  Optical cavities can support many transverse and longitudinal modes. A
paraxial scalar theory predicts that the resonance frequencies of these modes
cluster in different orders. A non-paraxial vector theory predicts that the
frequency degeneracy within these clusters is lifted, such that each order
acquires a spectral fine structure, comparable to the fine structure observed
in atomic spectra. In this paper, we calculate this fine structure for
microcavities and show how it originates from various non-paraxial effects and
is co-determined by mirror aberrations. The presented theory, which applies
perturbation theory to Maxwell's equations with boundary conditions, proves to
be very powerful. It generalizes the effective 1-dimensional description of
Fabry-Perot cavities to a 3-dimensional multi-transverse-mode description. It
thereby provides new physical insights in several mode-shaping effects and a
detailed prediction of the fine structure in Fabry-Perot spectra.
