Cusp-artifacts in high order superresolution optical fluctuation imaging

Superresolution Optical Fluctuation Imaging (SOFI) offers a simple and affordable alternative to the more sophisticated (and expensive) super-resolution imaging techniques such as STED, PALM, STORM, structured illumination, and other derivative methods. In SOFI, the calculation of high order cumulants provides higher resolution but drastically expands the dynamic range of the resulting image. In this study, we have identified another type of artifact for high order SOFI cumulants, dubbed as cusp artifacts. A series of realistic simulations are performed to study the cusp artifacts under the influences of various factors, including the blinking statistics, the spatial distribution of photophysical properties of the sample, the total number of frames processed per dataset, photobleaching, and noise. Experiments, simulations, and theory all show that high order cumulants and odd-order moments could suffer from cusp artifacts. These cusp artifacts also degrade the fidelity of bSOFI that has been proposed to solve the dynamic range expansion of image pixel intensities. Alternatively, cusp-artifacts could be altogether eliminated by utilizing even-order moments constructed directly or from cumulants for image reconstruction. Together with dynamic range compression, these approaches yield improved SOFI images. Our study provides new insight into the nature of high order SOFI images, outlines guidelines for developing and screening SOFI-optimized fluorescence probes, and suggests improved strategies for SOFI data acquisition.