This paper discusses the formation of the central light spot by means of a binary diffraction axicon with high numerical aperture, using a difference method of solving Maxwell's equations in the temporal region. It is shown that the broadening of the central light spot that unavoidably appears when the beam that illuminates the axicon is linearly polarized can be compensated by introducing a linear phase singularity (perpendicular to the polarization direction) into the beam. A very compact, weakly broadened light spot whose size in the immediate vicinity of the surface of the optical element is 37% less than the diffraction limit can be formed in this case by varying the substrate thickness.