  We present deep H$\alpha$ imaging of three nearby dwarf galaxies, carefully
selected to optimize observations with the Maryland-Magellan Tunable Filter
(MMTF) on the Magellan 6.5m telescope. An effective bandpass of $\sim$13\AA\ is
used, and the images reach 3$\sigma$ flux limits of $\sim$8$\times10^{-18}$
ergs s$^{-1}$ cm$^{-2}$, which is about an order of magnitude lower than
standard narrowband observations obtained by the most recent generation of
local H$\alpha$ galaxy surveys. The observations were originally motivated by
the finding that the H$\alpha$/FUV flux ratio of galaxies systematically
declines as global galactic properties such as the star formation rate and
stellar mass decrease. The three dwarf galaxies selected for study have star
formation rates, that when calculated from their H$\alpha$ luminosities using
standard conversion recipes, are $\sim$50\% of those based on the FUV.
Follow-up studies of many of the potential causes for the trends in the
H$\alpha$/FUV flux ratio have been performed, but the possibility that previous
observations have missed a non-negligible fraction of faint ionized emission in
dwarf galaxies has not been investigated. The MMTF observations reveal both
diffuse and structured H$\alpha$ emission (filaments, shells, possible
single-star HII regions) spanning extents up to 2.5 times larger relative to
previous observations. However, only up to an additional $\sim5$\% of H$\alpha$
flux is captured, which does not account for the trends in the H$\alpha$/FUV
ratio. Beyond investigation of the H$\alpha$/FUV ratio, the impact of the newly
detected extended flux on our understanding of star formation, the properties
of HII regions, and the propagation of ionizing photons warrant further
investigation.
