Category Archives: diffraction

Paraxiality

The pre­vi­ous post on the Gauss­ian beam not­ed that this beam is a solu­tion to the parax­i­al wave equa­tion and thus only accu­rate for small diver­gence angles. The lim­it giv­en in [1] was $w_0 \gt 2\lambda/\pi$ or $\theta \lt 0.5\mathrm{rad}$ or $\approx 29^\circ$. The Gauss­ian beam mod­el is of course not exact up to that […]

Scalar Diffraction - Fourier

In an ear­li­er post we had a look at var­i­ous dif­frac­tion for­malisms that either orig­i­nat­ed in the Huy­­gens-Fres­nel prin­ci­ple or led to essen­tial­ly the same results. The prin­ci­ple mod­eled a field dis­tri­b­u­tion in a aper­ture (or on a sur­face) as a source of infi­nite­ly many spher­i­cal waves whose ampli­tudes and phas­es were pre­scribed by the […]

Scalar Diffraction - Imagery

In this post on the prin­ci­ples of scalar dif­frac­tion there were quite a num­ber of inte­gral expres­sions for dif­frac­tion of light, start­ing from the Huy­gens-Fres­nel prin­ci­ple and apply­ing var­i­ous degrees of approx­i­ma­tion. Inte­gral for­mu­la­tions are usu­al­ly very abstract and not very illus­tra­tive. How­ev­er, with today’s avail­able com­put­er pow­er we can turn these inte­grals into…

Scalar Diffraction - Huygens, Fresnel, Fraunhofer

One can work years in fiber optic com­mu­ni­ca­tions and not real­ly have to care about dif­frac­tion, but when work­ing with free-space light prop­a­ga­tion and/or illu­mi­nat­ed sur­faces it’s bet­ter to know the dif­fer­ence between your Fres­nel and your Fraun­hofer dif­frac­tion, and what the heck the Huy­gens-Fres­nel prin­ci­ple is all about.