Nonlinear distortion in atomic force microscopy (AFM) measurements

摘要

In AFM measurements it is obvious that the shape of the tip scanning the surface function determines the measurement result: a certain tip radius will result in a remarkable distortion of edges. These effects are usually treated in a more or less heuristic way. Morphological operations to determine the tip shape were derived from image processing almost 15 years ago. They are also used to recalculate the original surface from the distorted measurement. They have also been explained as a convolution, which brings up the idea that a deconvolution could be applicable. The current paper deals with a mathematical model leading to a spectral description of the resulting signal. This is of interest in several aspects: (i) identification of the actual nonlinear nature of the distortion process, (ii) estimation of the influence of the tip geometry on reconstruction, (iii) consequences for the time/time-frequency-domain characteristics of the AFM and its closed-loop control. The presented approach is neither based on morphological image processing nor on convolution. It can be utilized to determine the obtainable quality of AFM measurements and the limits of surface reconstruction.