A method to correct hysteresis of scanning probe microscope images based on a sinusoidal model.

Piezoelectric actuators are widely used in scanning platforms of scanning probe microscopes (SPMs). However, the hysteresis of piezoelectric actuators reduces positioning accuracy and results in distorted SPM images. When regular raster scanning of SPM starts, the piezoelectric actuators move repeatedly at the same scanning range and frequency once the scanning parameters are set. In this study, a practical and simple mathematical model derived from experimental phenomenon, which is the combination of sinusoidal and linear functions, was proposed to describe the hysteresis behavior of piezoelectric actuators with repeated scanning. The model parameter was calculated from the coordinates of matched feature points in the trace and retrace images of ordinary sample obtained with an atomic force microscope (AFM). Experimental results show that the hysteresis of the scanned images is decreased from 107.46 pixels to 2.50 pixels after correction, with a width of 800 pixels. Hysteresis in other scanned images with different scanning frequencies and ranges was also corrected effectively using this model. The proposed model can be used to correct the hysteresis of AFM images without using any expensive displacement sensors or standard samples. The model is suitable and easy to be integrated into the scanning program of AFM without requiring hardware modifications.