New method to estimate step heights in scanning-probe microscope images

A new algorithm, the polynomial step-function fit (PSFF), is presented. The PSFF algorithm extracts step heights from noisy and distorted scanning-probe microscope (SPM) images. A one-dimensional, line-by-line implementation as well as a two-dimensional, full-image version are presented. The PSFF algorithm allows the correction of image distortions due to nonlinearities in the piezoelectric scanner and Abbe offset errors, but piezoelectric creep and hysteresis must be corrected separately, and may set the ultimate physical limitations on the accuracy of the PSFF algorithm. The PSFF algorithm is demonstrated with a real sample.