Superposition of waves and optical imaging

Abstract

In this chapter, the word “model” for the most part follows the common usage in optics. We often speak of the light ray model or the wave model. But a model is a conceptual tool for describing physical phenomena and so it is not enough to speak of an aspect of modelling. There are the internal relationships between the parts of the model and the rules of correspondence with observable phenomena to be considered; in short, a theory is always involved. Sometimes the theory is already available independently of the invention and comes ready to have something made of it. For example, Einstein’s model for a solid as a set of regularly arranged molecules connected by small springs can go on to be used in statistical mechanics1. Other times, the invention brings its theory with it. Such is the case in geometrical optics in its narrowest sense: that of Fermat’s principle applied to the light ray and its consequences. In other words, the rectilinear propagation of light in an homogeneous isotropic medium and, in short, SnelPs or Descartes’ laws. The wave model is generally introduced into teaching for diffraction and interference. It brings a whole arsenal of theorical constructs with it, not least the phase of the wave, the spatial and temporal coherence of several waves, and diffraction analysis using Huyghens-Fresnel sources, that is sources arranged on the diffracting elements and supposed to emit wavelets that are superposed on the other side of those elements.