  We analyze the exclusive $\phi$-meson photoproduction on both hydrogen and
deuterium targets based on the published data of CLAS, SAPHIR and LEPS
collaborations. A dipole-form scalar gravitational form factor is applied to
describe the $|t|$-dependence of the differential cross section. Based on the
average of all the near-threshold data from CLAS, SAPHIR and LEPS, we find that
the proton and deuteron mass radii are $0.75 \pm 0.02$ fm and $1.95 \pm 0.19$
fm respectively. The coherent and near-threshold quarkonium photoproduction
seems to be sensitive to the radius of the hadronic system. The
vector-meson-dominance model together with a low-energy QCD theorem well
describe the data of near-threshold $\phi$ photoproduction on the hadronic
systems.
