## 3 Results and Discussion
The color/gray-scales and RGB/gray values for SiO\({}_{2}\) thicknesses of 150 nm, and 280 nm are shown in panels (**b**) and (**c**), respectively. Starting from the RGB/gray intensity values, we can calculate the corresponding contrast. The optical contrast for a specific wavelength \(\lambda\) is defined as  
\[\mathrm{C(t,\tilde{n},\lambda)}=\frac{\mathrm{I_{sub}(\lambda)-I_{fake}(t,\tilde {n},\lambda)}}{\mathrm{I_{sub}(\lambda)}}, \tag{2}\]  
where I is the reflected light intensity and where the dependence from the complex refractive index of the material \(\tilde{n}\) and its thickness t are made explicit. \(\mathrm{I_{sub}}\) and \(\mathrm{I_{fake}}\) further depend on the refractive indexes of SiO\({}_{2}\) and Si and on SiO\({}_{2}\) thickness. \(\mathrm{I_{sub}(\lambda)}\) and \(\mathrm{I_{fake}(t,\tilde{n},\lambda)}\) can be computed as discussed in ref. [50]. However, this only allows for a direct comparison with experiments if the optical images are acquired under illumination at a specific wavelength, while a more complex theoretical framework is needed to calculate the RGB color values under white-light illumination [59]. Here, we similarly define the contrast \(\mathrm{C_{X}}\) as  
\[\mathrm{C_{X}(t)}=\frac{\mathrm{I_{X,sub}-I_{X,flake}(t)}}{\mathrm{I_{X,sub}}}, \tag{3}\]  
where X = R, G, B, L (L is the luminance, representing the gray-scale). Experimental values of \(\mathrm{C_{X}(t)}\) can be obtained from the intensity values provided in Figure 2, where the intensity of the substrate corresponds to hBN thickness t = 0 (\(\mathrm{I_{X,sub}=I_{X,flake}(t=0)}\)). A comparison between the RGB and gray-scale contrast obtained for the three SiO\({}_{2}\)/Si substrates with SiO\({}_{2}\) thicknesses of 70 nm, 150 nm, and 280 nm is presented in Figure 3.  
We performed a similar analysis for substrates with SiO\({}_{2}\) thicknesses of 90 nm, 215 nm, 271 nm, and 297 nm, starting from data available in the literature. In particular, (i) we considered the RGB values measured by [PERSON] et al. for hBN flakes on SiO\({}_{2}\)/Si substrates with SiO\({}_{2}\) thicknesses of 90 nm, as reported in Supplementary Table S1 of Ref. [59], and (ii) we determined the RGB values by analyzing the optical micrographs shown by [PERSON] et al. in Figure 15d-f of Ref. [55] for substrates with SiO\({}_{2}\) thicknesses of 215 nm, 271 nm and 297 nm. In both cases, the RGB values were interpolated, and the optical contrast was then calculated using Equation (3). The combined analysis of our experimental data and of those available in the literature allows us to explore the phase-space of hBN and SiO\({}_{2}\) thicknesses in order to identify the most suitable substrate for a desired target hBN thickness. This analysis is summarized in Figure 4a for RGB and gray-scale contrasts as 2D plots displaying the contrast magnitude \(\var  
Figure 3: RGB/gray contrast as a function of hBN thickness for substrates with SiO\({}_{2}\) thicknesses of 70 nm, 150 nm, and 280 nm. While the absolute contrast provides information on the visibility of flakes of a given thickness, for thin flakes, it is often needed to be able to discern contrast _variations_ to determine the number of layers. In that case, both the absolute value and the variance of the contrast are of importance. The latter can be quantified by the derivative of the contrast with respect to the hBN thickness t:  
\[\mathrm{D_{X}}=\frac{\mathrm{d}\mathrm{C_{X}}}{\mathrm{dt}}, \tag{4}\]  
where X = R, G, B, or L. The contrast derivative obtained from RGB and gray-scale data for all substrates is displayed in Figure 4b. Inspecting Figure 4a,b reveals that the choice of the most suitable substrate for the identification of hBN depends on the desired thickness. Figure 5 provides a zoomed-in overview of the plots of Figure 4 in the thin limit range, from 0.3 to 30 nm.