Roughness correction to the Casimir force: Beyond the proximity force approximation

We calculate the roughness correction to the Casimir effect in the parallel plates geometry, for metallic plates described by the plasma model. The calculation is perturbative in the roughness amplitude, with otherwise arbitrary values for the plasma wavelength, the plate separation and the roughness correlation length. The correction is found to be always larger than the result obtained in the Proximity Force Approximation.