Fraunhofer Diffraction

Abstract

We will develop a simple derivation of the Huygens-Fresnel integral based on an application of Huygens’ Principle and on the addition of waves to calculate an interference field starting with two apertures as in Young’s two slit experiment extending to N apertures and then a continuum distribution. A detailed look is made of the obliquity factor and a constant value is derived to be used in the simple derivation. We use one dimensional theory for most of the discussion but do present the results of diffraction from a circular aperture as it will be needed in our later discussion of imaging. A second description of the propagation of light, useful when using laser light sources, the gaussian wave, is introduced and examples are given of the use of the theory in geometrical optics and laser design.