The long-wave downwelling spectral radiance measurements performed by means of the Far-Infrared Radiation Mobile Observation System (FIRMOS) spectrometer at the summit of the Zugspitze (German Alps) in the winter 2018/19 allowed the retrieval of the optical and micro-physical properties of ice and mixed clouds, showing a good agreement of the statistical relationship between the ice water path and the ice optical depth with the ones from previous works. In this paper the optical depths retrieved from FIRMOS are initially compared with selected cases calculated from backscattering light detection and ranging (lidar) data by using a transmittance method. Then, in order to compare the whole FIRMOS dataset, the power-law relationship between backscattering and extinction is used to apply the Klett method and automatize the routine. Minimizing the root mean square differences, the exponent k of the power-law relationship is assessed to be 0.85 with a variability in the range of 0.60–1.10 for ice clouds and 0.50 with a variability within 0.30–0.70 for mixed clouds.