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Reconstructing the Distributed Force on an Atomic Force Microscope Cantilever



Ryan Wagner, Jason P. Killgore


A methodology to reconstruct a distributed force applied to an atomic force microscopy (AFM) cantilever given the shape in which it vibrates is developed. This is accomplished by rewriting Bernoulli Euler beam theory such that the force on the cantilever is approximated as a linear superposition of the theoretical cantilever eigenmodes. The weighting factors in this summation are calculated from the amplitude and phase measured along the length of the cantilever. The accuracy of the force reconstruction is shown to depend on frequency at which the measurement is performed, the number of discreet points measured along the length of the cantilever, and the signal to noise ratio of the measured signal. Proof of concept experiments are performed on an electrostatically excited cantilever and the expected force distribution is recovered. This force reconstruction technique offers previously unavailable insight into the distributed forces experienced by an AFM cantilever.


Atomic force microscopy, Vibrations, Forced Response


Wagner, R. and Killgore, J. (2017), Reconstructing the Distributed Force on an Atomic Force Microscope Cantilever, Nanotechnology (Accessed April 22, 2024)
Created February 7, 2017, Updated September 17, 2018