Cross-Correlation Increases Sampling in Diffusion-Based Super-Resolution Optical Fluctuation Imaging

Correlation signal processing of optical three-dimensional (x, y, t) data can produce super-resolution images. The second-order cross-correlation function XC ₂ has been 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 diffusing particles. We then expand our fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) analysis to use cross-correlation as a postprocessing computational technique to extract both dynamic and structural information on particle diffusion in nanoscale structures simultaneously. Cross-correlation maintains the same super-resolution as auto-correlation while also increasing the sampling rates to reduce 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.