We present calculations of the modification of the spontaneous emission rate from a point source dipole in a Fabry-Perot microcavity containing an optically thin dielectric aperture. The dielectric aperture is described as a passive current source which is driven by the spontaneous point source. The spontaneous emission rate is shown to depend on the details of the aperture design, and shows a strong enhancement on resonance due to 3-dimensional optical confinement by the dielectric aperture.