Reflectance Spectroscopy as a Novel Tool for Thickness Measurements of Paint Layers

Citation: Dal Fovo, A.; Martínez-Weinbaum, M.; Oujja, M.; Castillejo, M.; Fontana, R. Reflectance Spectroscopy as a Novel Tool for Thickness Measurements of Paint Layers. Molecules 2023,28, 4683. https://doi.org/10.3390/ molecules28124683 Academic Editor: Dimosthenis L. Giokas Received: 5 May 2023 Revised: 1 June 2023 Accepted: 6 June 2023 Published: 9 June 2023 Copyright: © 2023 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/). molecules Article Reflectance Spectroscopy as a Novel Tool for Thickness Measurements of Paint Layers Alice Dal Fovo 1,* , Marina Martínez-Weinbaum 2, Mohamed Oujja 2, Marta Castillejo 2 and Raffaella Fontana 1 1Consiglio Nazionale delle Ricerche-Istituto Nazionale di Ottica (CNR-INO), Largo E. Fermi 6, 50125 Florence, Italy; raf[email protected].it 2Instituto de Química Física Rocasolano, Spanish National Research Council (CSIC), C/Serrano 119, 28006 Madrid, Spain; [email protected] (M.M.-W.); [email protected] (M.O.); [email protected] (M.C.) *Correspondence: [email protected].it Abstract: A major challenge in heritage science is the non-invasive cross-sectional analysis of paintings. When low-energy probes are used, the presence of opaque media can significantly hinder the penetration of incident radiation, as well as the collection of the backscattered signal. Currently, no technique is capable of uniquely and noninvasively measuring the micrometric thickness of heterogeneous materials, such as pictorial layers, for any painting material. The aim of this work was to explore the possibility of extracting stratigraphic information from reflectance spectra obtained by diffuse reflectance spectroscopy (DRS). We tested the proposed approach on single layers of ten pure acrylic paints. The chemical composition of each paint was first characterised by micro-Raman and laser-induced breakdown spectroscopies. The spectral behaviour was analysed by both Fibre Optics Reflectance Spectroscopy (FORS) and Vis-NIR multispectral reflectance imaging. We showed that there is a clear correlation between the spectral response of acrylic paint layers and their micrometric thickness, which was previously measured by Optical Coherence Tomography (OCT). Based on significant spectral features, exponential functions of reflectance vs. thickness were obtained for each paint, which can be used as calibration curves for thickness measurements. To the best of our knowledge, similar approaches for cross-sectional measurements of paint layers have never been tested. Keywords: paintings; reflectance spectroscopy; OCT; LIBS; Raman spectroscopy; thickness measurements 1. Introduction In recent decades, a wide variety of scientific techniques have been tested and optimized for the study of cultural heritage (CH) objects. The need to preserve the material integrity of works of art has directed the research toward defining non-invasive analytical approaches based on the combined application of methodologies that do not involve sampling or risk of damage to the object. A major challenge in heritage science is the non-invasive cross-sectional analysis of the pictorial stratigraphy in paintings. Thickness measurement of the micrometric layers is essential, for instance, to monitor the removal of surface materials during the cleaning operation [ 1 ] or to assess the compactness and adhesion between layers. In a non-invasive approach, when low-energy probes are used, the presence of opaque media can significantly hinder the penetration of the incident radiation, as well as the signal collection from within the examined materials. One of the most widely used techniques for non-invasive stratigraphic measurements on paintings is Optical Coherence Tomography (OCT) [2,3]. Primarily applied in the field of ophthalmology, OCT is an interferometric method based on a Michelson interferometer, yielding 2or 3-dimensional tomographic imaging that allows the visualization of the internal