# Laser Beam Positioning by Using a Broken-Down Optical Vortex Marker
## 6 Experimental Results  
To verify the proposed solutions, measurements were made in the test system. The measuring system was set up so that only the intensity or the fringe field could be obtained. A stabilized He-Ne laser and an expander were used as the source. The measuring system was located in the room while the light beam went outside to the mirror and back; i.e., the influence of weather conditions was observed. The distance from the laser to the mirror was about 50 m, meaning that the optical path length was 100 m.  
Figures 7 and 8 show the measurement system, which was designed to verify if the proposed methods could be useful in a real situation. The configuration of the elements in both examples was the same, while the arrangement shown in Figure 8 shows the method of obscuring the reference wave responsible for the occurrence of bifurcated interference fringes. In such configurations, the system enables the recording of the intensity itself and the interference field. Figure 6: (**a**) Intensity of the vortex beam with a topological charge of \(m=5\) after separation into five vortices with topological charges of \(m=1\), (**b**) pseudo-phase, plotted as \(\arg(l_{con}(r,\theta))\) with the original phase map colored and superimposed. The red circles indicate the locations of the vortex points on both types of maps. Locating the vortex points that are at the bifurcation of the fringes requires the following steps: notches for fringe field analysis and the application of the optical Fourier transform. Then, from the map of the diffraction spectrum, the first diffraction order should be selected, and the inverse Fourier transform should be applied to the next limited area (without the zero order). In this way, we obtained the complex distribution and, after calculating the angle, we obtained the phase maps shown in Figures 9c and 10c. The jumps in the phase value appear on the obtained phase maps. It is important to find the ends of these lines, and image processing methods locate these ends with an accuracy not exceeding 1 pixel; to increase the accuracy of determining points, the authors used neural networks that analyzed selected regions with dimensions of 20 by 20 pixels, with the end of the phase jump line placed in the center of the cut area [34,35]. The learned artificial neural network locates vortex points with sub-pixel accuracy. For an algorithm based on neural networks, it makes no difference whether it looks for the end of the phase jump with phase or pseudo-phase maps. In both cases, the accuracies are the same. In Figures 9 and 10, the presence of vortex points is marked with green circles. It is possible to determine the location of optical vortices based on the bifurcation of the fringes, but these methods are not as accurate as the methods using phase fields. To locate bifurcations, one can also use algorithms based on neural networks. Information about the sign and topological charge of optical vortices can be easily read from the bifurcations of the interference fringes, while the localization itself is sensitive to noise and disturbances that occur during low-intensity recording. Figure 11 shows an example of the images recorded in the configuration of the measurement arrangement shown in Figure 8. In this case, no additional light beam is needed. The recorded intensity for the three separated vortices was subjected to the convolution operation. As a result of convolution, the pseudo-phase maps shown in Figure 11c were obtained. This method is simpler in terms of technology and calculations than the fringe-field method, and the obtained result has the same accuracy. In the measurement series, an exemplary measurement of which is shown in Figure 11, the minimization and pseudo-phase methods were used to locate vortex points. In half of the results, the minimum search method gave incorrect results due to turbulence. The pseudo-phase method worked properly on all captured images. Figure 10: Experimental results with a separated optical vortex with the topological charge of \(m=3\).