Modeling of force-volume images in atomic force microscopy

Atomic force microscopy (AFM) is a recent technique generating tridimensional images at nanometric scale whatever the nature of the chemical sample. An AFM microscope affords the measurement of interatomic forces exerting between a probe associated to a cantilever and a chemical sample. A force spectrum f(z) shows the force evolution as a function of the probe-sample distance z. A reproduction of this analysis in conjunction with the scan of the sample surface yields a force-volume image f(x, y, z). Today, the analysis of a force-volume image remains mainly descriptive. We introduce a signal processing formulation aiming at a precise characterization of each pixel (x, y) of the sample surface. The signal processing problems include the decomposition of a force spectrum into elementary patterns and the factorization of a force-volume image. We discuss the ability of decomposition methods to solve these problems and we illustrate the discussion by means of experimental data.