structure of pictorial layers with an axial resolution ranging from 1 to 10 µ m (in Molecules 2023,28, 4683. https://doi.org/10.3390/molecules28124683 https://www.mdpi.com/journal/molecules Molecules 2023,28, 4683 2 of 17 air). The incident radiation is backscattered by the material and the optical interference is observed whenever the signal superposes with the reference beam, within the coherence length of the light source. The measurement is based on the detection of signals generated at the interfaces between different media—i.e., when the incident radiation experiences a refractive index (n) mismatch. OCT has proven particularly effective in probing materials that are semi-transparent in the near-infrared (NIR) spectral range. This includes most varnishes applied by artists on the painting surface with a protective and/or aesthetic function [ 4 ]. By combining an OCT setup with confocal microscope optics, which enables the beam focussing inside the material rather than on the outer surface, even highly reflecting coatings can be measured [ 5 ]. Pictorial layers, however, are often composed of pigments with dispersion and/or absorption properties that do not allow their thickness to be assessed by OCT. Moreover, the n-mismatch causes a delay in the optical path of the reference beam and, therefore, the optically measured distances must be corrected to geometrical distances by dividing them by the refractive index of the material. In the NIR, the refractive index of semi-transparent materials used in paintings is conventionally given as 1.5. However, pictorial layers (pigment dispersed in the binder) are often highly heterogeneous and exhibit variable optical properties that result in different n values. Therefore, if n is not known, the correct thickness of the painting layers is not achievable. In recent decades, alternative methods to OCT have been proposed for the noninvasive in-depth analysis of paintings. Among others, Terahertz imaging [ 6 , 7 ] has proven effective in yielding 3D data sets of interfaces and projections of paintings in the presence of absorbing species. However, the low axial resolution achievable with THz radiation makes this method unfit for micrometric measurements of pictorial layers. The use of Nuclear Magnetic Resonance (NMR) to obtain stratigraphic information on easel and wall paintings is also well-documented in the literature [8,9]. NMR profiling was tested to investigate both signal intensity and transverse relaxation time distribution, showing that the dependence of signal intensity on relaxation times makes the interpretation of the stratigraphic information difficult [ 10 ]. The NMR-sensitive volume averages the effect of irregularities in the layers and the signal from adjacent layers. In addition, the application of this method is hampered by the lack of application-specific operating software, while the low mass sensitivity resulting from low NMR frequencies results in long measurement times. More recently, Nonlinear Optical (NLO) techniques [ 11 ] have been successfully used for cross-sectional analysis of a wide variety of artistic materials, including paint and varnish samples. The combined application of different NLO modalities allows for the acquisition of compositional and structural information based on the detection of fluorophores (by Multi-Photon Excitation Fluorescence, MPEF), crystalline or highly organized structures without inversion symmetry (by Second Harmonic Generation, SHG), or local differences in refractive index, i.e., interfaces (by Third Harmonic Generation, THG). While for MPEF and SHG, the main limitation in the stratigraphic analysis of paintings is the presence of highly diffusing and/or absorbing media (pigments) [ 12 ], the applicability of THG is confined to layers of transparent material, forward detection being the only possible configuration [13]. A cutting-edge methodology recently proposed for cross-sectional analysis in paintings is photoacoustics, which in a sense, can