Focusing of a singular beam in the presence of spherical aberration and defocusing

Focusing of a singular beam by a lens in the presence of spherical aberration and defocusing is studied by using Fresnel–Kirchhoff diffraction integral for two different values of topological charge. Results of intensity distribution and encircled energy are plotted for defocused observation planes. Spherical aberration spreads the dark core and reduces the intensity at maxima. The results have been verified by the optical transfer function (OTF) approach.