Double helix point spread function with variable spacing for precise 3D particle localization

Abstract

To extend the axial depth of nanoscale 3D-localization microscopy, we propose here a splicing-type vortex singularities (SVS) phase mask, which has been meticulously optimized with a Fresnel approximation imaging inverse operation. The optimized SVS DH-PSF has proven to have high transfer function efficiency with adjustable performance in its axial range. The axial position of the particle was computed by using both the main lobes’ spacing and the rotation angle, an improvement of the localization precision of the particle. Concretely, the proposed optimized SVS DH-PSF, with a smaller spatial extent, can effectively reduce the overlap of nanoparticle images and realize the 3D localization of multiple nanoparticles with small spacing, with respect to PSFs for large axial 3D localization. Finally, we successfully conducted extensive experiments on 3D localization for tracking dense nanoparticles at 8µm depth with a numerical aperture of 1.4, demonstrating its great potential.