Using cross-correlation to increase sampling in diffusion-based super-resolution optical fluctuation imaging.*

Correlation signal processing of optical 3D (x, y, t) data can produce super-resolution images. The cross-correlation function has been well-documented to produce super-resolution imaging with static and blinking emitters but not for diffusing emitters. Here, we both analytically and numerically demonstrate cross-correlation analysis for the diffusing particles. Then we expand our fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) analysis to use cross-correlation as a post-processed computational technique to extract both dynamic and structural information of particle diffusion in nanoscale structures simultaneously. We further show how this method increases sampling rates and reduces aliasing for spatial information in both simulated and experimental data. Our work demonstrates how fcsSOFI with cross-correlation can be a powerful signal processing tool to resolve the nanoscale dynamics and structure in samples relevant to biological and soft materials.