  Enhancement cavities where a beam of large size (several millimeters) can
resonate have several applications, in particular in atomic physics. However,
reaching large beam waists in a compact geometry (less than a meter long)
typically brings the resonator close to the degeneracy limit. Here we
experimentally study a degenerate optical cavity, 44-cm long and consisting of
two flat mirrors placed in the focal planes of a lens, in a regime of
intermediate finesse ($\sim 150$). We study the impact of the longitudinal
misalignement on the optical gain, for different input beam waists up to
5.6~mm, and find data consistent with the prediction of a model based on ABCD
propagation of Gaussian beams. We reach an optical gain of 26 for a waist of
1.4~mm, which can have an impact on several applications, in particular atom
interferometry. We numerically investigate the optical gain reduction for large
beam waists using the angular spectrum method to consider the effects of
optical aberrations, which play an important role in such a degenerate cavity.
Our calculations quantitatively reproduce the experimental data and will
provide a key tool for designing enhancement cavities close to the degeneracy
limit. As an illustration, we discuss the application of this resonator
geometry to the enhancement of laser beams with top-hat intensity profiles.
