  Graphene provides a fascinating testbed for new physics and exciting
opportunities for future applications based on quantum phenomena. To understand
the coherent flow of electrons through a graphene device, we employ a nanoscale
probe that can access the relevant length scales - the tip of a
liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the
graphene device below, creating a movable scatterer for electron waves. At
sufficiently low temperatures and small size scales, the diffusive transport of
electrons through graphene becomes coherent, leading to universal conductance
fluctuations (UCF). By scanning the tip over a device, we map these conductance
fluctuations \textit{vs.} scatterer position. We find that the conductance is
highly sensitive to the tip position, producing $\delta G \sim e^2/h$
fluctuations when the tip is displaced by a distance comparable to half the
Fermi wavelength. These measurements are in good agreement with detailed
quantum simulations of the imaging experiment, and demonstrate the value of a
cooled SPM for probing coherent transport in graphene.
