Focusing of a vortex carrying beam with Gaussian background by an apertured system in presence of coma

In this paper, diffraction pattern of a vortex carrying beam with a Gaussian background has been studied by using Fresnel-Kirchhoff diffraction integral, in the presence of third-order coma. Results of intensity distribution and encircled energy at the Gaussian plane have been presented for two values of the topological charge. Positional shift and splitting of the dark core have been investigated in detail. It is noticed that the diffraction pattern of a beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We have also verified our results by using the optical transfer function approach. Propagation of an apertured Gaussian background vortex beam through a π-phase shifter has also been studied for two values of the topological charge.