Structure function as a robust alternative to the correlation function in photon-count analysis

We present methodological advances in dynamic light scattering analysis through a multi-$\ensuremath{\tau}$ algorithm for the computation of both the intensity correlation function and the intensity structure function, combined with a semiempirical correction that systematically removes shot noise via conditional variance analysis. This unified framework enables consistent interpretation and direct comparison between correlation- and structure-function-based analyses. We validate the method across three experimental platforms: three-dimensional dynamic light scattering in polymer matrices, heterodyne dynamic light scattering in dense silica suspensions, and diffusing wave spectroscopy in turbid latex colloids. In all cases, the intensity structure function outperforms the correlation function. In three-dimensional dynamic light scattering, it yields mean-squared errors in model fits 5--$10\phantom{\rule{0.16em}{0ex}}%$ lower; in heterodyne light scattering, it reduces the standard error at short and intermediate lag times when averaging over multiple datasets; and in diffusing wave spectroscopy, it exhibits greater robustness to variations in instrumental parameters such as the coherence factor. These results establish the intensity structure function, enhanced by precise noise correction and efficient computation, as a stable, reliable tool for analyzing heterogeneous, nonergodic, and complex fluids. The approach sets a benchmark for extracting dynamic properties from photon time series and expands the possibilities for accurate, consistent analysis in advanced light scattering studies.