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

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Abstract

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 $\rho \lt {{1}}$, indicating that $\rho$ fraction of the emitter power is utilized. The $\rho$-power effective Fisher information and the $\rho$-power effective SNR are derived for the Airy and Gaussian point spread functions (PSFs). It is shown that as $\rho$ increases, the root mean square error of the Fisher information sharply drops to its lower bound, approximately $\rho = {0.8}$ 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.

© 2020 Optical Society of America

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Supplementary Material (1)

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Code 1       Matlab codes for figures.

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