The application of the dispersion matrix method in the geometric description of circular forms using optical equipment: theoretical development and experimental verification

• Published in: Measurement science & technology 2009-12, Vol.20 (12), p.125301-125301 (18)
• Main Authors: Gómez, E, Caja, J, Maresca, P, Barajas, C, Berzal, M
• Format: Article
• Language: English
• ISSN: 0957-0233; 1361-6501
• DOI: 10.1088/0957-0233/20/12/125301

The aim of this work is to develop a mathematical model for estimating the measurement uncertainty produced when describing circular forms using the coordinates of 'n' non-collinear points obtained using optical equipment such as microscopes or profile projectors. In order to do this, we have introduced the concept of the 'dispersion matrix' into this study; this is defined as an interval on the X and Y axes up to which the measurements of the 'n' points could plausibly deviate from their theoretical values so delimiting the possible error in the selection of the 'optical contacts'. The model considers the angular separation between the measurement points and also the magnification and resolution of the instrument. It has been validated by comparing the theoretical results obtained from simulations using the Monte Carlo method with those obtained from optical measurements of different ring gauges and reference discs. By applying the model proposed in this study, it is possible to quantify the uncertainty for an indirect measurement of circular features performed using the above-mentioned equipment and to establish those measurement conditions which limit the uncertainty to below any predetermined value.