Surface characterization, the nature of surfaces and the measurement of surfaces cannot be separated from each other. A deeper understanding of the surface geometry produced by better instrumentation often produces a new approach to characterization. Surface characterization is taken to mean the breakdown of the surface geometry into basic components based usually on some functional requirement. These components can have various shapes, scales of size, distribution in space, and can be constrained by a multiplicity of boundaries in height and position. Issues like the establishment of reference lines can be viewed from their ability to separate geometrical features or merely as a statement of the limit of instrument capability. Often one consideration determines the other! Ease of measurement can inuence the perceived importance of a parameter or feature. It is difcult to ascribe meaningful signicance to something which has not been or cannot be measured. One dilemma is always whether a feature of the surface is fundamental or simply a number which has been ascribed to the surface by an instrument. This is an uncertainty which runs right through surface metrology and is becoming even more obvious now that atomic scales of size are being explored. Surface, interface, and nanometrology are merging. For this reason what follows necessarily reects the somewhat disjointed jumps in understanding brought on by improvements in measurement techniques. There are no correct answers. There is only a progressively better understanding of surfaces brought about usually by an improvement in measurement technique. This extra understanding enables more knowledge to be built up about how surfaces are produced and how they perform. This chapter therefore is concerned with the nature of the geometric features, the signal which results from the measuring instrument, the characterization of this signal, and its assessment. The nature of the signal obtained from the surface by an instrument is also considered in this chapter. How the measured signal differs from the properties of the surface itself will be investigated. Details of the methods used to assess the signal will also be considered but not the actual data processing. This is examined in Chapter 3. There is, however, a certain amount of overlap which is inevitable. Also, there is some attention paid to the theory behind the instrument used to measure the surface. This provides the link with Chapter 4. What is set down here follows what actually happened in practice. This approach has merit because it underlies the problems which rst came to the attention of engineers in the early 1940s and 1950s. That it was subsequently modied to reect more sophisticated requirements does not make it wrong; it simply allows a more complete picture to be drawn up. It also shows how characterization and measurement are inextricably

entwined, as are surface metrology and nanometrology, as seen in all chapters but especially in Chapter 8. It is tempting to start a description of practical surfaces by expressing all of the surface geometry in terms of departures from the desired three-dimensional shape, for example departures from an ideal cylinder or sphere. However, this presents problems, so rather than do this it is more convenient and simpler to start off by describing some of the types of geometric deviation which do occur. It is then appropriate to show how these deviations are assessed relative to some of the elemental shapes found in engineering such as the line or circle. Then, from these basic units, a complete picture can be subsequently built up. This approach has two advantages. First, some of the analytical tools required will be explained in a simple context and, second, this train of events actually happened historically in engineering.