In recent work it has been shown that many types of surfaces used in engineering practice have a random structure. The paper takes, as a representation of the profile of such a surface, the waveform of a random signal; this is completely defined by two parameters, a height distribution and an auto-correlation function. It is shown how such a representation can be transformed into a model, appropriate for the study of surface contact, consisting of an array of asperities having a statistical distribution of both heights and curvatures. This theory is compared with the results of an analysis of surface profiles presented in digital form. The significance of these findings for the theory of surface contact and for the measurement and characterization of surface finish is discussed.

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Some important types of instrumentation for measuring surfaces both past and present are reviewed. Exhaustive lists of instruments and performance are not presented; rather more emphasis is placed on the philosophy of measurement. An attempt is made to classify the surface features and also the function of surfaces as a prerequisite to measurement. It is revealed that, as the push towards miniaturization is being taken beyond the nanometrology scale, some theoretical restrictions are likely to be encountered.

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This is the second part of the paper 'Paradigm shifts in surface metrology'. In part I, the three historical paradigm shifts in surface metrology were brought together, and the subsequent evolution resulting from the shifts discussed. The historical philosophy highlighted the fact that the paradigm shifts must be robust and flexible, meaning that surface metrology must allow for full control of surface manufacture and provide an understanding of the surface functional performance. Part II presents the current paradigm shift as a 'stepping stone', building on the above historical context. Aspects of surface geometry will also have to cater for surfaces derived from disruptive application, i.e. structured and freeform surfaces are identified candidates. The current shift is presented in three aspects: from profile to areal characterization; from stochastic to structured surfaces; and from simple geometries to complex freeform geometries, all spanning the millimetre to sub-nanometre scales. In this paradigm shift, the scale of surface texture is beginning to approach some of the geometrical features in micro/nano electro-mechanical systems devices and is becoming one of the most important functionality indicators. Part II will contextualize the current shifts in the discipline of surface metrology, and cement surface metrology in place in the ultra precision and nanotechnology age.

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