Various systems and methods for performing optical analysis downhole with an interferogram (a light beam having frequency components with a time variation that identifies those frequency components. The interferogram is produced by introducing an interferometer into the light path, with the two arms of the interferometer having a propagation time difference that varies as a function of time. Before or after the interferometer, the light encounters a material to be analyzed, such as a fluid sample from the formation, a borehole fluid sample, a core sample, or a portion of the borehole wall. The spectral characteristics of the material are imprinted on the light beam and can be readily analyzed by processing electronics that perform a Fourier Transform to obtain the spectrum or that enable a comparison with one or more templates. An interferometer designed to perform well in the hostile environments downhole is expected to enable laboratory-quality measurements.