Common causes:

This is frequently caused by internal reflections in the sample, beamsplitter, detector window, or other polished surfaces in the optical path. This is commonly referred to as channel spectra.

Suggestions:

Is the sine wave present without a sample in the beam? Can you see it in the single beam data? If so, then it is caused by some element of the optical system.

If sample causes the problem, try tilting the sample. Close examination of sample interferogram will reveal reflected interferograms. This will show up as small centerbursts symmetrically located on both sides of the main centerburst.