Application of orbital angular momentum to simultaneous determination of tilt and lateral displacement of a misaligned laser beam

We present an analysis of the combined effects of tilt and lateral displacement on the orbital angular momentum spectrum of a laser beam. Our theory explains the symmetries and properties of the spectrum under the influence of misalignments. We apply the theory to establish a reliable and efficient method for determining and subsequently eliminating tilt and lateral displacement. An improved technique for obtaining the orbital angular momentum spectrum employing Laguerre-Gaussian modes is proposed. Finally, a numerical experiment is carried out to verify the method.