Fresnel Diffraction.nb

In this section we will look at the Fresnel diffraction for both circular apertures and rectangular apertures. To help our physical understanding we will begin our discussion by describing Fresnel zones. In the study of Fresnel diffraction it is convenient to divide the aperture into regions called Fresnel zones. Figure 1 shows a point source, S, illuminating an aperture a distance z 1 away. The observation point, P, is a distance to the right of the aperture. Let the line SP be normal to the plane containing the aperture. Then we can write The aperture can be divided into regions bounded by concentric circles r = constant defined such that r 1 + r 2 differ by l ƒ 2 in going from one boundary to the next. These regions are called Fresnel zones or half-period zones. If z 1 and z 2 are sufficiently large compared to the size of the aperture the higher order terms of the expansion can be neglected to yield the following result.