanning electron microscopy–energy-dispersive
X-ray spectroscopy) [
4
,
5
] and XRF (X-ray fluorescence) [
6
–
9
]. This last acronym expressly
refers to the analysis of material obtained through X-ray fluorescence excited by X-rays; this
technique, multi-elemental and non-destructive, enables in situ analysis on a high number
of measuring points, as no actual sample collection is needed [
10
–
12
]. This last aspect, in
particular, allows us to classify XRF among the green analytical techniques, whose approach
within chemistry is to minimize, or even to eliminate, the use of toxic substances used in
the pre-treatments of the samples and the generation of waste, indeed employing screening
methods for simple on-site investigations, avoiding the processing of a large number of
samples [
13
–
15
]. This is a highly sustainable approach that minimizes the production of
hazardous waste with analytical practices that are friendly to the environment. Moreover,
the non-invasive approach allows us to perform sustainable analyses on objects as it does
not cause any damage or loss of material [16].
Even though XRF (X-ray fluorescence) is strictly an atomic method, this technique has
been developed mostly at research centers for nuclear physics [
3
,
17
–
19
] and it is considered
in several programs of the IAEA (International Agency for Atomic Agency) [
20
,
21
]. This is
Sustainability 2024,16, 2467. https://doi.org/10.3390/su16062467 https://www.mdpi.com/journal/sustainability

Sustainability 2024,16, 2467 2 of 17
due to both technical and historical reasons; indeed, radioactive sources have been used
for a long time as X-ray sources in XRF spectrometers, and the detection stage exploits
the same technology as Ion Beam Analyses (IBA) for which XRF is often a complementary
spectroscopic technique [
22
]. One of the variations of XRF is the mapping mode: elemental
analysis using MA-XRF spectrometers is non-destructive, rapid and, green, and can reveal
hidden sub-surface layers or restorations [
23
–
25
]. Thus, Macro X-ray Fluorescence [
26
] is
a non-destructive, non-contact analytical technique, widespread in the cultural heritage
(CH) domain [
27
,
28
], particularly in field activities due to its portability, resulting in
hardware being developed both by industrial companies [
29
] and in-house by research
centers [
30
–
34
]. Conceptually, MA-XRF shifts elemental analysis from a punctual to an
imaging technique [35].
2. Research Aim
The state-of-the-art MA-XRF instrumentation is represented by raster scanning, i.e.,
mapping acquisition mode, being a time- and space-ordered collection of spectra [
36
].
MA-XRF is typically adopted for elemental distribution characterization [
37
–
41
], and
also combined with several other techniques [
42
,
43
] and specific data handling [
44
]. In-
deed, even though there are works exploiting X-ray as radiation to perform stratigraphic
studies [
27
,
45
–
51
], MA-XRF has never been devoted to the determination of layer thick-
ness. Indeed, other methods can be used for 3D topography when given conditions are
present [
52
–
54
]. The present work aims at studying the thickness distribution of a pigment
layer over a lead white support through XRF mapping. The thickness of a layer is esti-
mated from the ratio of the absorption of the L lines from lead, related to the thickness
via the Lambert–Beer law. Lead was chosen due to its wide adoption as a ground layer in
artworks and in several pigments [
55
]. The instrumentation adopted in the present work
is the Bruker IRIS, a mobile MA-XRF scanning instrument from Bruker Nano Analytics
(Milano, Italy). IRIS is designed to perform in situ analysis in reduced time frames, and
this poses a major challenge for the integration time per pixel. Additionally, it must be
considered that the results from a stratigraphy may be difficult to present to non-technical
staff and to the public; this is a major issue to be considered when working in the CH
field. Suitable communication of data for artistic/historical interpretation [
56
] must be
taken into account; indeed, for this reason, we make it possible to present results through a
heatmap, an original, more effective and easier-to-interpret way of presenting information
to non-skilled final users.
3. Materials and Methods
3.1. Stand-Alone Layers (Standard for Calibration)
The pigments layers (pure pigment in binders; see Table 1for the details of thicknesses
and binders) used for the calibration of the absorption of X-ray fluorescence were painted
by the laboratory of diagnostic for artworks (DIART) of the department of Physics, State
University of Milan. The layers were produced around 10 years ago, also inducing some
aging effect on the binders; the thicknesses were measured as reported in Section 3.4.
The selected layers are all composed of azurite, an inorganic pigment regularly found
in historical paintings, with a blue color [
49
]. The layers were provided without support
and with different binders.
As a base for the layers, a 5 cm thick block of lead was used, to both mechanically
support the pigments and, at the same time, provide fluorescence of the lead lines, to
simulate a lead white infinite-thickness ground layer. This experimental approach gave us
the possibility of using relatively well-defined thicknesses, although it has some limitations
as it is a quite rough approximation for pigment layers. Indeed, the L
α
and L
β
intensities
are affected by the massive thickness of the Pb layer itself as they are subjected to different
auto-absorption depending on the finite/infinite thickness of the layer itself, as discussed
later in Section 4.3. We note here that no extraction or derivation was performed for the
less-than-infinite-thickness substrate as the thickness of the underlying layer is not known

