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We perform simulations to evaluate a recent experimental technique for usingin-line holographic microscopy and an effective-sphere model to measure thepopulation-averaged fractal dimension $D_f$ of an ensemble of colloidal fractalaggregates. In this technique, models based on Lorenz-Mie scattering by auniform sphere are fit to digital holograms of a population of fractalaggregates to determine the effective refractive indices $n_{eff}$ andeffective radii $a_{eff}$ of the aggregates. A scaling relationship between$n_{eff}$ and $a_{eff}$ based on the Maxwell Garnett effective-medium theorythen determines $D_f$. Here we use a multisphere superposition code tocalculate the exact holograms produced by aggregates with tunable fractaldimensions $D_f$. We show that $n_{eff}$ and $a_{eff}$ become less sensitive tothe aggregate orientation as $D_f$ increases. We also show that the MaxwellGarnett scaling relationship correctly determines $D_f$ to within 10.5\% whenmultiple scattering is negligible and the population-averaged coefficient ofdetermination $\langle R^2\rangle_p > 0.6$, indicating that the holograms arewell-described by the effective-sphere model.

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