Stochastic resonance and cooperative behavior in scanning probe microscopy

A substantial amount of scanning probe microscopy (SPM) imaging must be performed at nanometer or angstrom resolution. This requires a very high dynamic range from the z-displacement DAC or feedback ADC, so that this fine detail tends to be very coarsely digitized. This paper examines some nonlinear effects that occur at the level of least-bit digitization and that can affect the resolution of atomic-scale detail. In particular, the interactions of limit cycling and cooperative behavior are examined. We show that in most cases the maximum signal-to-noise ratio is obtained for some finite non-zero noise level, and that in some cases the optimum noise level can be predicted beforehand. In many cases, the correct noise level can be implemented by adjustment of feedback control parameters.