We demonstrate how the virtual photoproduction of vector mesons on nuclei scans the wave function of vector mesons from the large non-perturbative transverse size ρ∼ R_V down to the small perturbative size ρ∼ 1/√(Q^2). Thee mechanism of scanning is based on color transparency and QCD predicted spatial wave function of quark-antiquark fluctuations of virtual photons. A rich, energy- and Q^2-dependent, pattern of the nuclear shadowing and antishadowing is predicted, which can be tested at the European Electron Facility and SLAC.