Sustainability 2024,16, 2467 3 of 17
in real applications. Indeed, painting layers are intrinsically inhomogeneous and it is
not possible to measure the thickness of these underlaying layers with non-destructive
techniques. What we propose in the following is to use the output result as the mean value
for the thickness.
Table 1. Stand-alone layers of azurite and binders used for the method calibration.
Backing Sample
Name
Measure 1
[µm]
Measure 2
[µm]
Measure 3
[µm]
Instrument
Precision
[µm]
Average
Thickness
[µm]
σ[µm]
OC-FIX17 F4 56 68 57 1 60 7
Acetate F3 68 109 108 1 95 23
Standard A 126 128 80 1 111 27
Parafilm C1 127 136 132 1 132 5
Plastic C1 156 184 182 1 174 16
OC-FIX (Dis) B3 210 204 200 1 205 5
OC-FIX (Dis) B4 296 216 204 1 239 50
OC-FIX AR1 306 318 329 1 318 12
3.2. Layered Painting Samples (Mockup)
The experimental mockup (Figure 1), used to test the calibration obtained by the
samples described in Section 3.1, was created by DIART laboratory about 20 years ago,
so it can be considered fully aged for what concerns binder polymerization. In this study,
six regions (named A1, A2, A3, B1, B2 and B3; see Figure 1and description later in this
section) containing azurite and ultramarine blue in different layers were analyzed [
45
].
The support was wood, and the layer structure is described later in this same section. The
different horizontal darker strips on each blue layer are due to aging of the applied organic
protective varnishes, namely amber-based varnish, no varnish, glossy Dammar and mat
Dammar varnish.
Sustainability 2024, 16, x FOR PEER REVIEW 3 of 17
limitations as it is a quite rough approximation for pigment layers. Indeed, the Lα and Lβ
intensities are affected by the massive thickness of the Pb layer itself as they are subjected
to different auto-absorption depending on the finite/infinite thickness of the layer itself,
as discussed later in Section 4.3. We note here that no extraction or derivation was
performed for the less-than-infinite-thickness substrate as the thickness of the underlying
layer is not known in real applications. Indeed, painting layers are intrinsically inhomo-
geneous and it is not possible to measure the thickness of these underlaying layers with
non-destructive techniques. What we propose in the following is to use the output result
as the mean value for the thickness.
Table 1. Stand-alone layers of azurite and binders used for the method calibration.
Backing Sample Name
Measure 1
[µm] Measure 2
[µm] Measure 3
[µm]
Instrument
Precision
[µm]
Average
Thickness
[µm]
σ [µm]
OC-FIX17 F4 56 68 57 1 60 7
Acetate F3 68 109 108 1 95 23
Standard A 126 128 80 1 111 27
Parafilm C1 127 136 132 1 132 5
Plastic C1 156 184 182 1 174 16
OC-FIX (Dis)
B3 210 204 200 1 205 5
OC-FIX (Dis)
B4 296 216 204 1 239 50
OC-FIX AR1 306 318 329 1 318 12
3.2. Layered Painting Samples (Mockup)
The experimental mockup (Figure 1), used to test the calibration obtained by the sam-
ples described in Section 3.1, was created by DIART laboratory about 20 years ago, so it
can be considered fully aged for what concerns binder polymerization. In this study, six
regions (named A1, A2, A3, B1, B2 and B3; see Figure 1 and description later in this section)
containing azurite and ultramarine blue in different layers were analyzed [45]. The sup-
port was wood, and the layer structure is described later in this same section. The different
horizontal darker strips on each blue layer are due to aging of the applied organic protec-
tive varnishes, namely amber-based varnish, no varnish, glossy Dammar and mat Dam-
mar varnish.
(a) (b)
Figure 1. (a) Photo of the layers exploited to validate this study. The horizontal darker strips are due
to protective varnish made of organic elements. (b) Image reconstruction from IRIS software v.
1.3.0.11—Client Release of mapped surface reported for direct comparison with the following ele-
mental mapping elaborations.
Figure 1. (a) Photo of the layers exploited to validate this study. The horizontal darker strips are
due to protective varnish made of organic elements. (b) Image reconstruction from IRIS software
v. 1.3.0.11—Client Release of mapped surface reported for direct comparison with the following
elemental mapping elaborations.
For the A1–A3 samples, pigments (azurite on lead white, natural ultramarine—
ultramarine blue—on lead white and ultramarine blue over azurite on lead white) are

