Rayleigh–Sommerfeld diffraction and Poisson's spot

Abstract

When the Fresnel–Kirchhoff (FK) diffraction integral is evaluated exactly (instead of using the Fresnel approximation), the well-known mathematical inconsistency in the FK boundary conditions leads to unacceptable results for the intensity of Poisson's spot. The Rayleigh–Sommerfeld (RS) integral has no inconsistencies and leads to an accurate description. The case for RS is bolstered by the observation that it is equivalent to Fourier propagation.