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Chapter 1:
Electromagnetic Waves and Rays
Abstract
Light wave propagation is an electromagnetic phenomenon. It is governed by the same equations that are used for microwaves and other electromagnetic waves. In this chapter, we review the wave propagation equations, which are derived from Maxwell's equations. A question basic to imaging is whether or not we can justify considering electromagnetic waves to be rays, for this implies that we must ignore the diffraction phenomena associated with electromagnetic wave propagation that limit image quality. Nevertheless, many concepts fundamental to imaging derive from geometrical optics in which diffraction effects are excluded. Geometrical optics, by definition, deals only with rays. The Eikonal equation defines situations in which there is justification for not considering diffraction effects. If diffraction can be excluded, then electromagnetic propagation can be considered from the standpoint of ray propagation, which simplifies the mathematics. This is the thrust of Part 1 of this book. Effects of diffraction are added later in Part 3. Discrete changes in the refractive index or dielectric constant of propagation channels involve changes in ray direction at such interfaces as a result of reflection, refraction, or diffraction. Geometrical optics considers only the first two. The medium in which the image propagates can involve attenuation as well as image blur resulting from undesired changes in medium refractive index and light scattering by particulates, which give rise to random changes in the light's angle of arrival at the imager. The image formed at the receiver output is a result of refraction at discrete interfaces if the image propagates through ordinary lenses, or reflection at discrete interfaces if the image is reflected from mirrors. The fundamentals of such processes are treated here and utilized later for imaging. In nonhomogeneous media, the refractive index may change on a continual basis, thereby giving rise to continual changes in ray direction. Ray propagation in such media can be described via the ray equation. Chapter 1 concludes with an example involving use of the ray equation in a graded-index optical fiber. Such fibers are also used as lenses and are considered from that standpoint in Chapter 2.
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CHAPTER 1
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