The angular instrumental function of the sun aureole photometer is calculated for a set of scattering angles φ, and several kinds of the photometer geometry. The function takes into account the finiteness of angular dimensions of the sun and the device field of view. The equality of angular dimensions of the sun and the field of view is the condition of the optimum geometry. In this case, the instrumental function does not depend on the scattering angle φ in the range φ = 1 – 10°, and the distortions of the aureole scattering phase functions detected μ(φ, λ) are small. Numerical analysis of the sun spectrophotometer designed at the Institute for Atmospheric Physics demonstrates that the recorded μ(φ, λ) contain information about particles of the size up to r ≈ 50–60 mm with moderate errors (≈10–15%). The data of two complex experiments in 1992 and 1994 have been inverted based on the analysis performed. It is established that relatively narrow single-mode particle size distributions prevail in the translucent clouds. The characteristic dimensions are r ≈ 15–50 mm in Ci clouds; r ≈ 20 mm for As clouds; φ ≈2–3 mm for Ac clouds. The ice content was within the range 1–30 g/m2. The distributions are multimode for the cases of multilayer cloudiness.