Based on the Rayleigh-Sommerfeld vector diffraction theory, a diffraction system combining radial gratings and an axicon is used to obtain diffraction-free petal beams with reticulated two-dimensional optical lattices. The diffraction-free petal beam generated by a radially polarized beam is analyzed theoretically in detail, and its spatial optical field distribution is numerically simulated. Based on axicon processing, the effect generated by the non-ideal axicon on a non-diffracted petal beam is analyzed in detail. The results show that the number of optical lattices of diffraction-free petal beams increases with the radial cosine grating spokes. In contrast to ideal axicons, non-ideal axicons with hyperbolic vertices produce an oscillating effect on the optical field distribution, causing the two-dimensional optical lattices to disappear or blur. In the diffraction-free zone, the range of oscillatory influence decreases with the increasing beam waist radius of radially polarized beams. Moreover, when the beam waist radius reaches 5 mm, the oscillatory phenomenon disappears, and the reticulated feature and optical lattices are restored to the ideal situation. The results of this study have a certain reference significance as reference in the fields of multiparticle capture and particle micromanipulation.