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Rough interfaces of different media will transform the amplitude, phase, and correlation properties of the spatial structure of an optical radiation field in a random way. Modeling of such spatial transforms of the field has been of interest for investigation of rough surfaces for a long time. On the other hand, rough interfaces are encountered in technologies ranging from microstructures to automobile manufacturing. The surface roughness of solids such as metals, plastics, and semiconductors can have an important effect on their physical performance. Spectroscopy measurements in materials science usually require that the surface of the specimen be smooth enough to avoid scattering of the incident light by irregularities on the surface. Indeed, if the metal surface is not smooth enough, one can detect the correct shape, but incorrect values of the wavelength-dependent specular reflectance and subsequently the calculation of the magnitude of the optical constants of the metal, including the refractive index and the extinction coefficient, will yield erroneous results. Also, when we study different transparent crystalline materials with a spectrophotometer, we require that the surfaces of the samples be well prepared in order to measure the correct (scattering-free) optical density.
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