Geometric theory of Fresnel diffraction patterns - Part I. Basic ideas
The paper deals with a new approach to the subject of diffraction which enables the nature of the Fresnel pattern due to an obstacle or aperture of arbitrary form to be easily derived. Taking the hint suggested by observation, it is assumed that in the region of shadow the pattern is produced by the interference of radiations having their origin in the boundary of the aperture or the obstacle. In the region of light, the boundary radiation interferes with the primary incident waves and produces the fluctuations of intensity. The radiation from the boundary can again be effectively replaced by spherical waves originating from a finite number of point-sources on the boundary, called ‘poles’, at which the path to the point of observation from the boundary is a maximum or a minimum. This immediately gives a geometric definition of the poles as those points on the boundary whose projection on the plane of observation are the feet of the normals from the observation point to the projection of the boundary. Using this result, it is possible to geometrically map out the positions of maximum and minimum intensity in the diffraction pattern of an arbitrary aperture or obstacle. The relation between the Fresnel and Fraunhofer patterns of an aperture is discussed and it is shown that the Fresnel pattern approaches more and more to the other type as the size of the aperture is diminished or the distance to the observation screen is increased.