Fig. 3: Binary code matrices generated from nanopattern features.

a Example of binary code matrix extraction from positive phase defects of the self-assembled binarized nanopatterns (nanopattern engraved on a SiO₂ substrate) and (b) resulting binary code matrix of 10 × 10 pixels where white color represents the presence of a defect in the corresponding pixel area. c Bit uniformity of binary code matrices (red dots) and fractional HD between different binary code matrices (inter-HD, blue dots) as a function of the pixel size. Green line and shade represent the mean and standard deviation of the correlation length (ξ), respectively. d Fractional inter-HD versus bit uniformity, (e) unit entropy of binary code matrices versus bit uniformity (entropy was not evaluated for pixel sizes of 595 and 476 nm, since in this case it was observed a not null probability of having all 1-bit values across the matrix). In (c–e), dots are mean values while error bars represent the standard deviation calculated by considering 200 different binary code matrices obtained from different nanopattern images (area of 2.38 × 2.38 µm²). f Distribution of bit uniformity of binary code matrices, (g) distribution of fractional inter-HD, (h) heat-map matrix representing the fractional HD between each couple of binary code matrices (HD = 0 in case of intra-HD values on the diagonal where the image is compared with itself), and i. maximum encoding capacity of the system as a function of the image area (code matrices with pixel size of 238 × 238 nm² have been considered). j Analog code matrix where the pixel color represents the defect type. The pixel is blue in presence of positive phase dot defects; pixel is red in presence of positive phase terminal point defects; pixel is yellow in presence of positive phase 3-way junction defects; pixel is green in presence of positive phase dot and positive phase terminal point defects; pixel is orange in presence of positive phase point and positive phase 3-way junction defects; pixel is violet in presence of positive phase dot, positive phase terminal point, and positive phase 3-way junction defects.