Quantifying and enforcing two-dimensional symmetries in scanning probe microscopy images of periodic objects

The defining features of a scanning probe microscope (SPM) are a very fine "probe" that is scanned in two dimensions (2D), in very fine steps, very close to the surface of a sample, and a "probe sample interactions signal" that is recorded at each scanning increment. This signal may then be digitized and displayed as a function of the magnified scanning steps. A 2D-image of the probe-sample interactions may, thus, be obtained. Just like any other image, these images can be subjected to image processing routines in order to quantify the information that is contained. For SPM images of 2D periodic objects, crystallographic image processing (CIP) may be utilized advantageously to quantify and enforce the 2D symmetry in the images.