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In general, the most suitable characterization of rough surfaces has been given by the physical quantity of roughness. In recent years, however, it has become clear that a certain class of actual surfaces has complicated structures with scale-invariant features and is not effectively characterized only by the roughness since such structures do not have characteristic lengths [1]. The rough surfaces with scale-invariant features are called fractal surfaces.
Naoya Wada
"Optical evaluation of the fractality of rough surfaces using array illumination", Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27783F (1 September 1996); https://doi.org/10.1117/12.2299005
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Naoya Wada, "Optical evaluation of the fractality of rough surfaces using array illumination," Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27783F (1 September 1996); https://doi.org/10.1117/12.2299005