Abstract: An apparatus and a process for determining resonant frequencies for a cantilever used to measure tip-to-sample distances on a scanning force microscope. The process uses a non-linear equation and does not require knowledge of the shape of the cantilever to obtain the measured forces. As the tip-to-sample distance varies, the resonant frequency of the cantilever changes. Instead of measuring the positions of the tip and sample and the spring constant (k) of the cantilever, the present invention measures the resonant frequency at each data point. The shifts in frequencies contain the information necessary to reconstruct the force-distance curve.