• Quantifying and enforcing two‐dimensional symmetries in scanning probe microscopy images

The overall performance and correctness of the calibration of all kinds of traditional scanning probe microscopes can be assessed in a fully quantitative way by means of “crystallographic” processing of their two‐dimensional (2D) images from samples with 2D periodic (and preferably highly symmetric) features. This is because crystallographic image processing results in two residual indices that quantify by how much the symmetry in a corresponding scanning probe microscopy image deviates from the symmetries of the possible plane groups of the periodic features of the sample. When a most probable plane symmetry group has been identified on the basis of crystallographic image processing, the symmetry in the scanning probe microscopy image can be “enforced” in order to obtain “clearer” images, effectively removing the less than ideal “influence” of the microscope on the imaging processes. This paper illustrated the crystallographic image processing procedure for scanning tunneling microscopy images that were recorded from a monolayer of a phthalocyanine on two different types of substrates.