## 4 Results and Discussion  
Figure 3 shows the AoIs where thickness calculations were performed. Brighter spots present in the outbounds of AoI B are probably due to manufacturing defects and indicate a more intense signal of gold where attenuation effects are probably higher. For this reason, brighter spots were avoided. Area of Interest C was selected from the sample's region C rightmost portion (Figure 1). Manufacturing defects are clearly present in the lower-right part and were left outside. A total of 3320 spectra were evaluated to calculate the net peak areas and generate the elemental distribution maps. For the thickness calculation over the whole gilded area, 1368 spectra were considered; for AoIs B and C, 965 spectra were considered. The simulated spectra obtained from MC simulations were analyzed, and the mean thickness value obtained disregarding the resin layer (volume simulating region C) was \(0.19\pm 0.01\)\(\upmu\)m, demonstrating that the proposed algorithm and methodology is accurate and precise when evaluating the simulated spectra. High precision was expected when evaluating the simulated spectra, as the linear attenuation parameters for Equation (1) could be exactly set. When evaluating the simulated spectra representing region B, where a 50 \(\upmu\)m thick resin layer is present as an adhesive intermediate layer, the obtained gold leaf thickness is almost doubled: \(0.35\pm 0.01\)\(\upmu\)m. This may be due to the logarithmic nature of Equation (1), where small changes in the measured peak ratio cause large changes in the calculated thickness value, highlighting the need for a proper calculation or measurement of the substrate _thick ratio_. For the calculations, the parameters of Equation (1) remained unchanged, since the linear attenuation factors considered are solely those of the layer whose thickness is being estimated (i.e., the gold layer) and the _thick ratio_ is that of the substrate. Therefore, any further attenuation titanium lines have undergone, caused by the resin layer, could not be accounted and systematic errors were introduced, exaggerated by the logarithmic function. A workaround has been proposed by [PERSON] et al. [9], modifying Equation (1) to account for additional attenuation effects caused by a coating layer. In Figure 4, a significant decrease in the Ti-K-lines signal intensity can already be appreciated while traversing a 10 \(\upmu\)m thick resin layer. At 50 \(\upmu\)m thickness, about 20% of the Ti-K\({}_{\alpha}\) signal is absorbed by the layer. Figure 3: Elemental distribution map of Au-L series and areas of interest (AoIs) selected for calculating the gold leaf thickness. The calculated average thickness distribution obtained for AoI B and C are given in Table 1. Different from what was observed in the simulated spectra, there is no significant or immediately observable difference between the values (considering the standard deviation). This may be due to the statistics of the MA-XRF dataset, presenting a higher number of samples, and spectra with lower count statistics compared to traditional XRF spot analysis. Firstly, it must be noticed that the effective thickness of the resin applied to the substrate after drying can be considerably smaller than the 50 \(\upmu\)m used in the simulations, as previously mentioned. Secondly, the simulated resin layer is considered as a dense and homogeneous layer, disregarding the existence of pores or air between resin and gold leaf, which can result in a further increase in the attenuation effects compared to what is experimentally observed. The effects of a thinner resin layer and the presence of air (considering the sample was not burnished) are competitive; a thinner layer results in less observable effects in the final results as the presence of air reduces the layer (in this case resin + gold leaf) linear attenuation coefficients, resulting in a slightly overestimated result. The influence exerted by the background contribution over the calculated mean thickness was also tested with Monte Carlo simulated spectra.