Wavefront Transformations

Abstract

Historically, light was viewed as a stream of particles propagating with an infinite velocity. This model of light propagation gave rise to what we today call geometrical optics. In the framework of geometrical optics, light is assumed to propagate in free space along straight lines, light rays. Accordingly, all propagation effects can be derived from geometrical considerations. A fundamental aspect of light propagation, according to geometrical optics, is the formation of a completely dark shadow if a small light source illuminates an opaque obstacle (Fig. 4-1). However, more refined experiments demonstrated that there is also light in the shadow and this light is usually not uniformly distributed. As an extreme case, one may even see a relatively strong light spot at the center of the shadow of an opaque disc. This effect was then called diffraction as the obstacle diffracted light from its natural path on a straight line. Detailed analysis showed that this diffraction effect is not consistent with the particle nature of light and it led to the development of the wave theory. Traditionally, the wave theory of light was called physical optics in contrast with geometrical optics. In the framework of wave optics, geometrical optics can be still used as an approximation where the rays coincide, at each point, with the wave vector.