Fig. 1. The ratio of the inner and outer radius of the optimal annular spiral phase with different topological charges

Fig. 2. Comparison of the mode purity of the generated vortex beam with different mode by using DM with different arrangement of drivers，there are 15 drivers on the first ring，common difference=4，5，6，7，and five rings

Fig. 3. Schematic diagram of the DM with continuous surface and ring-arranged actuators

Fig. 4. Circular spiral wavefront generated by the DM with continuous surface

Fig. 5. Schematic diagram of using DM to generate vortex beams

Fig. 6. The intensity of the vortex beams generated by the DM with continuous mirror

Fig. 7. The phase of the vortex beams generated by the DM with continuous mirror

Fig. 8. The mode purity of obtained vortex beam with l=1~5 on u₂ plane

Fig. 9. The residual distribution of annular spiral wavefront generated via DM with continuous surface

Fig. 10. Amplitude profile（black solid curve）of the vortex beams created by focusing a circle spiral phase and the l_th Bessel function（blue dashed curve），The vertical dotted lines indicate the position of the second roots of the Bessel function

Fig. 11. The amplitude of the vortex beams after filtering

Fig. 12. The phase of the vortex beams after filtering

Fig. 13. The mode purity of vortex beams with l=1~5 after filtering

Fig. 14. The proportion of power loss after spatial filtering