Soot aggregate sizing through multiangle elastic light scattering: Influence of model error

Abstract

Inferring the size distribution and morphology of aerosolized soot aggregates from the angular distribution of elastically-scattered light involves solving an ill-posed inverse problem. Light scattering is often approximated using Rayleigh-Debye-Gans Fractal Aggregate (RDG-FA) theory, which is computationally-efficient but limited in accuracy. The resulting model errors are amplified by the ill-posed nature of the problem into large errors in the recovered soot parameters. More precise approaches, like the multi-sphere T-Matrix (MSTM) method, are too computationally-intensive to use in the inference procedure. The efficiency of RDG-FA and the accuracy of MSTM can be combined by modeling the approximation error. The error function is derived from a principal component analysis on error matrices generated for randomly-sampled aggregates having morphological fractal parameters sampled from distributions derived from published studies in the literature. The error model is then used to correct the RDG-FA kernel in the forward model for a particular set of fractal parameters. Finally, the corrected model is used to estimate probability densities of the size distribution and aggregate fractal parameters via Bayesian inference.