  We present a study on the optical losses of Fabry-P\'erot cavities subject to
realistic transverse mirror misalignment. We consider mirrors of the two most
prevalent surface forms: idealised spherical depressions, and Gaussian profiles
generated by laser ablation. We first describe the mode mixing phenomena seen
in the spherical mirror case and compare to the frequently-used clipping model,
observing close agreement in the predicted diffraction loss, but with the
addition of protective mode mixing at transverse degeneracies. We then discuss
the Gaussian mirror case, detailing how the varying surface curvature across
the mirror leads to complex variations in round trip loss and mode profile. In
light of the severe mode distortion and strongly elevated loss predicted for
many cavity lengths and transverse alignments when using Gaussian mirrors, we
suggest that the consequences of mirror surface profile are carefully
considered when designing cavity experiments.
