M. Berzal

Uncertainty in ellipse fitting using a flatbed scanner: development and experimental verification

In the field of dimensional metrology, the use of optical measuring machines requires the handling of a large number of measurement points, or scanning points, taken from the image of the measurand. The presence of correlation between these measurement points has a significant influence on the uncertainty of the result. The aim of this work is the development of an estimation procedure for the uncertainty of measurement in a geometrically elliptical shape, taking into account the correlation between the scanning points. These points are obtained from an image produced using a commercial flat bed scanner. The characteristic parameters of the ellipse (coordinates of the center, semi-axes and the angle of the semi-major axis with regard to the horizontal) are determined using a least squares fit and orthogonal distance regression. The uncertainty is estimated using the information from the auto-correlation function of the residuals and is propagated through the fitting algorithm according to the rules described in Evaluation of Measurement Data—Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’—Extension to any number of output quantities. By introducing the concept of cut-off length, it can be observed how it is possible to take into account the presence of the correlation in the estimation of uncertainty in a very simple way while avoiding underestimation.

A proposal for the metrological characterization of circular features with digital optical machines

This paper aims to analyze the different adjustment methods commonly used to characterize indirect metrology circular features: least square circle, minimum zone circle, maximum inscribed circle and minimum circumscribed circle. The analysis was performed from images obtained by digital optical machines. The calculation algorithms, self-developed, have been implemented in Matlab® and take into consideration as study variables: the amplitude of angular sector of the circular feature, its nominal radio and the magnification used by the optical machine. Under different conditions, it was determined the radius and circularity error of different circular standards. The comparison of the results, obtained by the different methods of adjustments used, with certified values for the standards, has allowed us to determine the accuracy of each method and its scope.

Alternative method for the metrological characterization of spur gears in the sub-millimeter range using optical equipment

The aim of this work is to develop a software that allows the inspection of spur gear manufactured in the sub-millimeter range. The measurements are made using a digital optical machine and using an analysis proprietary software implemented in Matlab®, which is able to handle images, captured using the digital optical machine. The software allows to evaluate the profile and pitch deviations as establish in the ISO/TR 10064-1:1992 standard [1].

Optimization of the method for measuring the insulation of circular section electrical and telecommunication conductors

The aim of this paper is to demonstrate an alternative method of measurement to be used in determining the minimum thickness of insulation on electrical and telecommunications conductors that are circular in section. As such, a critical analysis of the standard that is usually used in this type of measurement is undertaken and a new error-free methodology is proposed. The problem is reduced to obtaining the minimum separation between the two interior, eccentric circumferences. The method proposed indirectly determines this separation from four measurements between tangents to each circumference, two on the X-axis and two on the Y-axis, positioning the test piece to be measured in any position and taking any origin of coordinates at random. As such, errors derived from the skill of the operator are avoided, as the test piece can be positioned in any direction without the need to determine the thinnest section visually. This method does not involve increasing the uncertainty and is carried out using the same measuring instruments that the standard indicates (a microscope or profile projector).