Direct solar radiation measurements were performed both in a moderately polluted location of Southern Italy. We use a spectro-photo-radiometer covering the range 400 nm- 1100 nm, with a resolution of 3 nm, to obtain the aerosol optical depth. We use this data to compare two inversion techniques to deduce the aerosol size distribution. The first one is a modified Twomey non-parametric technique, with a second-derivative regularisation. It is applied to the discretized integral equation, relating aerosol optical depth to particles size distribution by Mie theory, and is valid without any restriction on wavelength or particle radius. The second method uses a new algorithm based on the Anomalous Diffraction Approximation (ADA) to Mie theory, applicable to spherical particles with radius large compared to the wavelength and refractive index close to 1. A specially designed set of ortho-normal basis functions, each possessing the spectral behavior of an extinction function, describes the measured spectral extinction. The expansion coefficients of this representation are obtained from a constrained least squares extinction fit. The fit cost function is minimized by a Generalized Reduced Gradient Method (GRGM), which allows the specification of additional constrains on the sought coefficients (e.g. positiveness).