Stability of the four vortices arrangement in the context of laser beam positioning

Remote positioning by precise measurements of lateral displacements of laser beams at large distances is inevitably disturbed by the influence of atmospheric turbulences. We test numerically the use of various arrangements of four single optical vortices for this purpose. Our previous work shows that using the single or higher order vortex beam (topological charge 4) gives better results than vortex free laser beam. We consider arrangement of four separated vortices with different topological sign and show that some configuration leads to comparable results, but there are small differences which are discussed in this paper.