Based on the Fresnel diffraction theory

the influence of the axicon with vertex manufacture precision is analyzed in detail. It is equal to a plano-convex lens focusing the beams when the vertex is machined to a circle. The blunt-tip region of a real axicon can be described actually by a hyperbola

and the aberration non-diffracting beams will be formed for the interference oscillation. We present the theoretical derivation

simulation analysis of the beam propagation and transformation with different vertex manufacture of the axicon. Finally

a method of modifying the influence of a hyperbola-tip axicon is proposed and the correction effect is ideal that is guiding significance to the application of the real manufacture axicon.