We employ the singular function theory, which is the natural framework within which to discuss the analysis of first kind Fredholm integral equations, to analyze fully the information available from an aerosol aureole scattering experiment. This information is, of course, of two kinds: first, the number of pieces of information available for a given experimental error level and, second, the type (or location) of this information. To appreciate fully the latter, we apply this theory to the inversion of eleven synthetic data sets. These inversions are compared with those obtained previously from an extinction experiment.