be considered complementary to OCT, as it takes advantage of the presence of non-transparent materials [ 14 , 15 ]. Acoustic waves are generated by the absorption of the radiation emitted by an intensity-modulated pulsed laser. The exponential attenuation of acoustic waves in the frequency domain, which depends on the absorption coefficient of the medium and the propagation path, can be exploited to measure the thickness of the examined material. Although early applications reveal the technique’s potential [16], to date, its use is limited to specific cases only. Molecules 2023,28, 4683 3 of 17 Given the above, it can be stated that, at present, there is no technique that can uniquely and non-invasively measure the thickness of heterogeneous and optically opaque materials such as pictorial layers. In this work, we explored the feasibility of achieving stratigraphic information of painting layers from their reflectance spectra measured by Diffuse Reflectance Spectroscopy (DRS) [ 17 ]. In heritage science, DRS is typically applied for the analysis of paintings in multiand hyper-spectral imaging modes or using fibre optics for point-wise measurements. The main objective is typically the identification and mapping of pigments and binders based on the absorption properties of electronic and vibrational transitions of molecules [ 18 ]. In the imaging mode, the use of the NIR spectral range allows for the visualization of hidden details underneath the painted surface related to the artistic working process, such as underdrawings and underpaintings. Diffuse reflectance is defined as the ratio of the irradiance of light reflected back to the detector to the irradiance on the surface of the object, as a function of wavelength. The measured light backscattered from the object includes contributions from the air/surface interface and varies with illumination and collection geometry. The spectral reflectance behaviour of pigments and pictorial layers has been extensively studied [ 19 – 21 ]. It has been shown that the reflectance signal measured from pigment mixtures in paintings is the result of the nonlinear combination of the reflectance of the individual pigments. To cope with the complexity of spectral data interpretation, as well as to reduce the high dimensionality of DRS imaging datasets, new approaches based on artificial intelligence (AI), e.g., deep neural networks (DNN), have been recently explored [22]. In this preliminary study, we tested the proposed approach by examining single layers of pure paint, thus avoiding the use of optical models to predict the reflectance of pigments in mixtures [ 23 ] and not taking into account the influence of the surface roughness on the spectra [ 24 ]. A mock-up was created for this specific purpose: ten acrylic paints were laid with increasing thicknesses, ranging from 50 to 350 µ m, on both white and black backgrounds. The chemical composition of each paint was first characterised by microRaman [ 25 ] and laser-induced breakdown spectroscopy (LIBS) [ 26 ]. The thickness of each layer was then measured by OCT, taking as a reference the portion of the visible substrate at the edge of the paint layer. The spectral behaviour was analysed by both Fibre Optics Reflectance Spectroscopy (FORS) and Vis-NIR multi-spectral reflectance imaging. Finally, for each acrylic paint, meaningful spectral features were identified to assess the dependence of the reflectance on the layer thickness, thus obtaining non-linear fitting curves. To the best of our knowledge, no similar approaches have been explored before for cross-sectional measurements of paint layers. 