An inverse problem solution for undetermined electrostatic force microscopy setups using neural networks

A technique that combines a theoretical description of the electrostatic interaction and artificial neural networks (ANNs) is used to solve an inverse problem in scanning probe microscopy setups. Electrostatic interaction curves calculated by the generalized image charge method are used to train and validate the ANN in order to estimate unknown magnitudes in highly undetermined setups. To illustrate this technique, we simultaneously estimate the tip-sample distance and the dielectric constant for a system composed of a tip scanning over a metallic nanowire. In a second example, we use this method to quantitatively estimate the dielectric constant for an even more undetermined system where the tip shape (characterized by three free parameters) is not known. Finally, the proposed method is validated with experimental data.