Thin-film photovoltaic cells with high reflectivity in the below-bandgap spectral region are ideally suited for thermophotovoltaics. This allows the below-bandgap radiation to be reflected back to the emitter, so that their energy can be used to reheat the source, rather than being lost. In this work, we present a substantial improvement in the theoretical thermophotovoltaic conversion efficiency in the presence of photon re-use. We also predict the achievable conversion efficiency for a system that uses In0.53Ga0.47As photovoltaic cells, and present an experimental optical cavity to be used for future efficiency measurements. Owing to recent advances in thin-film photovoltaics, thermophotovoltaic efficiencies above 50% may soon be realizable.