2. Results 2.1. Chemical Characterization of the Acrylic Paints with LIBS and Micro-Raman Spectroscopy The chemical composition of the ten acrylic paints was assessed by LIBS and microRaman spectroscopies (Table 1), using the information reported in the literature [ 27 – 32 ] and NIST [ 33 ] and IRUG [ 34 ] databases. Further information on the chemical composition of the phthalocyanine paints (PBC, PBL and PGL) can be found in our previous work [ 35 ]. Figure 1shows the LIBS (top) and micro-Raman (bottom) spectra of cobalt blue (CB), cadmium red (CR), cadmium yellow (CY) and primary blue cyan (PBC) acrylic paints. The spectra measured on the other analysed paints are displayed in Figure S1 in the Supplementary Material. For all paints, the chemical composition (Table 1) agrees with what was declared by the manufacturer (Table 2), except for the absence of titanium dioxide in permanent green light (PGL) and the presence of additional components in most of the analysed paints, ascribed to the binder and fillers. Specifically, atomic emissions of Mg, Si, Ca, Al, Sr, Ba and Na detected by LIBS are ascribed to fillers such as kaolin (Al 2 Si 2 O 5 (OH) 4 ), gypsum (CaSO 4·1/2 H 2 O), carbonates (CaCO 3 , MgCO 3 ), glass powder and barite (BaSO 4 ) [ 31 ]. The molecular bands of CN (Violet band), CH and C 2 (Swan bands) are due to the acrylic binder, as well as to the organic pigments. The LIBS results obtained Molecules 2023,28, 4683 4 of 17 in these findings agree with the ones by micro-Raman spectroscopy. Bands from calcium sulfate (1007 cm −1 ), calcium carbonate (1085 cm −1 ) and barium sulfate (985 cm −1 ) are observed in each acrylic paint and attributed to the fillers. Additional bands at 482, 600, 620, 837, 841, 1106, 1150–1200, 1240, 1305, 1449, 1452, 1728, 2411 and 2800–3100 cm −1 are attributed to the constituents of the polymeric binder [27–32]. Table 1. Summary of elemental and molecular composition of the acrylic paints as found by LIBS and micro-Raman spectroscopies. The main elemental components and the Raman characteristic bands are indicated in bold. Paint Identified Elemental Components by LIBS Identified Raman Bands [cm−1] and Relative Intensities *. In Brackets the Excitation Wavelength CB Mg, Si, Co,Al,CN, Ca, Sr, C2, Na 198 m, 408 w, 512 m, 609 w, 750 w, 1007 m, 1150–1200 w, 2411 s, 2800–3100 s (λexc = 532 nm) CR Mg, Si, Cd, Al, CN, Ca, Sr, CH, C2,Ba, Na 136 s, 200 s, 269 s, 488 w, 587 s, 841 w, 985 w, 1007 w, 1150–1200 w, 1305 w, 1452 m (λexc = 632 nm) CY Mg, Si,Cd, Al, CN, Ca, Sr, CH, C2,Ba, Na 212 s, 309 s, 353 w, 600 s, 841 w, 985 w, 1007 s, 1150–1200 w, 1305 m, 1449 s, 1728 w (λexc = 632 nm) PBC Mg, Si, Al, Cu,CN, Ca, Ti, CH, C2,Na 231 w, 255 w, 482 w, 590 m, 680 m, 747 w, 837 w, 841 w, 951 w, 1007 w, 1037 w, 1106 w, 1143 w, 1150–1200 w, 1305 m, 1341 w, 1451 m, 1527 s, 1595 w, 2672 w, 2870 w, 2976 w, 3056 w (λexc = 532 nm) PBL Mg, Si, Al, Cu, CN, Ca, Ti, Sr, C2, Na 142 w, 231 m, 255 m, 433 s, 482 w, 590 s, 609 s, 680 s, 747 w, 831 w, 841, 951 w, 1007 w, 1037 w, 1143 m, 1150–1200 w, 1200 w, 1341 s, 1451 s, 1527 s, 1595 w, 2870 w, 3056 w (λexc = 532 nm) PGL Mg, Si, Cd, Al, Cu, CN, Ca, Sr, CH, C2, Ba, Na 162 w, 505 w, 620 w, 685 s, 818 m, 978 w, 985 w, 1007 w, 1080 m, 1150–1200 m, 1200 m, 1284 s, 1340 m, 1388 s, 1503 s, 1536 s (λexc = 532 nm) PRM Mg, Si, Al, CN, Ca, CH, C2,Na 841 m, 1007 w, 1150–1200, 1240 m, 1316 s, 1570 s, 1592 s, 1645 s (λexc = 632 nm) PI Mg, Si, Al, Ti,CN,Ca, C2, Na 186 m, 223 w, 261 w, 318 w, 360 w, 401 w, 525 w, 600 w, 623 w, 646 w, 802 m, 922 w, 1066 w , 1090 m, 1162 m , 1150–1200 m, 1171 m, 1266 s, 1326 s, 1351 s, 1402 s, 1489 s, 1513 s, 1500 m, 1593 s, 1667 w (λexc = 532 nm) TW Mg, Si, Ti, CN, Ca, C2, Na 138 m, 230 m, 445 s, 609 s, 841 w, 1007 w, 1452 w, 2900–3100 s (λexc = 532 nm) ZW Mg, Zn,CN, Ca, CH, C2,Na 330 w, 381 w, 435 s, 620 m, 841 m, 1007 s, 1075 w, 1150 m, 1150–1200 m, 1449 m, 1452 s, 1728 m, 2800–3100 s (λexc = 532 nm) * s: strong; m: medium; w: weak. LIBS results reported in Table 1show the presence of the main paintings markers such as Co for cobalt blue (CB), Cd for cadmium red (CR) and cadmium yellow (CY), Cu and Ti for permanent blue light (PBL), Cu for permanent green light (PBC and PGL), CN and C 2 for primary red magenta (PRM), Ti, CN and C 2 for primary yellow (PI), Ti for titanium white (TW), and Zn for zinc white (ZW). Molecules 2023,28, 4683 5 of 17 Molecules 2023, 28, x FOR PEER REVIEW 6 of 17 Figure 1. LIBS (top) and micro-Raman (bottom) spectra of cobalt blue (a,e), cadmium red (b,f), cadmium yellow (c,g) and primary blue cyan (d,h) acrylic paintings, respectively. The micro-Raman spectra are baseline subtracted. 