Aberration resistant axial localization using a self-imaging of vortices

The vortex self-imaging (SI) implemented in optical imaging systems and its usage for a robust axial localization of point-like objects are presented. The vortex SI is used to generate a double-helix point spread function (DH PSF) maintaining its shape and size unchanged in a large working area. The robustness of the axial localization is demonstrated by a resistance against the spherical aberration. Using a thorough analysis, the experiments are optimized to achieve the highest localization sensitivity and to find a trade-off between the aberration stability of the DH PSF, the length of the localization range and the energy efficiency. The benefits of the method are achieved by applying the SI of nondiffracting vortices prepared by a spatial light modulator (SLM). The feasibility of the proposed technique is demonstrated by a defocusing induced rotation of the fixed and moving 1μm polystyrene beads, carried out in the transmitted light illumination.