Super-diffraction imaging in three-dimensional localization precision of the double-helix point spread function

Abstract

The combination of switch effect and single molecule positioning can realize the sample super diffraction resolution imaging, and double helix point spread function will be a single molecular orientation nanometer resolution extending from two dimensions to three dimensions. In this paper, three-dimensional (3D) positioning accuracy of the double helix point spread function is discussed. First, the theoretical localization accuracy for an unbiased estimator of the double-helix point spread function is compared with that for 3D localization using Fisher information and the influences of localization accuracy including photon number, varying levels of background and pixel size are analyzed. Second, based on the localization algorithm of gaussian fitting, which is usually adopted in data analysis of single molecular orientation in the experimental process, the axial localization accuracy of double helix point spread function is obtained by the error transfer function law. Computer simulation results show that under the condition of more than 1000 photons in number, the positioning accuracy of gaussian fitting localization algorithm and theory localization accuracy of Fisher information are in good agreement. The discussion of the paper provides not only the theoretical basis for 3D positioning accuracy of double helix point spread function, but also the theoretical guidance for the experiment at the same time.