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, for 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
quasistatic way. and presently there is great interest in
the AFM community to develop dynamic AFM methods which can
more rapidly extract the tip-surface forces while scanning
an oscillating cantilever over the surface. I will discuss
these developments, and our approach to this problem,
which is based on the nonlinear dynamics of the oscillating
cantilever when driven with two pure tones.
