The anomalous propagation of phase in the focus: A re-examination

The classical theory for focusing predicts that when a converging spherical wave is diffracted at an aperture on an opaque screen, the light ray undergoes a rapid π radian phase change in passing through its focus. In the present note, an objection to this prediction is put forward which embodies evidence that when the Fresnel number of the focusing system is of the order of unity or smaller, the phase change near the focus is neither rapid enough nor large enough to reach π radian and that, as a result, the anomalous propagation of the phase near focus is a specific phenomenon which is apparent only in systems of conventional optics, i.e., in systems with considerably large Fresnel numbers.