Sustainability 2024,16, 2467 4 of 17
spread in oil over a plaster priming, while for B1–B3 the same pigment combinations are
spread in egg tempera; in the following, the results will be presented for the oil layers. The
thicknesses obtained in past works from cross sections of the samples [45] are as follows:
Sample A1: 37 ±7.4 µm (azurite, upper layer) and 15 ±7.4 µm (lead white)
Sample A2: 22 ±1.5 µm (ultramarine blue, upper layer) and 7.4 ±7.4 µm (lead white)
Sample A3: 7.5
±
1.5
µ
m (ultramarine blue, upper layer), 18
±
1.5
µ
m (azurite, intermediate
layer) and 15 ±7.4 µm (lead white).
3.3. MA-XRF Instrumentation
The Ma-XRF spectrometer used was IRIS, a portable analytical instrument developed
by XGLab S.R.L. (Milano, Italy), part of the Bruker Nano Analytics Division [
57
,
58
]. It
combines two different non-destructive techniques, MA-XRF and Reflectance Spectroscopy
(RS), from visible to near-infrared (NIR). RS, not exploited in the present work, can be
useful as it can be considered to synergically integrate with XRF data in the case of pictorial
multilayers characterized by organic pigments [
59
,
60
], but also for glassy materials [
61
,
62
].
As for MA-XRF characteristics, the IRIS spectrometer has a maximum scanning speed of
42 mm s−1
and a source–object distance of about 10 mm if the system is properly aligned
using the integrated lasers. The integration time per pixel adopted was 60 ms; the X-ray
tube was 50 kV and 4 W with a rhodium anode, while the detector was a Silicon Drift
Detector (XGLab S.R.L., Milano, Italy) of 50 mm
2
with a 140 keV spectral resolution at
Mn-K
α
. The system is remotely controlled via PC, and an integrated CCD camera enables
the user to regulate the position in all directions. The device is provided as an integrated
solution from the manufacturer (XGLab), comprehensive of tube, detector, lamp and fibers,
camera, laser pointers, PC and mechanical components. The available collimators are
0.5 mm, 1 mm, 2 mm in diameter; in the present work, we used the 1 mm collimator. A
photoshoot of the measuring setup and its schematic representation are shown in Figure 2.
Sustainability 2024, 16, x FOR PEER REVIEW 4 of 17
For the A1–A3 samples, pigments (azurite on lead white, natural ultramarine—ultra-
marine blue—on lead white and ultramarine blue over azurite on lead white) are spread
in oil over a plaster priming, while for B1–B3 the same pigment combinations are spread
in egg tempera; in the following, the results will be presented for the oil layers. The thick-
nesses obtained in past works from cross sections of the samples [45] are as follows:
Sample A1: 37 ± 7.4 µm (azurite, upper layer) and 15 ± 7.4 µm (lead white)
Sample A2: 22 ± 1.5 µm (ultramarine blue, upper layer) and 7.4 ± 7.4 µm (lead white)
Sample A3: 7.5 ± 1.5 µm (ultramarine blue, upper layer), 18 ± 1.5 µm (azurite, intermediate
layer) and 15 ± 7.4 µm (lead white).
3.3. MA-XRF Instrumentation
The Ma-XRF spectrometer used was IRIS, a portable analytical instrument developed
by XGLab S.R.L. (Milano, Italy), part of the Bruker Nano Analytics Division [57,58]. It
combines two different non-destructive techniques, MA-XRF and Reflectance Spectros-
copy (RS), from visible to near-infrared (NIR). RS, not exploited in the present work, can
be useful as it can be considered to synergically integrate with XRF data in the case of
pictorial multilayers characterized by organic pigments [59,60], but also for glassy mate-
rials [61,62]. As for MA-XRF characteristics, the IRIS spectrometer has a maximum scan-
ning speed of 42 mm s−1 and a source–object distance of about 10 mm if the system is
properly aligned using the integrated lasers. The integration time per pixel adopted was
60 ms; the X-ray tube was 50 kV and 4 W with a rhodium anode, while the detector was a
Silicon Drift Detector (XGLab S.R.L., Milano, Italy) of 50 mm2 with a 140 keV spectral res-
olution at Mn-Kα. The system is remotely controlled via PC, and an integrated CCD cam-
era enables the user to regulate the position in all directions. The device is provided as an
integrated solution from the manufacturer (XGLab), comprehensive of tube, detector,
lamp and fibers, camera, laser pointers, PC and mechanical components. The available
collimators are 0.5 mm, 1 mm, 2 mm in diameter; in the present work, we used the 1 mm
collimator. A photoshoot of the measuring setup and its schematic representation are
shown in Figure 2.
Figure 2. (a) IRIS measuring setup with proper alignment over a pigment layer leaning on lead
support. (b) Schematic representation of measurement setup (L = laser pointers).
The motorized frame had dimensions of 40 cm × 60 cm, while the movement along
the measuring head axis was 2 cm from the start to the end point.
Figure 2. (a) IRIS measuring setup with proper alignment over a pigment layer leaning on lead
support. (b) Schematic representation of measurement setup (L = laser pointers).
The motorized frame had dimensions of 40 cm
×
60 cm, while the movement along
the measuring head axis was 2 cm from the start to the end point.
Data collection was performed using the IRIS control software, which automatically
collected, ordered and saved each spectrum into an HDF5 file. Each file was then processed
using a python script decompressing the HDF5 file, reading every spectrum (i.e., every
pixel’s information individually) and integrating over 3 different ROIs. The first ROI was
centered on the lead M
α
fluorescence line, and the second and third ROIs were centered,

Sustainability 2024,16, 2467 5 of 17
respectively, over the L
α
and L
β
lead lines. The extension of the ROIs was chosen as a
compromise between the ROIs adopted for the calibration, to collect a proper signal from
the higher flux of the infinite-thickness lead sample and to avoid spurious signals with
lower flux measurement in actual application. Due to the combination of short measuring
times (tens of seconds) and count rates being extremely limited in the peak regions, we did
not need to perform any background subtraction; fitting of the peaks was not applied due
to the very same reason.
3.4. Feeler for Thickness Measurement of Stand-Alone Layers
The instrumentation exploited to measure the thickness of the stand-alone pigment
layers was a feeler gauge with 0.1
µ
m sensitivity. We measured the thickness at 3 different
points and considered the average value and its standard deviation. The feeler measuring
area was 1 mm
2
. The uncertainty introduced by the feeler was small compared to variability
of the thicknesses themselves, being in the order of tens of microns; thus, the uncertainty
was mainly provided by the variability of the thickness itself, according to uncertainty
propagation.
4. Results and Discussion
The fluorescence lines used to study the thickness of the pigment layers via their
absorption were the ones emitted from lead. In particular, due to the energies of the
excitation spectrum, the energy resolution of the detector and the acquisition time per pixel,
M
α
, L
α
and L
β
were selected. The reason for using lead as a reference material is the
special role lead white has in paintings, as it was often used as a ground layer [
63
,
64
]. This
makes it a suitable reference material as source of X-ray fluorescence from the back of layers
with unknown thickness. Another primer often used in painting is calcium carbonate (or
calcite) [
65
,
66
]; this material was not taken into account in this first experimental attempt
as the calcium signal is not always visible in XRF spectra, even if the material is present in
the lower layers, due to the low energy of its characteristic X-ray emissions.
To compute the calibration curve for the azurite layers from the spectra acquired on
stand-alone layers, ROIs over the L
α
, L
β
and M
α
lead lines were collected and integrated
for each pixel. With an integration time of 60 ms, the produced background is typically
negligible, as also evident from Figure 3, so no background subtraction was computed. The
result from each pixel was then averaged and each layer provided one quadruplet (T, M, La,
Lb), where T stands for thickness, and M, La and Lb are the shortening for the absorption
edge of the respective lead fluorescence lines. The averaged values were considered for
two reasons:
i.
It is typically of no interest to evaluate the thickness over a specific pixel; instead, it is
more interesting to look at the mean layer thickness, thus working with a cluster of
pixels.
ii.
Measuring time is too low to obtain reliable results over a specific pigment unless we
consider more than one pixel, as real applications usually cannot perform multiple
measurements on the same pixel to reach a good counting statistic.
The measurement on the lead reference, that is the support lead block, is also obtained
as the average of a mapping acquisition. From these steps, the quantities I
0
for the reference
and I
x
for the x-th layer are obtained. The ratio of the two quantities is related to the
thickness T according to the Lambert–Beer law, Equation (1) [67].
Ix
I0
=e−µT≜Rx(1)
The law expressed here is derived by modeling the Poisson distribution of absorptions
in the case of a mono-elemental, homogeneous and thin medium. To address the multi-
element aspect, the equation is modified, adopting an equivalent
µ
for the mean Z of the
layer, assumed invariant for each sample of the same pigment, and for polychromatic beam

