Bayesian Uncertainty Evaluation in Vision-Based Metrology

Abstract

Metrology as the science of measurement is omnipresent in today’s society. Many applications in a variety of fields ranging from economy to science have a strong demand for reliable methods to quantify and compare measurement results. Depending on the specific application, this comparison can cover measurements acquired within the same minute by the same operator using the same measurement instrument under the same environmental conditions, or measurements acquired within a month by different operators and measurement instruments on two different continents. In either case, metrology has to provide means to ensure the validity of the comparison of those measurement results. Two aspects of metrology are of importance to us in the context of this paper: The traceability of the measurement result and the evaluation of the quality of the measurement result by means of its associated measurement uncertainty. Traceability: The measurement process is defined as a quantitative comparison of an unknown physical quantity – the measurand – with a known standard (cf. DIN1319 (1995)). Measurement results can thus only be compared on an international level provided compatible standards are available and used. Consequently, our society requires a worldwide system of physical standards which is accepted by and accessible to every nation. The first attempts to internationally standardise physical quantities date back to 1875, when the Bureau International des Poids et Mesures (BIPM) was founded on the basis of the Metre Convention (BIPM (2008)). At that time, international prototypes of the metre and the kilogram where physically built. The evolution of these references triggered the installation of seven base quantities. Since the 11th General Conference on Weights and Measurements in 1960, this system of base units is referred to as the International System of Units (SI) (BIPM (2006)). Today, standards are maintained and made available to the public of participating member states and associated economies by means of a hierarchical structure of international and national metrological institutes as outlined in Figure 1. The highest quality standards are available at BIPM and are used to derive secondary standards operated by national metrological institutions. These institutions, in turn, are responsible to pass standards on to subordinate laboratories and eventually to instrument manufacturers. This concept of traceability ensures that every measurement can be referred back to a physical standard by an unbroken chain of comparisons (International vocabulary of basic and general terms in metrology, VIM (1993)). An example of such a comparison chain is provided in Figure 2. An optical instrument is used to measure the position x of a