This contribution reports on some recently achieved results in aerosol size distribution retrieval in the Anomalous Diffraction Approximation (ADA) to Mie scattering theory. This approximation is valid for spherical articles that are large compared to the wavelength and have a refractive index close to 1. First, a new analytic inversion formula was derived, which allows the direct computation of the size distribution as an integral over the spectral extinction function. This formula is valid for particles that both scatter and absorb light and it also takes the dispersion of the refractive index into account. Secondly, an indirect inversion algorithm was developed, which can be used for scarce and noisy extinction measurements. It does not need a priori information about the shape of the size distribution. Using this indirect inversion algorithm, a global climatology of stratospheric aerosol properties was derived from SAGE II satellite extinction measurements, at an altitude of 22.5 km over the period 1985-1995. Maps of total surface area density, total number density and effective radius, as function of time and latitude, are shown.