Non-linear distortions caused by AFM-tip geometry and limitations of reconstruction on discrete data

摘要

In tactile measurement systems like AFM it is obvious that a certain tip shape will result in a remarkable blurring of edges and also a distortion of smooth surface functions. In previous papers the highly non-linear nature of the blurring process and the resulting distortions could be shown using expansions in frequency domain. Also limitations for the reconstruction of continuous sinusoidal surface functions were derived. In the first line the current paper delivers an extended mathematical approach describing the distortion process by recursive application of a phase-modulating factor, which is applicable on arbitrary functions and also on discrete data. Second, the approach is used to formulate the inverse problem and so delivers a possible reconstruction method. The reconstruction limit for the tip radius is extended.