Fig. 2

The influence of different factors on polarization resolving precision. a The effect of the excitation oblique angle \(\beta\) on the Cramér-Rao bound (CRB). The azimuth precision is scaled by the \(\sin \eta\) factor, with a total photon number N of 2000 and noise \(\sigma_{g}\) of 50. b The anisotropy of the dipole precision varies with the oblique angle \(\beta\) in (a). The anisotropies of precisions are calculated by subtracting the maximum precision value from the minimum precision value at a specific angle. The gray area is the recommended range for \(\beta\) = 15° ~ 60°. c The variation of anisotropy of \(\sigma_{\rho } \sin \eta\), \(\sigma_{\eta }\) and \(\sigma_{\Omega }\) with the oblique angle \(\beta\) under a total photon number N of 2000 and noise \(\sigma_{g}\) of 60. d Variations of orientation precisions with the total number of photons and polar angle. All plots are computed with \(\beta\) = 35° and noise \(\sigma_{g}\) = 0, 20 and 40, respectively. e The variation curves of the precision \(\sigma_{\rho }\) and \(\sigma_{\eta }\), respectively, with different SNRs of raw data. f The impact of polarization ratio on the precision \(\sigma_{\rho }\) and \(\sigma_{\eta }\), respectively. The full width at half maximum (FWHM) of the PSF is set to 250 nm