Local geometric error corrections for a metrological scanning probe microscope

A local geometric error correction method is developed for a metrological scanning probe microscope. The method corrects geometric errors in stage displacements using the interferometric measurements of angular position and known geometric offsets. Local and global error correction methods are considered and general scaling dependences on the number of measured steps or points are derived and compared. For the local method, the total uncertainty scales the same or decreases with a sufficient number of measurement steps compared with the global method. Implementation of the local geometric error correction method is demonstrated on measurements of a three-dimensional height standard artefact. The applied error correction method reduces the contribution of geometric errors to the uncertainty budget by two orders of magnitude. The presented approach can be extended to any scanning technique where a measurement translation mechanism can be identified and accurately quantified by relating the measured values with a measurand.