Perforated structures and methods for forming perforated structures are disclosed. The perforated structures include partial holes or blind-holes that pass partially through the substrate. The partial holes can be positioned proximate to through-holes that pass entirely through the substrate. The partial holes add mechanical strength to the perforated substrate. Described are methods for modifying the optical appearance of the partial holes such that the partial holes appear indistinguishable from the through-holes, which allows for flexibility in designing cosmetically appealing patterns within the perforated structures.