The surface morphology of low-energy Kr+-polished amorphous Si layers is studied by topographical methods as a function of initial substrate roughness. An analysis in terms of power spectral densities reveals that for spatial frequencies 2 X 10(-2)-2 x 10(-3) nm(-1), the layers that are deposited and subsequently ion polished reduce the initial substrate roughness to a rms value of 0.1 nm at the surface. In this system, the observed dominant term in linear surface relaxation, proportional to the spatial frequency, is likely to be caused by the combined processes of (a) ion-induced viscous flow and (b) annihilation of (subsurface) free volume during the ion-polishing treatment. Correspondingly, a modification of the generally assumed boundary conditions, which imply strict surface confinement of the ion-induced viscous flow mechanism, is proposed. Data on surface morphology are in agreement with the optical response in extreme ultraviolet from a full Mo/Si multilayered system deposited onto the modified substrates. (c) 2010 American Vacuum Society. [DOI: 10.1116/1.3428545]