Spatially modulated Fourier transform spectrometers (FTS) have a throughput advantage over dispersive spectrometers, since an FTS does not require a slit in order to achieve spectral resolution. The traditional implementation of FTSs employs a scanning Michelson interferometer, but since this interferometer is temporally modulated, it is difficult or impossible to use with a target whose spatial and/or spectral signature is changing rapidly. The less common spatially modulated approach to FTS allows all spectral channels to be acquired simultaneously, but cylindrical optics are required to create an imaging version of this type of spectrometer [an imaging fourier transform spectrometer (IFTS)]. This combination of cylindrical and spherical optics, used to achieve both spectral and spatial resolution, increases the difficulty of understanding and controlling the aberrations. An understanding of the effects of these aberrations is essential to developing a spatially modulated IFTS with good spectral and spatial resolution. A spatially modulated IFTS based on a Sagnac interferometer is described, and the effects of aberrations on the spectral resolution, spatial resolution, and modulation are discussed.