Force Curves Restoration in Atomic Force Microscopy (AFM) Resonant Modes*

Abstract

Extraction of quantitative nanomechanical data in AFM Resonance modes, such as Amplitude and Frequency Modulation, is a challenging task. It requires either restoration of the force curve for analysis or using experimental data from the Resonant modes directly to estimate parameters of the unknown force. In many situations, force restoration is preferable, because direct parameter estimation methods work only if adequate parametric force model is available (which is rarely the case). At the same time, the force curve provides the most valuable source for material characterization, even when not parameterized. This paper describes a novel approach to force curve restoration from AFM Resonant mode experimental data. The approach is based on Krylov-Bogoliubov-Mitropolsky (KBM) asymptotic dynamics of AFM. Tikhonov regularization is used in case of noisy measurements, when the problem of force restoration becomes ill-posed.