Statistical precision in super-resolution optical fluctuation imaging.

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by calculating the spatiotemporal cross-cumulants of independent stochastic intensity fluctuations of emitters. Ideally, SOFI eliminates any noise that is not correlated over time, but in practice, due to limited data lengths, the statistical uncertainty of cumulants will affect the continuities and homogeneities of SOFI images. Since the variance and signal-to-noise ratio (SNR) characterize cumulant statistical uncertainty, we determined theoretical expressions for these based on a single dataset. From a simulation of temporal fluctuations of blinking fluorescent emitters, we calculated the quantitative relation between the SNR of cumulants and multiple parameters of the blinking signal, such as the on-time ratio, acquisition frame to average blinking rate ratio, sequence length, and photon amplitude, which not only provides a physical interpretation for SOFI phenomena but also theoretical guidance to achieve optimal practical outcomes.