In order to understand the dynamics of granular flows, one must have knowledge about the solid volume fraction. However, its reliable experimental estimation is still a challenging task. Here, we present the application of a stochastic-optical method (SOM) [L. Sarno et al., Granul. Matter 18, 80 (2016)10.1007/s10035-016-0676-3] to an array of spheres arranged according to faced-centered cubic lattices, where spheres' locations are known a priori. The purpose of this study is to test the robustness of the image binarization algorithm, introduced in the SOM for the indirect estimation of the near-wall volume fraction through an optically measurable quantity, defined as two-dimensional volume fraction. A comprehensive range of volume fractions and illumination conditions are numerically and experimentally investigated. The proposed binarization algorithm is found to yield reasonably accurate estimations of the two-dimensional volume fraction with a root-mean-square error smaller than 0.03 for all investigated illumination conditions. A slightly worse performance is observed for samples with relatively low volume fractions (<0.3), where the binarization algorithm occasionally cannot identify the surface elements in the second and third layers of the regular lattice.