  Fabry-P\'erot (FP) cavities are fundamental and ubiquitous optical elements
frequently used in various sensing applications. Here, we introduce a general
theoretical framework to study arbitrary light-cavity mode interactions for
planar FPs and show how optical aberrations, intrinsic to the interrogating
beam or due to imperfect cavities, reduce optical sensitivity by exciting
higher-order spatial modes in the cavity. We find that particular Zernike
aberrations play a dominant role in sensitivity degradation, and that the
general loss of sensitivity can be significantly recovered by appropriate
wavefront correction or mode filtering. We then demonstrate our theoretical
findings also experimentally and show that in practice the sensitivity of
realistic planar FP sensors can be improved up to three-fold by a synergistic
combination of adaptive optics and passive mode filtering.
