Atomic Force Microscopy (AFM) is a powerful tool to map the topography of a wide variety of surfaces at the nanometer scale, from insulators to conductors, both soft and hard matter. Beyond topography mapping, the surface analysis power of the AFM lies in it's ability to measure tip-surface forces. Today, such measurements can only be done in a quasi-static way. However, the most sensitive AFM imaging methods are dynamic techniques, which exploit a cantilever resonance to map surfaces. Presently there is great interest in the AFM community to develop dynamic AFM methods which can extract the tip-surface forces. I will discuss these developments, and our approach to this problem, which is based on the nonlinear dynamics of the engaged cantilever when driven with two pure tones.
