Computational assessment of an effective-sphere model for characterizing colloidal fractal aggregates with holographic microscopy.

• 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. 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 D f 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 n eff and effective radii a eff of the aggregates. A scaling relationship between n eff and a eff based on the Maxwell Garnett effective-medium theory then determines D f. Here we use a multisphere superposition code to calculate the exact holograms produced by aggregates with tunable fractal dimensions D f. We show that n eff and a eff become less sensitive to the aggregate orientation as D f increases. We also show that the Maxwell Garnett scaling relationship correctly determines D f 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. [ABSTRACT FROM AUTHOR]