Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference

Recovering the size distribution of aerosolized soot aggregates from multiangle elastic light scattering data requires the inversion of an integral equation, which is a mathematically ill-posed problem. This paper demonstrates how maximum a posteriori (MAP) inference can be used to stabilize the inversion by introducing prior information about the size distribution of the soot aggregates. Results show that the size distribution can be recovered using only simple smoothness and non-negativity priors if the aggregate number density is known, but otherwise it is necessary to specify additional information about the presumed distribution shape.

Research Highlights► Recovering aggregate sizes from a soot-laden aerosol using multiangle light scattering. ► Underlying problem is mathematically ill-posed. ► Maximum a posteriori (MAP) inference augments data with prior assumptions. ► Smoothness and nonnegativity priors may be sufficient to recover a distribution.