Fig. 1. Far-field distribution of Gaussian vortex beams diffracted by different line structures. (a) Horizontal line; (b) vertical line; (c) crosshair; (d)-(f) the far-field diffraction results corresponding to (a)-(c); (g)-(i) the correspond phase distributions of (d)-(f)

Fig. 2. Far-field diffraction results of the crosshair detection method

Fig. 3. Far-field diffraction results of three line structure and star patterned structure

Fig. 4. (a) Schematic diagram of the crosshair position offset and (b) it's far-field diffraction results

Fig. 5. Far-field diffraction results for changing the direction of the crosshair offset

Fig. 6. Far-field diffraction distributions of a 10th-order topological charge vortex beam passing through different apertures

Fig. 7. Experimental light path diagram of the crosshair detection method

Fig. 8. Experimental device and the generated vortex beam

Fig. 9. Experimental results of the crosshair detection method

Fig. 10. Experimental results after thresholding

Fig. 11. Experimental results of the crosshair center position offset