  The transparency of metal foils for ultracold neutrons (UCNs) plays an
important role in the design of future high-density UCN sources, which will
feed a number of fundamental physics experiments. In this work, we describe and
discuss the measured transmission of a collimated beam of very slow neutrons
(UCNs and very cold neutrons) through foils of Al, Cu, and Zr of various
thicknesses at room temperature. Our goal was to separate scattering and
absorption in the sample bulk from surface scattering, and to quantify the
contribution of the surface. We were able to demonstrate that the surface
roughness of these foils caused a significant fraction of UCN scattering. The
surface roughness parameter $b$ extracted from UCN measurements was shown to be
of the same order of magnitude as the surface parameter determined by
atomic-force microscopy. They lie in the order of several hundreds of
angstroms. Using the formalism developed here, transmission data from previous
neutron-optical experiments were re-analyzed and their surface roughness
parameter $b$ was extracted.
