Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data

- Fractal aggregate size distributions are inferred from elastic light scattering.
- Angular light scattering is modeled with Rayleigh-Debye-Gans Fractal-Aggregate theory.
- Bayesian inference is used to quantify uncertainty.
- Quasi-continuous wide-angle light scattering data narrows credibility intervals.
- Approximation error highlights uncertainty due to RDG-FA model error.

Inferring the size distribution of aerosolized fractal aggregates from the angular distribution of elastically scattered light is a mathematically ill-posed problem. This paper presents a procedure for analyzing Wide-Angle Light Scattering (WALS) data using Bayesian inference. The outcome is probability densities for the recovered size distribution and aggregate morphology parameters. This technique is applied to both synthetic data and experimental data collected on soot-laden aerosols, using a measurement equation derived from Rayleigh-Debye-Gans fractal aggregate (RDG-FA) theory. In the case of experimental data, the recovered aggregate size distribution parameters are generally consistent with TEM-derived values, but the accuracy is impaired by the well-known limited accuracy of RDG-FA theory. Finally, we show how this bias could potentially be avoided using the approximation error technique.