A Fourier transform infrared (FT-IR) spectrometer has been combined with a PL apparatus for the study of semiconductors. Fourier transform spectroscopy has certain advantages for PL, especially in the infrared, including improved signal to noise, higher abscissa precision and resolution. A brief review of the technique is given and we discuss, as examples, the optimization of the FT-IR apparatus for the study of near gap dopant states and deep trap related transitions in epitaxial Si films grown by molecular beam epitaxy (MBE) and double modulation techniques for the study of narrow gap materials, such as InSb. In studying arsenic doped MBE silicon, we found bound-exciton (BE) peaks associated with substitutional As atoms to be the dominant features in the 4.2 K PL spectra from 6 pm thick films grown on n+ (Sb-doped) substrates at growth temperatures ranging from 500 to 800 C. For samples grown at the lower temperatures ~500 C, we observed additional, lower energy, no-phonon peaks due to residual ion-induced lattice defects and a broad, possibly trap related, background rising towards 750 meV (6000 cm-1). These features were not observed in the spectra of samples grown at higher temperatures and this work, which has been cross referenced with other techniques such as deep level transient spectroscopy (DLTS), will lead to optimization of growth conditions for ion-doped n and p type MBE silicon. In the study of materials with narrower gaps such as InSb, a technique using double modulation - interferometer and excitation source - was used to remove the effects of the thermal background radiation. This technique is described and compared with the conventional subtraction procedure. A 77 K InSb detector was used to observe and resolve near gap emission at 5.3 pm and a HgCdTe detector to discover longer wave impurity related emission. The results obtained include the effects of sample temperature 5-20 K and pump laser power density on the individual lines in the spectra.