Some problems in the characterisation of surface microtopography

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Abstract
The difficulties of describing real rough surfaces in mathematical terms are introduced. The statistical treatment of height distributions leads to the application of time series analysis. But real surfaces often behave as non-stationary random processes, implying that their geometrical properties are not intrinsic constants but depend on sampling interval and sample length. Current attempts to incorporate these ideas into international roughness standards are described. Recent developments in fractal geometry have suggested a way forward, and some evidence is presented that rough surfaces on a nanometric scale may behave as self-affine fractals. Finally the difficulties of generalizing from two-dimensional descriptions to three- dimensional surfaces are discussed with particular reference to anisotropy.

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