  An ongoing challenge in atomic force microscope (AFM) experiments is the
quantitative measurement of cantilever motion. The vast majority of AFMs use
the optical beam deflection (OBD) method to infer the deflection of the
cantilever. The OBD method is easy to implement, has impressive noise
performance and tends to be mechanically robust. However, it represents an
indirect measurement of the cantilever displacement, since it is fundamentally
an angular rather than a displacement measurement. Here, we demonstrate a
metrological AFM that combines an OBD sensor with a laser Doppler vibrometer
(LDV) to enable accurate measurements of the cantilever velocity and
displacement. The OBD/LDV AFM allows a host of quantitative measurements to be
performed, including in-situ measurements of cantilever oscillation modes in
piezoresponse force microscopy (PFM). As an example application, we demonstrate
how this instrument can be used for accurate quantification of piezoelectric
sensitivity, a longstanding goal in the electromechanical community.

Mesoscale and Nanoscale Physics