Sustainability 2024,16, 2467 6 of 17
absorption. In the case of superimposed layers, the effective absorption is the sum of the
absorptions from the individual layers. This implies that the derived calibration curve is
valid for any pigments showing an equivalent Z equal to or close to the one of the several
considered stand-alone layers of azurite spread in oil.
Sustainability 2024, 16, x FOR PEER REVIEW 6 of 17




=



≜


(1)
The law expressed here is derived by modeling the Poisson distribution of absorp-
tions in the case of a mono-elemental, homogeneous and thin medium. To address the
multi-element aspect, the equation is modified, adopting an equivalent µ for the mean Z
of the layer, assumed invariant for each sample of the same pigment, and for polychro-
matic beam absorption. In the case of superimposed layers, the effective absorption is the
sum of the absorptions from the individual layers. This implies that the derived calibra-
tion curve is valid for any pigments showing an equivalent Z equal to or close to the one
of the several considered stand-alone layers of azurite spread in oil.
In the following, the ratio Rx is used instead of µ, because the uncertainty propagation
will dramatically affect the confidence of the results. Furthermore, since this method can
be calibrated to directly relate the ratio to the thickness, the need to find a characteristic
curve for the aenuation coefficient can be bypassed. The results are shown in Figure 4,
where the dots are the values, the lines the 2-sigma uncertainty on the thickness and the
triangles are the 1sigma uncertainty on the mean ratio value.
Figure 3. Reference Lα line compared to the thickest layers available (linear scale), counts vs. keV.
Figure 3. Reference Lαline compared to the thickest layers available (linear scale), counts vs. keV.
In the following, the ratio R
x
is used instead of
µ
, because the uncertainty propagation
will dramatically affect the confidence of the results. Furthermore, since this method can be
calibrated to directly relate the ratio to the thickness, the need to find a characteristic curve
for the attenuation coefficient can be bypassed. The results are shown in Figure 4, where
the dots are the values, the lines the 2-sigma uncertainty on the thickness and the triangles
are the 1sigma uncertainty on the mean ratio value.
Sustainability 2024, 16, x FOR PEER REVIEW 6 of 17




=



≜


(1)
The law expressed here is derived by modeling the Poisson distribution of absorp-
tions in the case of a mono-elemental, homogeneous and thin medium. To address the
multi-element aspect, the equation is modified, adopting an equivalent µ for the mean Z
of the layer, assumed invariant for each sample of the same pigment, and for polychro-
matic beam absorption. In the case of superimposed layers, the effective absorption is the
sum of the absorptions from the individual layers. This implies that the derived calibra-
tion curve is valid for any pigments showing an equivalent Z equal to or close to the one
of the several considered stand-alone layers of azurite spread in oil.
In the following, the ratio Rx is used instead of µ, because the uncertainty propagation
will dramatically affect the confidence of the results. Furthermore, since this method can
be calibrated to directly relate the ratio to the thickness, the need to find a characteristic
curve for the aenuation coefficient can be bypassed. The results are shown in Figure 4,
where the dots are the values, the lines the 2-sigma uncertainty on the thickness and the
triangles are the 1sigma uncertainty on the mean ratio value.
Figure 3. Reference Lα line compared to the thickest layers available (linear scale), counts vs. keV.
Figure 4. Lead attenuation, average value of intensity per line over reference versus measured
thickness. The interpolation was made using 5 samples, thus excluding those which completely
absorb the radiation.

Sustainability 2024,16, 2467 7 of 17
4.1. Thickness–Absorption Relation from Stand-Alone Layers
For higher-thickness layers, the peak intensities are obviously lower due to the greater
absorption; in these cases, the statistical noise on the XRF spectra becomes the dominant
contribution (Figure 3).
The consequence is that the material becomes opaque, and the ratio is then insensitive
to thickness variations. Thus, the ratio is highly unstable and may increase rapidly (Figure 5,
top). This always applies to the M
α
line, which was thus excluded from the application due
to its low energy and inability to provide sensitivity at any of the considered thicknesses
(Figure 5, bottom). This could be exploited under suitable conditions, such as with increased
flux and measuring time and reduced layer thicknesses. Moreover, the energy region of the
Pb M
α
line may also present several other lines, and in that case, a simple integral over the
spectrum ROI is not enough, and gaussian fitting, or even deconvolution processing, could
be required to obtain a proper analysis and meaningful results.
Sustainability 2024, 16, x FOR PEER REVIEW 7 of 17
Figure 4. Lead aenuation, average value of intensity per line over reference versus measured thick-
ness. The interpolation was made using 5 samples, thus excluding those which completely absorb
the radiation.
4.1. Thickness–Absorption Relation from Stand-Alone Layers
For higher-thickness layers, the peak intensities are obviously lower due to the
greater absorption; in these cases, the statistical noise on the XRF spectra becomes the
dominant contribution (Figure 3).
The consequence is that the material becomes opaque, and the ratio is then insensitive
to thickness variations. Thus, the ratio is highly unstable and may increase rapidly (Figure
5, top). This always applies to the Mα line, which was thus excluded from the application
due to its low energy and inability to provide sensitivity at any of the considered thick-
nesses (Figure 5, boom). This could be exploited under suitable conditions, such as with
increased flux and measuring time and reduced layer thicknesses. Moreover, the energy
region of the Pb Mα line may also present several other lines, and in that case, a simple
integral over the spectrum ROI is not enough, and gaussian fiing, or even deconvolution
processing, could be required to obtain a proper analysis and meaningful results.
Figure 5. (Top) Three thickest layers available (opaque region). Thickness uncertainty not shown
for sake of clarity; (boom) lead Mα line, mostly insensitive to thickness variation. Uncertainty not
reported for sake of clarity.
Figure 5. (Top) Three thickest layers available (opaque region). Thickness uncertainty not shown
for sake of clarity; (bottom) lead M
α
line, mostly insensitive to thickness variation. Uncertainty not
reported for sake of clarity.

