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Chapter 7:
Interference in Thin Films: Theory
This chapter presents the tools for the understanding, description, and design of thin film interference structures, which we will mainly use to describe the multilayer x-ray mirrors shown already in Fig. 4.1. The theory of the propagation of a wave in a layered structure is the one-dimensional case of the general problem of describing the propagation of a wave through a three-dimensional structure. This problem occurs in many parts of physics. The band structure of solids is caused by the propagation of an electron wave function in a periodic structure. X-ray diffraction in crystals or light diffraction in holograms, the reflection and transmission of thin film coatings for light and x rays, the propagation and scattering of radio waves in the atmosphere and along the surface of the earth, and the propagation of acoustic or seismic waves inside a planet or a sun can all be described by similar theories. The inversion of this problem, the deduction of a structure from a measurement of the diffracted, scattered, or reflected radiation field, has been a very active field for the past century. Every imaging system uses a solution of this inversion problem. The determination of the structure of crystals and molecules from an x-ray diffraction pattern has been an active field since 1912. The mapping of the interior of the earth in the search for oil or for geological faults is achieved by solving the inverse scattering problem. The design of a coating with specific properties, or the characterization of a thin film structure from its measured performance, is also a special case of this general inversion problem.
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