  We show that the recently proposed ionic microscope set-up [Kollath et.al,
PRA, \textbf{76}, 063602 (2007)] could be adapted to measure the \textit {local
single-particle energy distribution} of a degenerate Fermi gas \textit{in situ}
with the resolution on the nanometer scale. We study an ion held in a Paul trap
in an atomic Fermi gas and compute the two-photon Raman photo-association rate
of the ion and an atom. We show that, as a function of the detunings between
the frequencies of the two incident lasers and energies in the atom-ion system,
the photo-association rate directly measures the single-particle energy
distribution in the Fermi gas around the ion. We describe an experiment to
measure the photo-association rate of a trapped ion and argue that, as the
position of the ion can be scanned through the Fermi gas, this experiment
directly probes the local energy and spin-state distribution of the Fermi gas.
