We have been working on a long-term project for developing a variety of infrared immersion gratings for near- to mid-infrared wavelengths. The transmittance of material is essential to realize high-efficiency immersion gratings for astronomical applications. For a typical grating, the attenuation coefficient αatt must be <0.01 cm−1 for the absolute diffraction efficiency of >70%. However, as there are few reports of αatt < 0.01 cm−1 for infrared optical materials in the literatures, we performed high-accuracy measurements of αatt for a variety of infrared materials applicable to immersion gratings. We have already reported αatt at room temperature for single-crystal Si, single-crystal Ge, CVD-ZnS, CVDZnSe, and high-resistivity single-crystal CdZnTe (Ikeda et al. 2009, Kaji et al. 2014, and Sarugaku et al. 2016). Next, we proceeded with the measurements of αatt at cryogenic temperatures of 20–80 K range, which is the typical operational temperatures of infrared instruments, and for which the shifts of the band gap and/or the sharpness of the lattice absorption lines from the corresponding room temperature values are expected. Thus, we developed a new cryogenic FTIR system that enables high-accuracy measurements at cryogenic temperatures. The system has a mechanism with which two sample cells and a reference cell can be easily and quickly switched without any vacuum leak or temperature change. Our preliminary measurement of Ge using this cryogenic FTIR system found that both the cut-on and cut-off wavelengths shift to the shorter (from 2.0 to 1.7 μm) and longer (from 10.6 to 10.9 μm) wavelengths, respectively, when the temperature is decreased from room temperature to the cryogenic temperature (<28 K). We plan to complete cryogenic measurements for a variety of infrared materials by the end of 2016.