Raman spectroscopy is a well understood phenomenon and can be useful for remote material identification. Raman spectroscopy is performed by directing a laser (pump) beam onto a specimen, an extended scene, to induce Raman scatter. Since Raman scatter is a relatively weak phenomenon, a telescope is often used to collect the scattered signal and a narrow band filter is used to reject the pump scatter. The Raman scatter is processed using a spectrometer to identify the Raman signal. This spectrometer could be a dispersive (grating) spectrometer or a Fourier Transform Imaging Spectrometer (FTIS) using a traditional Michelson interferometer. We propose an experiment using an FTIS but with a Fizeau interferometer that takes the form of a multi-aperture imaging system to identify the Raman scattering. An advantage to using an FTIS with a Fizeau interferometer is it occurs naturally in a multi-aperture imaging system, i.e., no additional hardware is needed obtain spectral information. Therefore, a multi-aperture system can have both high spatial and spectral resolution. In this paper, the processing of the data for the Fizeau FTIS is similar to the standard methods but can be enhanced with non-linear restoration algorithms.