  Perturbative corrections to the Casimir free energy due to macroscopic
roughness of dielectric interfaces are obtained in the framework of an
effective low-energy field theory. It describes the interaction of
electromagnetic fields with materials whose plasma frequency $\omega_p$
determines the low-energy scale. The na\"ive perturbative expansion of the
single-interface scattering matrix in the variance of the profile is sensitive
to short wavelength components of the roughness correlation function. We
introduce generalized counter terms that subtract and correct these
high-momentum contributions to the loop expansion. To leading order the counter
terms are determined by the phenomenological plasmon model. The latter is found
to be consistent with the low-energy description. The proximity force
approximation is recovered in the limit of long correlation length and gives
the upper limit for the roughness correction to the Casimir force. The
renormalized low-energy theory is insensitive to the high-momentum behavior of
the roughness correlation function. Predictions of the improved theory are
compared with those of the unrenormalized model and with experiment. The
Casimir interaction of interfaces with low levels of roughness is found to be
well reproduced by that of flat parallel plates with the measured reflection
coefficients at a distance that is slightly less than the mean separation of
the rough surfaces.
