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Coating design involves generating the design of an optical coating for a particular application and the conditions of manufacturing. It is part of the manufacturing process of optical coatings itself. It gives the layer sequence for the production run, assists the monitoring of the deposition process during the run, and enables a reverse engineering after the run. It is also particularly part of any R&D in optics in general and goes hand in hand with the optic design itself (Fig. 15.1). Necessarily, it has to use corresponding thin-film design software. Optical coatings consist of thin films of different materials and thicknesses. Thin films are deposited onto a substrate, and the optical application of such a coating is based on the interference effect of light within the thin films and between the ambient media. The propagation of light as an electromagnetic wave is described by Maxwell's equations. Under defined conditions, there are solutions that describe the interference effect exactly. Various recurrent calculating techniques exist to evaluate the effect of optical coatings, but the most versatile method is based on the matrix formulation of Maxwell's equations. Each individual thin film is described by a characteristic matrix including refractive index, extinction coefficient, and physical thickness of the film in dependence on the wavelength of light. The optical coating is described by the product of all the characteristic matrices and the vector whose elements depend on the refractive index of the substrate.
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