Global $q$-dependent inverse transforms of intensity autocorrelation data

We present a new analysis approach for intensity autocorrelation data, as measured with dynamic light scattering and X-ray photon correlation spectroscopy. Our analysis generalizes the established CONTIN and MULTIQ methods by direct nonlinear modeling of the $g_2$ function, enabling decomposition of complex dynamics without a priori knowledge of experimental scaling factors. We describe the mathematical formulation, implementation details, and strategies for solution, as well as demonstrate decompositions of soft matter dynamics data into distributions of diffusion rates/velocities. The open-source MATLAB implementation, including example data, is publicly available for adoption and further development.