A long-time issue that thin films supported on a substrate with low refractive index cannot be subjected to multiple-angle incidence resolution spectrometry (MAIRS) has been resolved, and an advanced MAIRS technique has been developed. Infrared multiple-angle incidence resolution spectroscopy (IR MAIRS) is being recognized as a powerful spectroscopic tool for revealing molecular orientation in thin films or molecular adsorbates. MAIRS has been, however, employed with only IR spectroscopy thus far, since MAIRS requires high refractive index substrates such as germanium and silicon, and shorter wavelength regions have no appropriate substrates. Although one of the most commonly useful substrates for IR spectroscopy is CaF2, unfortunately it cannot be employed for IR MAIRS because of the low refractive index. To overcome this experimental limitation, the principle of MAIRS has been studied theoretically, and it has been found that polarization effects on transmission intensity is the main cause that disturbs a proper MAIRS analysis. As a result, now it is possible to employ IR MAIRS for analysis of thin films on CaF2 by removing the s-polarization and by use of the advanced MAIRS algorithm.