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 estima ting the relaxation time spectrum from the correlation time function. This estimation is frequently done by regularization methods. To obtain good res ults with this step, the statistical errors of the correlation time functio n must be taken into account [J. Phys. A 6, 1897 (1973)]. So far error mode ls assuming independent statistical errors have been used in the estimation . We show that results for the relaxation time spectrum are better if corre lation between statistical errors is taken into account. There are two poss ible 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 mod el derived by Schatzel. On the other hand, they can be computed directly fr om the time series of the scattered light. Simulations demonstrate that the best results are obtained with the latter method. This method requires, ho wever, storing the time series of the scattered light during the experiment . Therefore a modified experimental setup is needed. Nevertheless the simul ations also show improvement in the resulting relaxation time spectra if th e error model of Schatzel is used. This improvement is confirmed when a lat tice with a bimodal sphere size distribution is applied to experimental dat a, (C) 1999 Optical Society of America.