When a circularly-symmetric light beam with optical vortex (OV) diffracts at an opaque screen with the sharp edge, the OV core is displaced from the beam axis and, in case of the m-charged incident OV, decomposed into |m| single-charged ones. By means of numerical simulations and based on examples of incident beams with topological charges |m| = 1, 2, 3 we show that, while the screen edge monotonously advances towards the beam axis, the OVs in the diffracted beam cross section move away from the incident beam axis along spiral-like trajectories. The trajectories contain fine structure details that reflect the nature and peculiar spatial configuration of the diffracting beam. For the Kummer beams' diffraction, the trajectories contain self-crossings and regions of 'backward' rotation (loops); in the case of Laguerre–Gaussian beams, the trajectories are smoother. The numerical results are supported by analytical approximations and conform to experiments. The general shape of the trajectories and their local behavior show high sensitivity to the diffraction conditions (spatial structure of the diffracting beam, its disposition with respect to the screen edge, etc), which can be used in diverse metrological applications.

Based on the Kirchhoff–Fresnel approximation, we consider the behavior of optical vortices (OV) upon propagation of diffracted Laguerre–Gaussian (LG) beams with topological charge m = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), these OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam, so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results are expected to be useful in OV metrology and OV beam diagnostics.

In this paper, we present the results of a comparative analysis of the sensitivity of interferograms to wavefront aberrations recorded with flat and cylindrical reference beams. Our results show that compared to classical linear interferograms based on flat wavefronts, cylindrical interferograms have at least 10% higher sensitivity for radially asymmetric types of aberrations and a 30% decrease in average absolute error for aberration recognition using a convolutional neural network. The use of cylindrical reference beams leads to an increase in the sensitivity of interferograms for detecting medium and strong aberrations.

We analyze transformations of circular Laguerre–Gaussian beams with zero radial index after passage through the double-phase-ramp (DPR) converter and study the behavior of optical vortices in the propagating transformed beam. Direct and inverse DPR converters are considered, and informative features of the complete set of optical vortices are revealed. For the input beam with even azimuthal index, such a reaction may cause the sign reversal of the axial optical vortex. The results can be used for creation of light beams with prescribed singular skeleton, for the beam diagnostics, and in high-resolution metrology.

We study the system of phase singularities (‘singular skeleton’) formed when a quasi-plane wave (QPW) input beam diffracts at a double-phase-ramp (DPR) converter. The external (OV positions and 3D trajectories) and internal (ellipticity and orientation angle of the equal-intensity ellipses in the OV-core area) singular-skeleton features are investigated both theoretically and in experiments. The results are presented in comparison with the singular skeleton formed by the DPR when the incident beam is Gaussian. In contrast to the limited number of OVs in the synthesized OV chain, divergent 3D OV trajectories and variable OV morphologies depending on their off-axis distances, which is typical for the Gaussian input beam, it is shown that the QPW-generated diffracted beam carries a rectilinear chain of equidistant optical vortices (OV) with identical morphology parameters. Such singular-skeleton configurations can be useful for the applications to metrology and micromanipulation, in particular, for the multi-particle optical trapping and guiding.