Effect of holes and vortices on beam quality

The effect of a vortex on the invariant quality factors of a light beam is studied. It is shown that a vortex degrades beam quality. The beam intensity at the eye of the vortex necessarily vanishes, creating a hole in the intensity distribution. The degradation in the beam quality is shown to be due partly to the vortex phase and partly to the hole. The results are illustrated graphically. An important inequality to be obeyed by the beam-quality parameters is exhibited.