Computational methods in nanometrology: the challenges of resolution and stochasticity

Nanometrology is vital for the advancement of nanotechnology but faces significant computational demands due to the complexity of measurements at the nanoscale. This review identifies two primary challenges: first, achieving super-resolution in microscopy imaging, where capturing detailed nanoscale information over large areas is handled with various strategies; second, characterizing the stochastic nature of nanostructure morphologies, which requires advanced methods to accurately analyze random and disordered features. We examine the limitations of existing image enhancement techniques and explore computational strategies for analyzing both discrete and continuous nanostructured surfaces. Addressing these challenges emphasizes the critical need for developing new computational methods to enhance precision and reliability in nanoscale measurements, thereby fostering continued innovation in nanotechnology.