Harmonic Bounds in Atomic Force Microscopy

The paper addresses the problem of evaluating magnitude bounds on higher harmonics of the periodic tip oscillation in an Atomic Force Microscope (AFM). The suggested approach considers a class of nonlinearities well suited to the tip-sample interaction in AFMs, and reduces the bounding problem to an optimization problem. For a relaxation of the problem a solution in a closed form is provided and reduces the conservativeness of estimates existing in literature.