2.2. Thickness Measurements with OCT Figure 1. LIBS (top) and micro-Raman (bottom) spectra of cobalt blue ( a , e ), cadmium red ( b , f ), cadmium yellow ( c , g ) and primary blue cyan ( d , h ) acrylic paintings, respectively. The micro-Raman spectra are baseline subtracted. Molecules 2023,28, 4683 6 of 17 Table 2. List of the ten analysed acrylic paints with their chemical composition and commercial code. Paint with Acronym Chemical Composition and Commercial Code (Maimeri Brera™) Cobalt Blue (CB) Cobalt(II) Aluminate [CoAl2O4], PB28—77346 Cadmium Red Medium (CR) Cadmium Selenide Sulphide [Cd2SSe], PR108—77202 Cadmium Yellow Medium (CY) Cadmium Sulphide [CdS], PY35—77205 Primary Blue Cyan (PBC) Copper Phthalocyanine β[C32H16CuN8], PB15:3—74160 Permanent Blue Light (PBL) Titanium Dioxide [TiO2] PW6—77891, Chlorinated Phthalocyanine [C32HCl15CuN], PG7—74260, Copper Phthalocyanine β[C32H16CuN8], PB15:3—74160 Permanent Green Light (PGL) Arylide yellow, PY97—11767, Titanium Dioxide [TiO2], PW6—77891, Chlorinated Phthalocyanine [C32HCl15CuN], PG7—74260 Primary Red Magenta (PRM) Quinacridone [C20H12N2O2], PV19—73900 Primary Yellow (PI) Arylide Yellow, PY97—11767 Titanium White (TW) Titanium Dioxide [TiO2], PW6—77891 Zinc White (ZW) Zinc Oxide [ZnO], PW4—77947 2.2. Thickness Measurements with OCT Four xz tomograms (8 × 0.6 mm 2 , pixel size 3.5 µ m 2 ) were acquired in each painted area. Given the low transparency of most of the analysed paints, the layer thickness was measured by taking the signal generated at the interface air-background (visible at the edges of each painted area) as a reference, as shown in Figure 2. The thickness of each pictorial layer was calculated as the average over 20 values, resulting in a range between a minimum of 45 µ m (area 1) to a maximum of 350 µ m (area 5) for all acrylics. For each thickness, the error, i.e., the standard deviation, resulted below 6 µ m for all areas, demonstrating the micrometric homogeneity of the paint layers. Only three acrylics, namely PBC (Figure 3), PRM, and PY, showed sufficient transparency to enable the evaluation of their refractive index, which was calculated by dividing the thickness measured with OCT by the real one. The resulting nvalues at 1300 nm, i.e., at the OCT radiation wavelength, are in the range of 1.35–1.40 for both PBC and PRM, and 1.45–1.50 for PY. Molecules 2023, 28, x FOR PEER REVIEW 7 of 17 2.2. Thickness Measurements with OCT Four xz tomograms (8  0.6 mm2, pixel size 3.5 µm2) were acquired in each painted area. Given the low transparency of most of the analysed paints, the layer thickness was measured by taking the signal generated at the interface air-background (visible at the edges of each painted area) as a reference, as shown in Figure 2. The thickness of each pictorial layer was calculated as the average over 20 values, resulting in a range between a minimum of 45 µm (area 1) to a maximum of 350 µm (area 5) for all acrylics. For each thickness, the error, i.e., the standard deviation, resulted below 6 µm for all areas, demonstrating the micrometric homogeneity of the paint layers. Only three acrylics, namely PBC (Figure 3), PRM, and PY, showed sufficient transparency to enable the evaluation of their refractive index, which was calculated by dividing the thickness measured with OCT by the real one. The resulting n values at 1300 nm, i.e., at the OCT radiation wavelength, are in the range of 1.35–1.40 for both PBC and PRM, and 1.45–1.50 for PY. Figure 2. Assemblies of OCT tomograms acquired in Cobalt Blue (CB) paint laid on white (a) and black (b) backgrounds. For each area (1–5), thickness values are reported in red and calculated as the geometrical distance between the air–paint and the paint–background