  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 $\langle R^2\rangle_p > 0.6$, indicating that the holograms are
well-described by the effective-sphere model.
