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

- Using error approximation technique is discussed to combine the efficiency of Rayleigh-Debye-Gans Fractal-Aggregate theory (RDG-FA) with the accuracy of multi-sphere T-Matrix (MSTM) method for recovery of soot morphological parameters in multiangle elastic light scattering (MAELS) setup.
- Error approximation technique builds a statistical model of the model error by sampling the difference the low order (RDG-FA) and high order (MSTM) schemes.
- Bayesian inference is used to recover the probability densities of unknown soot morphological parameters by accounting for the deterministic structure of the model error.

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.