Formal theory of measurement in surface topography representation

Surface topography measurement has always involved the representation of surface topography by statistical parameters and functions based on a single profile or parallel multiple profiles in the Euclidean or fractal dimensions. In this paper, we intend to formalise the process of surface topography measurement using the representational theory of measurement in the hope of bridging the large epistemological gap between measurement theorists and surface metrologists. A brief description of the formal measurement theory is given. Conceptualisation of the nature of surface topography measurement is presented in terms of multidimensional implementation of the theory. It is shown as a result of this conceptual formalism that current surface topography representation techniques are fundamentally inadequate to qualify as measurement processes as dictated by this theory. The representational measurement theory may help formulate new methodologies for surface topography representation.