interfaces, with the laer highlighted by the light-blue line. Figure 2. Assemblies of OCT tomograms acquired in Cobalt Blue (CB) paint laid on white ( a ) and black ( b ) backgrounds. For each area (1–5), thickness values are reported in red and calculated as the geometrical distance between the air–paint and the paint–background interfaces, with the latter highlighted by the light-blue line. Molecules 2023,28, 4683 7 of 17 Molecules 2023, 28, x FOR PEER REVIEW 7 of 17 2.2. Thickness Measurements with OCT Four xz tomograms (8  0.6 mm2, pixel size 3.5 µm2) were acquired in each painted area. Given the low transparency of most of the analysed paints, the layer thickness was measured by taking the signal generated at the interface air-background (visible at the edges of each painted area) as a reference, as shown in Figure 2. The thickness of each pictorial layer was calculated as the average over 20 values, resulting in a range between a minimum of 45 µm (area 1) to a maximum of 350 µm (area 5) for all acrylics. For each thickness, the error, i.e., the standard deviation, resulted below 6 µm for all areas, demonstrating the micrometric homogeneity of the paint layers. Only three acrylics, namely PBC (Figure 3), PRM, and PY, showed sufficient transparency to enable the evaluation of their refractive index, which was calculated by dividing the thickness measured with OCT by the real one. The resulting n values at 1300 nm, i.e., at the OCT radiation wavelength, are in the range of 1.35–1.40 for both PBC and PRM, and 1.45–1.50 for PY. Figure 2. Assemblies of OCT tomograms acquired in Cobalt Blue (CB) paint laid on white (a) and black (b) backgrounds. For each area (1–5), thickness values are reported in red and calculated as the geometrical distance between the air–paint and the paint–background interfaces, with the laer highlighted by the light-blue line. Figure 3. OCT results on Primary Blue Cyan paint laid on white background (PBCw); ( a ) microscope image of one of the five paint surfaces, with the red arrow indicating the location and length of the acquired section; ( b ) zoom-in of layer 3 delimited by the red rectangle in respective tomogram, enabling the assessment of the optical and real thicknesses used for calculating the refractive index of the acrylic paint; ( c ) OCT tomograms acquired on the five areas with increasing thickness (1–5), showing the transparency of the paint layer to the radiation probe. 2.3. Thickness Measurements with Reflectance Spectroscopy FORS and multi-spectral data were compared for each paint, as shown in Figure 3a–d . In the graphs, the average spectra of each painted area (1 → 5) are plotted together with the spectrum of the underlying substrate (white or black background). First and second derivatives were computed for all spectra to facilitate the identification of the spectral feature best representing the reflectance dependence on the material thickness. For all paints, the trend of the reflectance as a function of the thickness is expressed by an exponential function, following the equation: y=y0+AeR0x(1) where y= R%, y0= offset, A= initial value, R0= growth constant, and x= layer thickness. In the case of CB paint, the maximum reflectance R% values in the 808–811 and 710–760 nm ranges were selected for the white and the black background series, respectively, and plotted as a function of the thickness (Figure 4e,f). We noticed that the presence of the black background affects the position of the point of maximum reflectance, causing a blue shift as the thickness of the paint layer decreases and becomes gradually more transparent. In the presence of the white background, however, the point of maximum R remains around 810 nm regardless of the thickness of the paint layer. The resulting exponential fit curves (coefficient of determination R 2 > 0.98) show a good match between FORS and reflectance scanning results. Molecules 2023,28, 4683 8 of 17 Molecules 2023, 28, x FOR PEER REVIEW 9 of 17 Figure 4. Results