Focusing of a vortex carrying beam with Gaussian background by a lens in the presence of spherical aberration and defocusing

Diffraction pattern formed by a lens for a vortex containing truncated beam with Gaussian background, and in the presence of spherical aberration and defocusing has been studied by Fresnel–Kirchhoff diffraction integral. For the study, two different values of topological charge are selected. Compensation of aberration in the presence of appropriate value of defocusing is investigated. Presence of spherical aberration results in an increase in the size of the dark core of the diffraction pattern. Results are also presented for the encircled energy. Some results are also presented for the influence of truncation parameter of the beam, on the point spread function at different observation planes.