  We apply a perturbative approach to evaluate the Casimir energy for a
massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary
conditions on two surfaces. One of the surfaces is assumed to be flat, while
the other corresponds to a small deformation, described by a single function
$\eta$, of a flat mirror. The perturbative expansion is carried out up to the
fourth order in the deformation $\eta$, and the results are applied to the
calculation of the Casimir energy for corrugated mirrors in front of a plane.
We also reconsider the proximity force approximation within the context of this
expansion.
