A theoretical discussion of the problem of diffraction of spherical scalar waves incident upon a thin black infinite half-plane, which makes use of Maggi’s transformation, has previously appeared in the literature. However, previous treatments have been limited solely to the diffracted component. From the results of previous investigators a simple expression for the total energy distribution, which is suitable for computational purposes, is derived. The results are shown to reduce to Kirchhoff’s formulation of the same problem, for field points not far removed from the shadow-boundary-plane. A rapid approximation method, applicable to the cases of plane and cylindrical waves, is also given. Experimental results were obtained from a photometer employing a refrigerated multiplier phototube. It is shown that the theoretical and experimental intensity distributions agree only when the radius of the point source aperture becomes indefinitely small. Tests with metallic and nonmetallic screens indicate that the nature of the edge of the diffracting screen (for points far removed from the screen) is of minor importance. Possibly of somewhat greater significance, but yet minor, is the nature of the body of the diffracting screen, a metallic screen tending to displace the fringes toward the shadow-boundary-plane.
KEITH LEON McDONALD and FRANKLIN S. HARRIS,JR., "Diffraction of Spherical Scalar Waves by an Infinite Half-Plane," J. Opt. Soc. Am. 42, 321-327 (1952)