Fresnel`s Zones

 To explain the basic laws of light propagation near obstacles (apertures, slits, opaque disks), Fresnel complemented Huygens' principle with a postulate stating that every point on a primary wave front serves as the source of spherical secondary wavelets. The amplitude of the field at any point is the superposition of all these wavelets, of their amplitudes and phases. This postulate is called the Huygens-Fresnel principle. The Huygens-Fresnel principle allows to solve a number of diffraction problems and to calculate a variety of diffraction patterns. One of such problems is that of diffraction on a circular aperture or a disk. If a point source and the viewed point are on the axis of the system, the wave front can be conveniently divided into circular Fresnel zones. Calculations show that areas of the Fresnel zones are equal. The amplitudes of secondary wavelets in the viewed point are equal as well. However, the phases of oscillations in the point P, excited by neighboring zones, differ by π. This explains why the light intensity will be zero if the number of zones on the aperture is an odd number, and will reach its maximum if the number of such zones is an even one. When the shadow covers only odd or only even Fresnel zones, a large increase in intensity occurs at point P, as only odd or only even oscillations are in phase. Devices that produce such selective shadows are called the Fresnel zone plates. They act like lenses. In diffraction on a round disk, a bright spot is always present in the center of the diffraction pattern (the Poisson bright spot), as predicted by the theory of Fresnel zones. A general diffraction pattern on a round obstacle is rather complex. It can be found for each viewed point by adding oscillations from secondary sources. Calculating the result of interference of the secondary wavelets is a complex mathematical problem, but you can solve it with the help of a computer simulation.