Tolerance of an OAM Michelson interferometer to cylindrical lens displacement

Abstract

The interference of two vortex beams with opposite topological charges, $\pm\ell$, results in a petal beam with $n = 2\ell$ bright lobes. We collimate an He-Ne laser unto a spatial light modulator resulting in a vortex beam of topological charge, $\ell = 3$. We collimate the beam once more to ensure a planar wave front when utilizing a Michelson interferometer setup with an added cylindrical lens in one arm. The cylindrical lens reverses the topological charge of the component beam allowing for the formation of a petal beam. We displace the cylindrical lens incrementally by a translational stage and capture the changes in the interference pattern and analyze them using the correlation coefficient. We determine that the tolerance of our OAM Michelson interferometer to cylindrical lens displacements is $0.110(5) mm$, with a value of $0.908$ for the correlation coefficient. Our results may have implications for precision measurements involving the rotational properties of the petal beam.