Scanning electron microscopy with very slow electrons offers a novel tool enabling one to image the graphene samples at nanometer or even sub-nanometer lateral resolution in transmitted as well as reflected electrons and to count reliably the atomic layers in both imaging modes. The study was performed on graphene prepared by chemical vapor deposition on thin copper foil. Observation by slow electrons has also confirmed the underlayer mechanism of nucleation and growth bellow already existing graphene layers on copper. Moreover, electrons with impacted energy below 100eV can be used for “cleaning” of a material. It leads to elimination of the contamination process during the measurement, which enables to observe the predicted oscillations in reflection mode and to measure the transmissivity of various stacks of layers in transmission mode down to units of eV.