We shall investigate the effects of surface vibrations and hydrogen-metal coupling on the quantum tunneling diffusion of atomic hydrogen and deuterium on nickel and platinum in the temp- erature range 30K to 200K. We shall also explore the coherence of the tunneling motion through its dependence on adsorbate coverages and surface-impurity concentrations. A newly developed linear optical diffraction technique of very large dynamic range will be employed. %%% The research is intended to advance our understanding of the physics of surfaces and of quantum-mechanical effects in condensed matter.