Sustainability 2024,16, 2467 8 of 17
4.2. Calibration Curve
To eliminate the dependence from the intensity of the substrate I
0
, it is possible to
exploit the ratio of the L
α
and the L
β
lines, according to the Lambert–Beer law, for the two
different energies of the lines [Equation (2)] [68,69].
Lα
Lβ
=e−x∗[µ(ELα)−µ(ELβ)] (2)
As shown in Figure 6, the ratio of the two lines can be as good a predictor as the
regression applied to the intensity of a single line over the substrate. For thickness 0, the
reported ratio is calculated from the lead substrate signals. Uncertainty on thickness is not
reported for the sake of clarity, but it can be found in previous graphics, while for the L
line ratio, the green and red points are the two-times expanded uncertainty for the ratio.
For the 205
µ
m thickness, the lower extended uncertainty value is reported to be negative,
but obviously, the true value of a thickness cannot be lower than 0. This result means that
the intensity lines could be nearly zero and thus affected by a very large error. Please note
that R-squared provides an indication of better/worse fitting of a curve compared to other
fitting curves under specific assumptions (e.g., single-variable fitting). The obtained value
indicates that measurements are affected by high scattering. The functional shape of the
curve has not been deduced from our results, but it is based on X-ray absorption laws, and
is exponential.
Sustainability 2024, 16, x FOR PEER REVIEW 8 of 17
4.2. Calibration Curve
To eliminate the dependence from the intensity of the substrate I0, it is possible to
exploit the ratio of the Lα and the Lβ lines, according to the Lambert–Beer law, for the two
different energies of the lines [Equation (2)] [68,69].




=



∗
[

(


)






]
(2)
As shown in Figure 6, the ratio of the two lines can be as good a predictor as the
regression applied to the intensity of a single line over the substrate. For thickness 0, the
reported ratio is calculated from the lead substrate signals. Uncertainty on thickness is not
reported for the sake of clarity, but it can be found in previous graphics, while for the L
line ratio, the green and red points are the two-times expanded uncertainty for the ratio.
For the 205 µm thickness, the lower extended uncertainty value is reported to be negative,
but obviously, the true value of a thickness cannot be lower than 0. This result means that
the intensity lines could be nearly zero and thus affected by a very large error. Please note
that R-squared provides an indication of beer/worse fiing of a curve compared to other
fiing curves under specific assumptions (e.g., single-variable fiing). The obtained value
indicates that measurements are affected by high scaering. The functional shape of the
curve has not been deduced from our results, but it is based on X-ray absorption laws,
and is exponential.
Figure 6. Exponential regression for the ratio of the Lα and Lβ lead lines. Uncertainty on layer thick-
ness is not reported for sake of clarity.
4.3. Thickness Maps of MOCKUP Layers
Computing the ratio of Lα line emission over Lβ line emission for lead can provide
an estimate of azurite layer thickness. The energy intervals selected for the two lines were
as follows:
10.1 keV ≤ Lα ≤ 10.9 keV 12.2 keV ≤ Lβ ≤ 13 keV
A visual representation of a spectrum with highlighted ROIs is shown in Figure 7,
left, with red bars and green bars delimiting, respectively, Lα and Lβ peaks. The spectral
peaks obtained from these regions are also shown superimposed in Figure 7, right.
The novelty of the present work lies in the application of the ratio method [69] within
a fast scan, that is, when we are dealing with a low count rate for each single spectrum, as
is typical in MA-XRF; in this case, even if we expect quite large errors, we demonstrate
that the method is highly useful to check the average thickness of pictorial layers. Indeed,
the map obtained upon integrating the whole spectrum and the one that originated from
Figure 6. Exponential regression for the ratio of the L
α
and L
β
lead lines. Uncertainty on layer
thickness is not reported for sake of clarity.
4.3. Thickness Maps of MOCKUP Layers
Computing the ratio of L
α
line emission over L
β
line emission for lead can provide
an estimate of azurite layer thickness. The energy intervals selected for the two lines were
as follows:
10.1 keV ≤Lα≤10.9 keV 12.2 keV ≤Lβ≤13 keV
A visual representation of a spectrum with highlighted ROIs is shown in Figure 7, left,
with red bars and green bars delimiting, respectively, L
α
and L
β
peaks. The spectral peaks
obtained from these regions are also shown superimposed in Figure 7, right.
The novelty of the present work lies in the application of the ratio method [
69
] within
a fast scan, that is, when we are dealing with a low count rate for each single spectrum, as
is typical in MA-XRF; in this case, even if we expect quite large errors, we demonstrate
that the method is highly useful to check the average thickness of pictorial layers. Indeed,
the map obtained upon integrating the whole spectrum and the one that originated from

