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.