Ferroelectrets, i.e., soft materials with electric charges deposited on the surfaces of internal voids, are well known for their potential in transducer applications and energy harvesting. Due to their regular geometry and optical transparency, tubular channel ferroelectrets (manufactured by laminating polymer films around a polytetrafluoroethylene template which is later removed) are well-suited for studying the process of charge deposition. Understanding how space charges are formed on the internal surfaces will lead to improvements in the charge density and in the piezoelectric performance of these films. In this work, the inception voltage for dielectric barrier discharges (and hence the onset of charge deposition) was measured using two independent techniques, fluorescence imaging and the laser intensity modulation method (LIMM). The results (around 1.4-1.7 kV, depending on the void height) are in agreement within ±50 V. The internal electric field distribution was calculated using finite element analysis (FEA). Combined with Paschen's law, these calculations explained the experimentally observed discharge patterns, starting from the channel edges in thick samples, but glowing more uniformly in films with void heights of 50 μm or less. A time-dependent FEA simulation of the LIMM measurement reproduced the observed thermoelastic resonances and their effect on the LIMM signal, and explained its seemingly erratic behavior. This approach has great potential for analyzing LIMM and thermal pulse data obtained in inhomogeneous materials.