Sustainability 2024,16, 2467 9 of 17
integrating around the L
α
lead peak are shown in Figure 8, upper row. In both images,
especially in the one referring to the whole spectrum, the small holes (about 2 mm
2
) left
from the sampling are evident. This aspect is quite interesting as it allows us, when applied
to real cases, to clearly highlight the presence of an eventual lack of painting materials,
and thus, to conduct mapping of the conservation state. This approach also allows us to
compare MA-XRF with imaging methods [35].
Sustainability 2024, 16, x FOR PEER REVIEW 9 of 17
integrating around the Lα lead peak are shown in Figure 8, upper row. In both images,
especially in the one referring to the whole spectrum, the small holes (about 2 mm2) left
from the sampling are evident. This aspect is quite interesting as it allows us, when ap-
plied to real cases, to clearly highlight the presence of an eventual lack of painting mate-
rials, and thus, to conduct mapping of the conservation state. This approach also allows
us to compare MA-XRF with imaging methods [35].
(a) (b)
Figure 7. Example XRF spectrum of a single pixel, showing highlights of Lead Lα and Lβ lines with red
and green vertical lines respectively (a) and Lα (black) and Lβ (red) peaks superimposed (b).
The map in the left part of the middle row in Figure 8 was obtained considering the
sulfur Kα (2.3 keV) and Kβ (2.5 keV) lines from gesso primer on the integral of the spec-
trum between 2.2 keV and 2.6 keV. In this map, the organic finishing layers are also clearly
underlined and give a different result depending on their composition and thickness. This
allows us to discriminate different surface layers on the same color/part of a painting, and
thus, to speculate about the presence of restorations. In this way, MA-XRF proves once
again to be competitive against imaging analyses, and can be considered a useful tool each
time a surface light element layer must be evaluated, as well as for detecting the presence
of patinae in metallic historical objects [70–72]. Indeed, considering emissions at such low
energies, and thanks to the high performance of the IRIS X-ray detector, it is even able to
highlight dark stains in mockups with oil as a binder due to oil spreading in the primer.
From the ROIs reported in Figure 7, the integrals were computed, and then, from the
ratio of the integrals of the two emission lines, the thickness was calculated with the in-
verted formula obtained from the calibration procedure, shown in Equation (3). The out-
put is represented, as in the right part of the middle row in Figure 8, via heatmap ploing.
The plot was created using the Python open-source library Seaborn.

=
−


.

ln
∑

(

)

.





.


∑

(

)
 



.




.

(3)
We would like to stress that the aim of this study is to provide a tool for presenting
an average estimation of the thickness of a layer to non-technical users. The discussion of
uncertainties on the experimental coefficients of the calibration and their propagation is
beyond the aim of our work, since the aim is not to provide a precise estimation of the
layer thickness (a pixel is not representative of an inhomogeneous layer), but rather, to
create a representation tool. The aim is neither to provide a metrological reference for the
thickness measurement nor to validate a theoretical curve.
The resulting map showed two issues:
i. The obtained image was transposed with respect to the actual object;
ii. The support is represented as a mid-thickness layer, which is incorrect.
Figure 7. Example XRF spectrum of a single pixel, showing highlights of Lead L
α
and L
β
lines with
red and green vertical lines respectively (a) and Lα(black) and Lβ(red) peaks superimposed (b).
The map in the left part of the middle row in Figure 8was obtained considering
the sulfur K
α
(2.3 keV) and K
β
(2.5 keV) lines from gesso primer on the integral of the
spectrum between 2.2 keV and 2.6 keV. In this map, the organic finishing layers are also
clearly underlined and give a different result depending on their composition and thickness.
This allows us to discriminate different surface layers on the same color/part of a painting,
and thus, to speculate about the presence of restorations. In this way, MA-XRF proves once
again to be competitive against imaging analyses, and can be considered a useful tool each
time a surface light element layer must be evaluated, as well as for detecting the presence
of patinae in metallic historical objects [
70
–
72
]. Indeed, considering emissions at such low
energies, and thanks to the high performance of the IRIS X-ray detector, it is even able to
highlight dark stains in mockups with oil as a binder due to oil spreading in the primer.
From the ROIs reported in Figure 7, the integrals were computed, and then, from
the ratio of the integrals of the two emission lines, the thickness was calculated with the
inverted formula obtained from the calibration procedure, shown in Equation (3). The
output is represented, as in the right part of the middle row in Figure 8, via heatmap
plotting. The plot was created using the Python open-source library Seaborn.
T=−1
0.003ln ∑10.9 keV
E=10.1 keV I(E)/∑13 keV
E=12.2 keV I(E)
1.6227 (3)
We would like to stress that the aim of this study is to provide a tool for presenting
an average estimation of the thickness of a layer to non-technical users. The discussion of
uncertainties on the experimental coefficients of the calibration and their propagation is
beyond the aim of our work, since the aim is not to provide a precise estimation of the layer
thickness (a pixel is not representative of an inhomogeneous layer), but rather, to create a
representation tool. The aim is neither to provide a metrological reference for the thickness
measurement nor to validate a theoretical curve.

