Non-iterative holographic axial localization using complex amplitude of diffraction-free vortices

We present a novel technique of digital holography using digitally implemented diffraction-free vortices for a precise three-dimensional (3D) localization of point-like objects. The localization is realized by the processing of the holographic image reconstructed at arbitrarily selected plane. Separating a single radial component of the spatial spectrum and modulating its phase by a virtual spiral mask, the holographic images of individual object points are transformed to the image structures analogous to the diffraction-free vortex beams. The real part of the complex amplitude of the digital vortices creates the shape-invariant patterns rotating due to a defocusing. Determining the angular rotation, the axial positions of the individual point objects are specified over a wide axial range. In the proposed method, a single in-line hologram is processed without phase shifting and multiplane reconstruction, so that a dynamic localization and tracking of particles becomes possible. The principle of the method is presented in a unified computational model valid for both coherent and incoherent techniques of digital holography. The functionality of the method has been verified in experiments of the Fresnel incoherent correlation holography (FINCH) and its flexibility presented by controlled variations of the localization sensitivity. The application potential has been demonstrated by the defocusing image rotation of fixed fluorescent microspheres and the 3D localization and tracking of moving polystyrene beads resulting in the trajectory reconstruction of a selected particle.