Information sufficient segmentation and signal‐to‐noise ratio for 3D astigmatism stochastic optical localization nanoscopy

It is known that 80% power effective data segmentation with Airy and Gaussian point spread functions (PSFs) for 2D imaging achieves sufficient Fisher information and is appropriate to define signal-to-noise ratio (SNR) of a data frame. This letter investigates information-sufficient data segmentation with an astigmatic PSF for 3D imaging. The SNR and the root mean square error (RMSE) of Fisher information for rho-power effective segmentation are derived. Numerical evaluations in various conditions of emitter axial locations and noise levels are carried out. It is found that the 80% power effective segmentation with the 3D astigmatic PSF also achieves sufficient Fisher information and is appropriate to define SNR. The results are applicable to data segmentation and SNR computation in experiments and simulations.