Corrections for accurate measurements of particle extinction in scattering media using collimated and diffuse...

Light extinction is widely used to study particles in sprays, soot-forming combustion, and multiphase reactive flows. However, quantitative interpretation of extinction signals remains challenging when particles have a sufficiently large scattering albedo, meaning that incident photons are scattered much more than they are absorbed. This is especially true when experiments involve large apertures and diffuse illumination, resulting in the collection of a substantial portion of the scattered light. Here, an analytic model is developed that quantifies the fraction of single-scattered light collected in such a measurement. This model predicts the correction factor necessary to obtain the true optical depth from measured extinction. Model predictions are validated against experiments and Monte Carlo simulations, showing good agreement across the Rayleigh, Lorenz-Mie, and geometric regimes at low optical depths for both collimated and diffuse illumination schemes. Furthermore, in some regimes, model accuracy is shown to extend to high optical depths, and reasons therefor are discussed. For common measurements based on the diffuse back-illumination extinction imaging (DBI-EI) technique, the model proposed here establishes a practical foundation for quantitative interpretation of measured light extinction from scattering particles with substantially less computational cost and complexity compared to established Monte Carlo methods.