Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distances from the screen. On account of the bidirectional nature of diffraction by metallic screens the Rayleigh-Sommerfeld integrals themselves cannot be used for irradiance calculations, but must first be resolved into their forward and reverse components and it is found that Kirchhoff's integral is the appropriate measure of the forward irradiance. Because of the inadequate boundary conditions assumed in their derivation the Rayleigh-Sommerfeld and Kirchhoff integrals do not correctly describe the flow of energy through the aperture.