A high-efficiency Kalman filtering imaging mode for an atomic force microscopy with hysteresis modeling and compensation

Abstract With the rapid development of nano-science, an atomic force microscopy (AFM) has been playing an increasingly important role in many fields. Nevertheless, hysteresis nonlinearity of a piezoelectric scanner affects the positioning accuracy and then the imaging performance of an AFM system, besides, the low data utilization rate of a traditional AFM tremendously limits the performance of the system. In this paper, Back Propagation Neural Networks (BPNN) is first used to model and compensate for hysteresis nonlinearity, afterwards, a Kalman filtering based method is proposed to replace the traditional data processing mode to improve system efficiency and image quality. To be specific, consider the hysteresis effect of a piezoelectric scanner, a two hidden layers BPNN is utilized for hysteresis modeling. Subsequently, a method based on cubic spline interpolation is proposed to compensate for hysteresis behavior. After that, to fully utilize the data of current scanning point and its adjacent points, the least square method is used to match sample height information in forward and backward scanning processes. Finally, for each scanning point, Kalman filtering is applied to process all the data with weighting factors recursively to acquire an optimal outcome, which yields more accurate height information than existing methods utilizing only forward scanning data. Experimental results are collected to demonstrate the effectiveness of the proposed method.