In situ measurements of angular scattering intensities (ASIs) related to single ice crystals of cirrus clouds were obtained for the first time with the airborne Polar Nephelometer instrument. These observations were performed in the southern mid-latitudes during the INCA project. The analysis of the data shows that the well marked peaks of the ASIs are undoubtedly attributed to quasi-specular reflections from crystal facets and the refracted rays passed through the ice crystals. Emphasizing that it is not enough to know the shape of the crystal, but also the internal structure is of great importance. Ray tracing simulations reproduce most of the observed ASIs features. The model of surface roughness, which assumes the Weibull statistics, enables to reproduce the quasi-specular external reflection from crystal facets. It follows from the retrievals that the surface of the crystals was deeply rough and the amount of the internal inclusions (air bubbles) was quite high.