Computationally modeling the use of digital holographic microscopy to characterize colloidal fractal aggregates

Recent experiments suggest that digital holographic microscopy can be used to determine the average fractal dimension of an ensemble of colloidal fractal aggregates [1]. We present computational results that clarify the range of validity of this approach. In the experiments, an aggregate in solution is illuminated with coherent light, and the interference pattern formed between scattered and unscattered light, or hologram, is recorded. Fitting an effective-sphere scattering model to a hologram allows an effective radius r_eff and effective refractive index n_eff to be determined for each aggregate. Once r_eff and n_eff are determined for an ensemble of aggregates, a scaling relationship between r_eff and n_eff derived from the Maxwell Garnett effective medium theory yields the average fractal dimension. In our study, we computationally generate holograms of aggregates of known geometry (and hence, fractal dimension) and fit effective-sphere models to those holograms. We then determine whether the scaling relationship between r_eff and n_eff correctly determines the fractal dimension. Our results suggest that this approach is useful for loosely-packed aggregates whose extent does not greatly exceed the wavelength of the incident light.

[1] C. Wang et al., Soft Matter (2016).