Charge distribution from SKPM images

Inferring the surface charge distribution from experimental Kelvin probe microscopy measurements is usually a hard task. Although several approximations have been proposed in order to estimate the effect of these charges, the real inverse problem has not been addressed so far. In this paper, we propose a fast and intuitive method based on Fast Fourier Transform algorithms that allows the surface charge distribution to be obtained directly from the experimental Kelvin voltage measurements. With this method, quantitative physical information such as the total charge and charge position is accessible even in complex charge distributions such as highly insulating polymer surfaces. Moreover, one of the strongest points is that sub-tip resolution is achieved, and therefore the usually unknown charge size can be estimated.