  Imaging the vibrations of nanomechanical resonators means measuring their
flexural mode shapes from the dependence of their frequency response on
in-plane position. Applied to two-dimensional resonators, this technique
provides a wealth of information on the mechanical properties of
atomically-thin membranes. We present a simple and robust system to image the
vibrations of few layer graphene (FLG) resonators at room temperature and in
vacuum with an in-plane displacement precision of $\approx0.20$ $\mu$m. It
consists of a sturdy vacuum enclosure mounted on a three-axis micropositioning
stage and designed for free space optical measurements of vibrations. The
system is equipped with ultra-flexible radio frequency waveguides to
electrically actuate resonators. With it we characterize the lowest frequency
mode of a FLG resonator by measuring its frequency response as a function of
position on the membrane. The resonator is suspended over a nanofabricated
local gate electrode acting both as a mirror and as a capacitor plate to
actuate vibrations at radio frequencies. From these measurements, we estimate
the ratio of thermal expansion coefficient to thermal conductivity of the
membrane, and we measure the effective mass of the lowest frequency mode. We
complement our study with a globally gated resonator and image its first three
vibration modes. There, we find that folds in the membrane locally suppress
vibrations.
