Cramér-Rao bounds for particle size distribution estimation from multiangle dynamic light scattering

We derive the Cramér-Rao lower bounds (CRB) for parametric estimation of the number-weighted particle size distribution (PSD) from multiangle Dynamic Light Scattering (DLS) measurements. The CRB is a useful statistical tool to investigate the optimality of the PSD estimators. In the present paper, a Gaussian mixture (GM) model of the multimodal PSD is assumed and the associated Fisher information matrix (FIM) is determined. The usefulness of multiangle DLS in significantly decreasing the CRB is demonstrated. The mean square error (MSE) of the PSD GM model parameters estimation by the Bayesian inference method proposed in [1] is compared to the derived CRB for a simulated monomodal PSD. Results show that the MSE achieves the derived CRBs for the unbiased estimators of the PSD GM model parameters.