Sustainability 2024,16, 2467 10 of 17
Sustainability 2024, 16, x FOR PEER REVIEW 10 of 17
The solutions we adopted are the following:
i. The information from the image was stored using the Python Pandas open-source
library, exploiting the DataFrame built-in object. DataFrames are created as tables
that collect keys in the form of [row][column]. On the contrary, the IRIS software
creates a matrix of the type [column][row][spectrum], and populates it starting from
the boom left, scanning towards the right and ending at the top right. Therefore, it
is necessary to lock the columns and range on the rows.
ii. Since the wood support presents noise in the lead line regions, due to backscaered
radiation from the excitation source, the contrast can be highly increased considering
a threshold to be overcome by at least one of the ROIs’ integrals. That threshold was
set as the number of bins in the ROI times a constant of 1.1.
Sustainability 2024, 16, x FOR PEER REVIEW 11 of 17
Figure 8. Upper row—result from whole XRF spectrum integration (left) and result from Pb Lα
integration (right). Middle row—left: integrated count map between 2.2 and 2.6 keV, where the
bands and pigment layers are clearly visible considering sulfur K line aenuation, emied from the
gesso primer; right: straightforward computation of thicknesses example. Lower row—fast-scan-
ning thickness map (left) and high-resolution thickness map (right).
The output from the fast acquisition and from the high-spatial-resolution acquisition
obtained after these implementations are shown, respectively, in the lower row of Figure
8. The parameters of the acquisitions are described in Table 2.
Table 2. Acquisitions parameters.
Fast Scanning High-Resolution Scanning
Time [s] 389.1 1188.0 s
Number of pixels 99 × 132 200 × 199
Pixel dimensions [mm × mm] 2 × 1.512 1 × 1
Collimator diameter [mm] 2 1
Integration time [ms/pixel] 30 30
Current [mA] 100 200
Tension [kV] 50 50
Filtering, anode materials No filter, Rh No filter, Rh
Applying Equation (3), an estimation of the local thickness is provided. Every pixel
providing a ratio over 1.7 was set to 0 thickness, representing the value from lead direct
fluorescence.
From both the fast-scanning and high-resolution acquisitions, the thickness map was
thus successfully obtained. It is worth recalling that fast and high-resolution scans are
performed with different integration times and collimator diameters. Due to inhomoge-
neity of the substrate, the difference in collimator diameters may affect the output result
of the thickness estimation, since the averaging effect of a smaller collimator is reduced
compared to a larger one, producing different results, as evident in Figure 8.
The mean estimated thicknesses of azurite of the three samples spread in oils (A1, A2
and A3 in Figure 1) are, respectively, A1 = 93 ± 59 µm, A2 = 63 ± 63 µm and A3 = 96 ± 58
µm. The expected thickness for azurite layers, reported in Section 3.2, are 37 ± 7.4 µm for
A1, no azurite layer for A2, and 18 ± 1.5 µm for A3. For the A1 layer, the thickness estima-
tion is coherent, inside the error, with the one measured from the cross section. For A2, a
layer made of ultramarine blue alone (no azurite present, so no Cu signal besides the back-
ground), the result is negligible, and this indicates the absence of the investigated pig-
ments and the Cu signal to be below the detection limit of the spectrometer. Moreover, in
Figure 8. Upper row—result from whole XRF spectrum integration (left) and result from Pb L
α
integration (right). Middle row—left: integrated count map between 2.2 and 2.6 keV, where the
bands and pigment layers are clearly visible considering sulfur K line attenuation, emitted from the
gesso primer; right: straightforward computation of thicknesses example. Lower row—fast-scanning
thickness map (left) and high-resolution thickness map (right).
The resulting map showed two issues:
i. The obtained image was transposed with respect to the actual object;

Sustainability 2024,16, 2467 11 of 17
ii. The support is represented as a mid-thickness layer, which is incorrect.
The solutions we adopted are the following:
i.
The information from the image was stored using the Python Pandas open-source
library, exploiting the DataFrame built-in object. DataFrames are created as tables
that collect keys in the form of [row][column]. On the contrary, the IRIS software
creates a matrix of the type [column][row][spectrum], and populates it starting from
the bottom left, scanning towards the right and ending at the top right. Therefore, it is
necessary to lock the columns and range on the rows.
ii.
Since the wood support presents noise in the lead line regions, due to backscattered
radiation from the excitation source, the contrast can be highly increased considering
a threshold to be overcome by at least one of the ROIs’ integrals. That threshold was
set as the number of bins in the ROI times a constant of 1.1.
The output from the fast acquisition and from the high-spatial-resolution acquisition
obtained after these implementations are shown, respectively, in the lower row of Figure 8.
The parameters of the acquisitions are described in Table 2.
Table 2. Acquisitions parameters.
Fast Scanning High-Resolution Scanning
Time [s] 389.1 1188.0 s
Number of pixels 99 ×132 200 ×199
Pixel dimensions [mm
×
mm]
2×1.512 1 ×1
Collimator diameter [mm] 2 1
Integration time [ms/pixel] 30 30
Current [mA] 100 200
Tension [kV] 50 50
Filtering, anode materials No filter, Rh No filter, Rh
Applying Equation (3), an estimation of the local thickness is provided. Every pixel
providing a ratio over 1.7 was set to 0 thickness, representing the value from lead direct
fluorescence.
From both the fast-scanning and high-resolution acquisitions, the thickness map was
thus successfully obtained. It is worth recalling that fast and high-resolution scans are
performed with different integration times and collimator diameters. Due to inhomogeneity
of the substrate, the difference in collimator diameters may affect the output result of the
thickness estimation, since the averaging effect of a smaller collimator is reduced compared
to a larger one, producing different results, as evident in Figure 8.
The mean estimated thicknesses of azurite of the three samples spread in oils (A1,
A2 and A3 in Figure 1) are, respectively, A1 = 93
±
59
µ
m, A2 = 63
±
63
µ
m and
A3 = 96 ±58 µm.
The expected thickness for azurite layers, reported in Section 3.2, are
37 ±7.4 µm
for A1, no azurite layer for A2, and 18
±
1.5
µ
m for A3. For the A1 layer,
the thickness estimation is coherent, inside the error, with the one measured from the
cross section. For A2, a layer made of ultramarine blue alone (no azurite present, so no
Cu signal besides the background), the result is negligible, and this indicates the absence
of the investigated pigments and the Cu signal to be below the detection limit of the
spectrometer. Moreover, in cases whereby a Cu signal is present from impurities of the
materials layered, the calibration obtained in this work would obviously not be useful for
calculating the lapis lazuli layer thickness. For the A3 layer, the obtained average thickness
is highly overestimated and not in good agreement with measured one. In this peculiar
case, the azurite layer is not the upper layer, but it is covered by an ultramarine blue
layer. Considering the chemical composition of lapis lazuli [
73
], which can be written as
(Na,Ca)
8
(SO
4
,S,Cl)
2
(AlSiO
4
)
6
, and also considering the dilution in linseed oil, which can be

