The effect of astigmatism on the diffraction of a vortex carrying beam with a Gaussian background

The effects of astigmatism and defocusing on the intensity distribution and encircled energy for a beam with an on-axis vortex embedded in a Gaussian background have been investigated using the Fresnel–Kirchhoff diffraction integral. A study has been carried out for two values of the topological charge for a truncated beam, and the stability of the optical vortices under the influence of aberration has been analysed. Some results are also presented for the influence of the truncation parameter of the beam. The aberration results in flattening of the dark core, and elongation of the core along a particular direction, thus resulting in a tail-shaped point spread function. Twofold symmetry is observed for selected defocused planes, and the diffraction pattern becomes more complex with an increase in the value of the aberration. The combined effect of astigmatism and coma on the PSF is also investigated.