## 4 Results and Discussion
Figure 5 shows a linear fitting comparison between values obtained using the SNIPBG method and without considering any background contribution. Different gold leaf thicknesses were simulated, from 0.25 \(\upmu\)m up to 2.0 \(\upmu\)m, on top of a pure lead substrate. Lead L-lines present a considerably higher signal-to-noise ratio that can better highlight the background contribution effects. It must be observed that the simulation setup used to account for background contributions does not represent the experimental setup. Its purpose was to emphasize any contributions, if present, and point out if corrections must be made and when. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{4}{c}{**Average Gilding Thickness (\(\upmu\)m)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**With Resin**} & \multicolumn{2}{c}{**Without Resin**} \\ \cline{2-5}  & Mean & Std. deviation & Mean & Std. deviation \\ \hline Simulated Sample & 0.35 \(\upmu\)m & 0.01 \(\upmu\)m & 0.19 \(\upmu\)m & 0.01 \(\upmu\)m \\ Real Sample\({}^{\text{\textdagger}}\) & 0.16 \(\upmu\)m & 0.09 \(\upmu\)m & 0.23 \(\upmu\)m & 0.13 \(\upmu\)m \\ \hline \multicolumn{5}{c}{\({}^{*}\) AoI B contains 715 sampled spectra; \({}^{*}\) AoI C contains 250 sampled spectra.} \\ \end{tabular}
\end{table} 
Table 1: Average golf leaf thickness calculated over AoIs B (with resin) and C (without resin). Figure 4: Transmission of Ti-K\(\upalpha\) and Ti-K\(\upbeta\) lines through a resin layer (11 wt% H, 11 wt% O, and 78 wt% C). It can be observed that in the lower end, for very thin leaves, the background contribution does not significantly impact the results. As the overlapping layer thickness increases, discrepancies start to appear, and a background estimation method is required to achieve the best results. To assess if any difference would be noticed in the experimental data (acquired with a Ta-target tube), and because the simulated data (Figure 5) was obtained using a different, Ag-target tube profile, the prepared sample was also evaluated without background subtraction. This factor can be crucial when verifying the influence of background effects on the thickness calculations, as different tubes will present different emission spectra. In any case, the mean thickness values were not significantly impacted. AoI B + AoI C mean thickness, considering the background contribution, was \(0.18\pm 0.10\)\(\upmu\)m vs. \(0.17\pm 0.10\)\(\upmu\)m without it. Moreover, the relatively low counts of the present MA-XRF dataset are not enough to create an appreciable continuum which, in this case, can be disregarded. A 3D-heightmap of the thickness values calculated for AoIs B and C is shown in Figure 6. A concentration of slightly higher values is observed in the rightmost part of AoI C.  
The grouped bins histograms of AoI B and C are shown in Figure 7. The distributions shown in the histograms exhibit an asymmetric shape (with skewness values 0.51 and 0.85, respectively) and a deviation from a normal distribution is evident for AoI C (kurtosis 1.1). As for AoI B, it can be observed that the calculated thicknesses are slightly inaccurate (more than 50% of the calculated thicknesses are lower than 0.15 \(\upmu\)m). However, it is useful to underline that the means in Table 1 are calculated from histograms and, therefore, can be affected by the distribution shape as underlined above. The inaccurate results may be, in a first approach, attributed to the presence of resin, which presents significantly different physical properties compared to the gold leaves, introducing several outliers to the distribution, and changing the histograms' appearance (truncated distribution). The resin presence is not accounted for by the measuring system (Equation (1)), and, as previously discussed, will introduce systematic under- or overestimations.