Fresnel Diffraction by a Circular Disk

In this chapter, a representation of a spherical wave diffracted by a perfectly conducting circular disk is derived. The analysis can be adapted to a circular aperture as well as to a spherical cap. Some of the same procedure for the solution construction already introduced for a straight-line branch curve can be carried over to this representation. The difference in the two cases can be exploited to provide a guide to generalizing the Sommerfeld method. This discussion is typically divided into four parts: (1) the definition of a suitable coordinate system; (2) an algebraic analysis of how the branch points of the distance function explicitly depend on the point of observation, P; (3) a construction of the multiple-valued solution for a point-radiation source in the two leaved space; and (4) the application of the solution to the diffraction problem.