## 3 Results and Discussion  
Figure 1 shows typical optical micrographs of hBN flakes with similar thicknesses of \(\approx\)135 nm on the three different SiO\({}_{2}\)/Si substrates with SiO\({}_{2}\) thicknesses of 70 nm (top), 150 nm (middle), and 280 nm (bottom). From these images, the corresponding RGB images were extracted numerically. As shown in panel (a), the region of the hBN flake with 132.9 nm thickness shows a pink color on the 70 nm substrate. A hBN flake with similar thickness (134.8 nm) on the 280 nm substrate shows a similar magenta color. In contrast, a 136.0 nm thick hBN flake deposited on the 150 nm substrate shows a very different greenish color. A clear color contrast difference between the flakes on the different substrates can also be noticed by looking separately at the RGB channels and at the gray-scale images. Panel (b) analogously shows color, RGB and gray images for thin flakes of about 6 nm on  
the three different substrates, revealing a clear color and contrast difference depending on the substrate. These exemplifying images reveal the major role played by the substrate in determining the color and contrast of the hBN flakes, calling for the need to define an optimal parameter space for the identification of specific hBN layer thicknesses. For the present work, a similar color and thickness analysis was performed for about 120 hBN flakes, thus allowing us to establish a correspondence between the RGB values and the hBN layer thicknesses. The RGB color scales, the gray-scale, and RGB/gray intensity values _vs_ hBN thicknesses obtained for the three different substrates are shown in Figure 2.  
While numerical software programs to simulate the color of thin films on substrates were developed [66; 67; 68], we found discrepancies between the simulated colors and our experimental data. These might be due to the high sensitivity of numerical [66; 67; 68] and analytical [50; 59] methods to input parameters, such as the refractive indices of the material and substrate. Our experimental data in Figure 2 might serve as a benchmark for the future optimization of such methods. The RGB/gray values feature oscillating behaviors as a function of hBN thickness that are strongly color- and substrate-dependent. While the three RGB channels separately provide information on the RGB contrast, white-light sources are typically used in optical microscopes to identify 2D flakes. To obtain an overall understanding of the magnitude of the optical contrast in an image acquired with white light, it can be useful to merge the information obtained using the RGB channels into a single, gray-scale variable: luminance. Figure 1: (**a**) Optical images (left) of three hBN flakes on SiO\({}_{2}\)/Si substrates with SiO\({}_{2}\) thicknesses of 70 nm (top), 150 nm (middle), and 280 nm (bottom). The three flakes have similar thicknesses of about 135 nm, but show a different color depending on the substrate. From the color images, the RGB channels were extracted (center). The color images were also converted to gray-scale images (right). (**b**) Same for thin flakes with a thickness of about 6 nm. Here, luminance describes the brightness of the gray-scale image. Following the BT.601 standard, the luminance, \(\rm I_{L}\), can be calculated using [69]  
\[\rm I_{L}=0.299\cdot R+0.587\cdot G+0.114\cdot B, \tag{1}\]  
where the coefficients that multiply the RGB channels reflect the human perception of brightness for different colors. The use of luminance allows for a simple methodology to obtain quantitative information on color images through a single variable, or can be also useful to analyze images acquired with microscopes equipped with black-and-white cameras. Figure 2: (**a**) Color scale showing the color of hBN flakes as a function of thickness on substrates with SiO\({}_{2}\) thickness of 70 nm (top), corresponding gray-scale (middle), and corresponding RGB/gray values (points: experimental values; lines: interpolation of the experimental points; red, green, blue and gray data correspond to the RGB/gray channels).