Diffraction of light by an opaque sphere 1: Description and properties of the diffraction pattern

In this paper we discuss the diffraction pattern resulting from the propagation of light past an opaque obstacle with a circular cross section. A mathematical description of the diffraction pattern is obtained in the Fresnel region using scalar diffraction theory and is presented in terms of the Lommel functions. This description is shown experimentally to be quite accurate, not only for near axis points within the shadow region but also well past the shadow's edge into the directly illuminated region. The mathematical description is derived for spherical wave illumination and an isomorphic relation is developed relating it to plane wave illumination. The size of the central bright spot (as well as the subsequent diffraction rings), the axial intensity, and the intensity along the geometric shadow are characterized in terms of point source location and the distance of propagation past the circular obstacle.