of diffuse reflectance spectroscopy on Cobalt Blue (CB) paint. Spectra acquired on each thickness layer (CB1-5) with FORS (a,b) and with the multi-spectral scanner (c,d) are reported with the spectra of the background (white or black). Maximum reflectance R% values in the 808–811 and 710–760 nm ranges are plotted as a function of the five OCT thicknesses (e,f). The length of the error bars is the standard deviation of each dataset. Red lines represent the fitting exponential functions. Figure 4. Results of diffuse reflectance spectroscopy on Cobalt Blue (CB) paint. Spectra acquired on each thickness layer (CB1-5) with FORS ( a , b ) and with the multi-spectral scanner ( c , d ) are reported with the spectra of the background (white or black). Maximum reflectance R% values in the 808–811 and 710–760 nm ranges are plotted as a function of the five OCT thicknesses ( e , f ). The length of the error bars is the standard deviation of each dataset. Red lines represent the fitting exponential functions. The spectral feature selected for the analysis in the FORS spectra was not always identifiable in the spectra from the spectral cube due to the significantly lower spectral resolution of the multi-spectral scanner. Therefore, in order to evaluate the applicability of the proposed method in multi-spectral imaging mode, matching key points were found in the two datasets. With this aim, the results of PBC laid on the white background are shown in Figure 5as an example. The spectral region between 600 and 1200 nm was chosen as significant for our computation: the multi-peak FORS spectra were fitted with a Molecules 2023,28, 4683 9 of 17 5th-degree polynomial (Figure 5a) to reconstruct the shape of the multi-spectral spectrum. Maximum reflectance at 950 nm was then considered for both datasets. The resulting exponential fitting functions of the two DRS data show good accordance (Figure 5e). The same maximum was considered for the paint laid on the black background (Figure 5b,d,f) without fitting the FORS spectra to retrieve the same spectral feature. In this case, the reflectance measured on the thickest layer (PBC5 = 284 ± 10 µ m) was excluded from the exponential fitting calculation (Figure 5f), since it clearly deviated from the increasing trend, being lower than that of PBC4. This measurable thickness threshold has also been found in other pigments for thicknesses exceeding 270 microns. Remarkably, this limit of detectability was exclusively found in the FORS spectra. This is possibly due to the different measurement configurations between the two DRS modalities, which results in a greater homogeneity of illumination and, therefore, depth of detection achievable with the multi-spectral scanner than with fibre optics. Molecules 2023, 28, x FOR PEER REVIEW 10 of 17 Figure 5. FORS (a,b) and multi-spectral scanner (c,d) results on Primary Blue Cyan (PBC) paint. The R% values at 950 nm are plotted with the five OCT thicknesses (e,f). The length of the error bars is the standard deviation of the dataset. Red lines represent the exponential fitting of the experimental points. Optimal agreement between FORS and multispectral data was found in acrylics showing high transparency in the NIR range. As an example, results on PRM on a black background are shown in Figure 6a–c. As for highly scattering pigments, such as ZW shown in Figure 6d–f, an exponential fit curve could be derived only in the presence of the black background. Additionally, in this case, the detection limit found with FORS is 250 microns for both PRM and ZW, corresponding to the thickness of area 5. Figure 5. FORS ( a , b ) and multi-spectral scanner ( c , d ) results on Primary Blue Cyan (PBC) paint. The R% values at 950 nm are plotted with the five OCT thicknesses ( e , f ). The length of the error bars is the standard deviation of the dataset. Red lines represent the exponential fitting of the experimental points. Molecules 2023,28, 4683 16 of 17 9. 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