Fresnel Diffraction

Abstract Fresnel diffraction is an approximate solution of the Huygens–Fresnel integral assuming the phase of the wavefront in the aperture has a quadratic dependence upon aperture coordinates. Only that portion of the aperture near the line connecting source and observation points contributes to Fresnel diffraction. For different symmetries, the integral is solved using different mathematical techniques. With separable rectangular coordinates, a table of Fresnel integrals or a graphical technique based on a plot of the Fresnel integral called the Cornu spiral is used. For circular symmetric apertures, a geometrical construction called Fresnel zones is used. The impact of the obliquity factor in calculating the contribution of Fresnel zones is discussed. The existence of Poisson’s spot behind an opaque screen and the performance of a pinhole camera are derived. The design of a zone plate is discussed. The Fresnel zone construction is used to provide additional physical insight into Fermat’s principle.