Determining the number of components required to analyze mixed solutions. In the experiments shown here, the number of components needed in the global-fit analysis of the data was known, but in practice this might not always be the case. In the case of a sample with an unknown number N of components, this number (provided that it is not too large) can be determined from a singularvalue decomposition (or any other decomposition strategy, e.g. principal component analysis) of the two-dimensional A(λ,t) data set. By equation 3, the data is a sum of N products of λ and t-dependent left-and right-singular vectors. In fact, a singular-value decomposition of the data of Fig. shows two significant components (all components with smaller weights containing noise), and a singular-value decomposition of the data of Fig. shows three (see SI). Thus the number of species to be used in analyzing the data (N in eq. 3) can be determined from the data itself. It should be noted that the number obtained in this way provides a lower bound for the true number of species, because if two species have very similar or identical UV/Vis spectra, and/or have very similar diffusion coefficients, then they will give rise to a single singular vector in the singular-value decomposition of the time-dependent data. A next step in the case of an unknown number of components could be to perform a least-squares fit of eq. 2 to time-dependent absorption at the wavelengths where the absorption spectrum of the sample has a maximum. For highly complex systems an iterative deflation of the components/singular values can provide an accurate estimation of the true number of components. Moreover, methods such as multivariate curve resolution applied iteratively can also be used to resolve such complex systems. Continuous size distributions. An analysis in terms of a discrete set of sizes and spectra might not work in the case of polydisperse mixtures with continuous size distributions, such as polymer or nanoparticle solutions. Fortunately, extensive data-analysis methods have been developed for NMR-DOSY on such samples, and we think that this theoretical framework can be adapted without too much difficulty to analyze the optical DOSY data.