Information sufficient segmentation and signal-to-noise ratio in stochastic optical localization nanoscopy

In stochastic optical localization nanoscopy, it is common practice that a localization algorithm segments the power-effective pixels, which are brighter than a threshold, and discards the rest of a data frame. In this scenario, we investigate the power-effective Fisher information and the power-effective signal-to-noise ratio (SNR) with respect to an index ρ<1, indicating that ρ fraction of the emitter power is utilized. The ρ-power effective Fisher information and the ρ-power effective SNR are derived for the Airy and Gaussian point spread functions (PSFs). It is shown that as ρ increases, the root mean square error of the Fisher information sharply drops to its lower bound, approximately ρ=0.8 for both PSFs. This result suggests that the 80%-power effective data in the emitter localization are information sufficient, and the 80%-power effective SNR is appropriate to indicate the quality of a data frame in the presence of noise.