Lommel transforms in diffraction theory

Radial functions of diffraction fields are usually expressed in terms of Hankel transforms of corresponding radial functions of (circular) aperture illumination field. For certain simple types of discontinuity of illumination within the aperture, it is more appropriate to use Lommel transforms. It is pointed out that the Lommel-Weber functions are Hilbert transforms of the more familiar Bessel functions, and that their relevant properties can easily be seen as a direct consequence of this relationship.