In this section, we present a system for measuring circular magnet rings, such as the one shown in figure 3. The magnet ring measurements are direct, in the sense of the definition given in section 2: they do not require comparison to a reference shape. Consequently, no matching is done this time. The specification of magnet ring measurements and a description of the optical gauge system for magnet rings are given below, in sections 6.1 and 6.2, respectively.