Computational assessment of an effective-sphere model for characterizing colloidal fractal aggregates with holographic microscopy. (October 2019) - Fung, Jerome; Hoang, Samantha
Highlights: Simulations assess an approach for optically characterizing fractal aggregates. Digital holograms of aggregates analyzed by modeling aggregates as spheres. Criteria for determining the validity of effective-sphere approach presented. Abstract: We perform simulations to evaluate a recent experimental technique for using in-line holographic microscopy and an effective-sphere model to measure the population-averaged fractal dimension Df of an ensemble of colloidal fractal aggregates. In this technique, models based on Lorenz–Mie scattering by a uniform sphere are fit to digital holograms of a population of fractal aggregates to determine the effective refractive indices neff and effective radii aeff of the aggregates. A scaling relationship between neff and aeff based on the Maxwell Garnett effective-medium theory then determines Df . Here we use a multisphere superposition code to calculate the exact holograms produced by aggregates with tunable fractal dimensions Df . We show that neff and aeff become less sensitive to the aggregate orientation as Df increases. We also show that the Maxwell Garnett scaling relationship correctly determines Df to within 10.5% when multiple scattering is negligible and the population-averaged coefficient of determination ⟨ R 2 ⟩ p  > 0.6, indicating that the holograms are well-described by the effective-sphere model.