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Chapter 1:
Basic Concepts of the Statistical Theory of Light Scattering
1.1 Introduction In practice, one deals mostly with objects having a continuous and, as a rule, rough surface. The surface of an object is formed under the influence of numerous random factors, such as nonideal mechanical processing, effects of temperature, and so on. As a result, the surface of an object is almost always of random shape and can generally be described by a random function of space coordinates and time. Recall that a random function of one parameter—say, time—is called a single-parameter random process. Further consideration shows that random functions depend on four (three coordinates plus time) or more parameters. Such functions are called multiparameter random processes or random fields. This term should be used particularly for functions describing wave fields scattered by objects with random surfaces. Evidently, such fields have random structure. It is clear that the study of wave scattering by objects with rough surfaces should be considered a statistical problem that involves finding probability characteristics of the scattered field, including distribution functions, field moments, and correlation properties, from given probability characteristics of the surface. In this chapter, we consider the basic concepts relating to the probability characteristics of random surfaces and the random fields scattered by them. The main results of the theory of diffraction by random surfaces in the Kirchhoff approximation are reviewed. Field correlation characteristics and moments scattered by moving or standing objects are considered. 1.2 Random surfaces and fields scattered by them; the Kirchhoff method Consider the surface of an arbitrarily rough object in motion. During the course of its motion, the surface can be deformed by various forces. It is usually difficult to describe the space-time characteristics of such a surface. However, for a random surface in practice, its deviation from the mean smooth surface is small compared with the curvature radius of this surface. Such random deviations appear due to uncontrollable effects of the formation and processing of surfaces.
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