Abstract
TOPOGRAPHY is often considered as a narrow bandwidth of features covering the form or shape of the surface. After detailed study of many measurements we consider that as well as the possibility of a dominant range of features there is always an underlying random structure where undulations in surface height continue over as broad a bandwidth as the surface size will allow. We consider this a result of many physical effects each confined to a specific waveband but no band being dominant. We invoke the central limit theorem and show through Gaussian statistics that the variance of the height distribution of such a structure is linearly related to the length of sample involved. In another form, the power spectral density, this relationship is shown to agree well with measurements of structures taken over many scales of size, and from throughout the physical universe.
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SAYLES, R., THOMAS, T. Surface topography as a nonstationary random process. Nature 271, 431–434 (1978). https://doi.org/10.1038/271431a0
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DOI: https://doi.org/10.1038/271431a0
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