Influence of correlated errors on the estimation of the relaxation time spectrum in dynamic light scattering

An important step in analyzing data from dynamic light scattering is estimating the relaxation time spectrum from the correlation time function. This estimation is frequently done by regularization methods. To obtain good results with this step, the statistical errors of the correlation time function must be taken into account [J. Phys. A 6, 1897 (1973)]. So far error models assuming independent statistical errors have been used in the estimation. We show that results for the relaxation time spectrum are better if correlation between statistical errors is taken into account. There are two possible ways to obtain the error sizes and their correlations. On the one hand, they can be calculated from the correlation time function by use of a model derived by Schätzel. On the other hand, they can be computed directly from the time series of the scattered light. Simulations demonstrate that the best results are obtained with the latter method. This method requires, however, storing the time series of the scattered light during the experiment. Therefore a modified experimental setup is needed. Nevertheless the simulations also show improvement in the resulting relaxation time spectra if the error model of Schätzel is used. This improvement is confirmed when a lattice with a bimodal sphere size distribution is applied to experimental data.