In the present paper, we determine the conditions necessary for the generation of phase singularities in the far-field by a phase bar or a trench. The ultimate goal of our work is to link object parameters to a topological distribution of pairs of singularities. We apply scalar theory and show that objects smaller than the diffraction limit are not capable of generating singularities. Supplementary rigorous electromagnetic theory is applied to determine this feature size for a real structure. Topological behavior by changing a typical object parameter and stability of the position of phase singularities in the presence of neighboring scatterers are analyzed.