  A dual-excitation method for resonant-frequency tracking in scanning probe
microscopy based on amplitude detection is developed. This method allows the
cantilever to be operated at or near resonance for techniques where standard
phase locked loops are not possible. This includes techniques with non-acoustic
driving where the phase of the driving force is frequency and/or position
dependent. An example of the later is Piezoresponse Force Microscopy (PFM),
where the resonant frequency of the cantilever is strongly dependent on the
contact stiffness of the tip-surface junction and the local mechanical
properties, but the spatial variability of the drive phase rules out the use of
a phase locked loop. Combined with high-voltage switching and imaging,
dual-frequency, resonance-tracking PFM allows reliable studies of
electromechanical and elastic properties and polarization dynamics in a broad
range of inorganic and biological systems, and is illustrated using lead
zirconate-titanate, rat tail collagen, and native and switched ferroelectric
domains in lithium niobate.