Sustainability 2024,16, 2467 12 of 17
considered to be linoleic acid [
45
], the variation in the absorption coefficient, respectively,
for the L
α
and L
β
Pb lines does not significantly affect the ratio. Once again, we cannot use
the obtained calibration for calculating the thickness of the lapis lazuli layer.
A fundamental aspect to be taken into account is that, as already indicated in
Section 3.1,
underlying lead white layers in paintings do not have infinite thickness [
74
]; in extreme
cases, the lead-based preparatory layer can be so thin that no signal from lead would pass
the azurite layer, even if it is a rare situation. It is worth noting that the overestimation
of the layer thickness is due, in part, to the strong hypothesis made when performing the
calibration: the lead support must be sufficiently thick to be approximated as infinite for X-
ray penetration compared to the pigment layer thickness. That is, the actual lead white layer
could produce fewer L signals. It has been demonstrated [
68
] that the value for Au (La/Lb),
due to self-attenuation, does not change in an appreciable manner with thickness, reaching
an almost constant value for a thickness of about 20
µ
m, implying that the results for the A1
layers are less affected by this aspect. As shown from the invasive analysis results [
45
], the
lead white layer is typically thinner than the blue layer, so the fluorescence from the lead
cannot build up completely, resulting in L
β
line underestimation and subsequent thickness
overestimation. This effect can be effectively mitigated by calibrating the instrument on
lead white pigment layers instead of a thick block of metallic lead. For metals, it has been
demonstrated that when the incident radiation is sufficiently higher than the absorption
edge, the ratio in the case of infinite thick and thin samples can be calculated as the ratio of
the linear attenuation coefficient (in cm
−1
) at the energy of its L
α
with that one at the energy
of its Lβ[69]. This could suggest a correction factor to use for refining of our method.
A further aspect to be taken into account to explain the difference from the measured
thickness of the A3 sample is the percentage of binder in the pictorial layers, which may
vary with the different adsorption properties of the pigments themselves, i.e., azurite and
lapis lazuli may require different oil concentrations to be conveniently applied. In this
regard, the results obtained in the already quoted work [
45
] on the same mockups also
show an overestimation of the azurite layer when it is supposed to be in a mixture with
90% binder, which is the case for our stand-alone calibration samples.
We must thus keep in mind that this kind of calculation must forcibly be considered for
estimations, as it is also an estimation of the measured average value over a hand-layered
pigment; in fact, the pigment layers spread out by a brush by the artist’s hand, as in our case,
makes the layers not constant in thickness. Indeed, the non-uniform layers are highlighted
in the reported thickness maps and are also evident from the large errors reported in the
thickness determination obtained by cross-section measurements [45].
Moreover, in real cases, lead can be present in pigment layers, as white lead in mixtures,
or as lead-based pigment, such as lead-based yellows or reds; in these situations, this
method is obviously not applicable.
5. Conclusions
When dealing with analyses of art objects, sustainability must be intended regarding
the possibility of performing material characterization with virtually no impact on the
object itself. In the present paper, MA-XRF—a strictly non-invasive technique—is exploited
to evaluate pigment layer thickness. The measuring of several azurite layers of increasing
thicknesses allowed us to effectively produce a calibration curve, which mapped the ratio of
the intensities of the transmitted fluorescence of L
α
and L
β
lines on a lead-based supporting
block through the layers to the thickness of these layers. After the calibration curve was
obtained, the method was tested on a group of layers of azurite and ultramarine blue with
the thicknesses of the whole structure measured. The resulting heatmaps can be useful in
presenting the results and obtaining an estimate of the thickness of the pigment depositions.
Thickness maps are an effective tool both for conducting a more accurate analysis of
the pigments on a painting and as preliminary screening to identify areas for an invasive
analysis. The obtained results demonstrate that typical scanning times are sufficient to
apply this method. The methodology can be applied using a unique calibration curve

Sustainability 2024,16, 2467 13 of 17
in the case of pigments with a mean Z equivalent, simplifying the calibration procedure.
Furthermore, heatmaps are easier to present both to the public and to non-scientific staff,
helping in results communication and project validation.
The present research can be extended in terms of both the analytical techniques employed
and in terms of pigments and testing, and finally, in terms of data analysis. The X-ray tech-
nique can be complemented by other techniques, such as Reflectance Spectroscopy [
75
–
78
],
or X-ray Diffraction [
79
–
81
], also using its Synchrotron-based version [
82
,
83
], or other
techniques [84–86],
like Optical Coherence Tomography (OCT) [
87
,
88
] and Terahertz To-
mography [
89
–
91
]. This approach would give two main benefits: better characterizing
multi-layer thicknesses and accounting for pigment dilution.
In terms of pigments, there are a huge number of pigments that can be measured
to obtain specific calibration curves, and also the effects introduced by the superposition
of layers.
Finally, the data analytics procedure can be improved by introducing image processing
to further increase the contrast and enhance the edges. The source of the high uncertainty
achieved is related mainly to a lack of uniformity over the pigment layers, adequate for
human handwork processes over dimensions in the order of tens of microns, and to short
measuring time; recall that the time per pixel employed was 0.03 s. Finally, it is important
to consider that in such an application the objective is to obtain an estimate of the order of
magnitude of the thickness of a sample, such as tens or hundreds of microns.
The maps show that the simple correlation from the Lambert–Beer law can provide
meaningful results and can be applied to portable X-ray instrumentation once the calibra-
tion curves are provided.
We can therefore observe another interesting result from the Bruker IRIS MA-XRF
scanner, which is the possibility to detect the different varnish layers from the absorption
on Sulfur K lines and to clearly show the conservation state of an investigated painting.
This non-invasive approach paves the way to the fully sustainable evaluation of layer
thickness, avoiding sampling and thus the use of toxic substances and the generation of
waste. XRF proved once again to allow fast and simple on-site investigations without
the necessity of processing a large number of samples, thus going in the direction of the
sustainable and responsible preservation and management of cultural heritage materials.
Author Contributions: Conceptualization, R.Z., L.B. and N.L.; methodology, R.Z., L.B. and N.L.; inves-
tigation, R.Z.; data curation, R.Z.; writing—original draft preparation, R.Z. and L.B.;
writing—review
and editing, L.B. and N.L.; supervision, N.L. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data are available on request to the corresponding author.
Acknowledgments: The authors would like to especially thank XGLab, Alessandro Tocchio and
Michele Occhipinti for their availability in operating the IRIS instrument and their technical assistance
related to the instruments.
Conflicts of Interest: Author Riccardo Zito is employed by XGLAB—Bruker Nano Analytics. The
remaining authors declare that the research was conducted in the absence of any commercial or
financial relationships that could be construed as a potential conflict of interest.
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