Statistical Optics

Abstract

Statistical optics is the study of the properties of random light. Randomness in light arises because of unpredictable fluctuations of the light source or of the medium through which light propagates. Natural light, e.g., light radiated by a hot object, is random because it is a superposition of emissions from a very large number of atoms radiating independently and at different frequencies and phases. Randomness in light may also be a result of scattering from rough surfaces, diffused glass, or turbulent fluids, which impart random variations to the optical wavefront. The study of the random fluctuations of light is also known as the theory of optical coherence. In the preceding chapters it was assumed that light is deterministic or “coherent.” The dependence of the wavefunction on time and position is perfectly periodic and predictable. On the other hand, for random light, the dependence of the wavefunction on time and position is not totally predictable and cannot generally be described without resorting to statistical methods. In this chapter, we define two statistical averages used to describe random light: the optical intensity and the mutual coherence function. Temporal and spatial coherence are delineated, and the connection between temporal coherence and monochromaticity is established. The examples of partially coherent light provided demonstrate that spatially coherent light need not be temporally coherent, and that monochromatic light need not be spatially coherent. One of the basic manifestations of the coherence of light is its ability to produce visible interference fringes. One section is devoted to the laws of interference of random light. The transmission of partially coherent light in free space and through different optical systems, including image-formation systems, is discussed. A brief introduction to the theory of polarization of random light (partial polarization) is provided.