  We determined the ultracold neutron (UCN) production rate by superthermal
conversion in the solid deuterium (sD$_2$) moderator of the UCN source at the
Paul Scherrer Institute (PSI). In particular, we considered low amounts of less
than $20\,$mol of D$_2$, deposited on the cooled moderator vessel surfaces in
thin films of a few mm thickness. We measured the isotopic ($ c_\text{HD} < 0.2
\, \% $) and isomeric ($ c_\text{para} \le 2.7 \, \% $) purity of the deuterium
to conclude that absorption and up-scattering at $5\,$K have a negligible
effect on the UCN yield from the thin films. We compared the calculated UCN
yield based on the previously measured thermal neutron flux from the heavy
water thermal moderator with measurements of the UCN count rates at the
beamports. We confirmed our results and thus demonstrate an absolute
characterization of the UCN production and transport in the source by
simulations.
