  We study interfaces with periodic boundary conditions in the low temperature
phase of the improved Blume-Capel model on the simple cubic lattice. The
interface free energy is defined by the difference of the free energy of a
system with anti-periodic boundary conditions in one of the directions and that
of a system with periodic boundary conditions in all directions. It is obtained
by integration of differences of the corresponding internal energies over the
inverse temperature. These differences can be computed efficiently by using a
variance reduced estimator that is based on the exchange cluster algorithm. The
interface tension is obtained from the interface free energy by using
predictions based on effective interface models. By using our numerical results
for the interface tension $\sigma$ and the correlation length $\xi$ obtained in
previous work, we determine the universal amplitude ratios $R_{2nd,+} =
\sigma_0 f_{2nd,+}^2= 0.3863(6)$, $R_{2nd,-} = \sigma_0 f_{2nd,-}^2= 0.1028(1)
$ and $R_{exp,-}=\sigma_0 f_{exp,-}^2= 0.1077(3)$. Our results are consistent
with those obtained previously for the three-dimensional Ising model,
confirming the universality hypothesis.
