Determination of best objective function for evaluating geometric deviations

Laser scanning equipment and coordinate measuring machines are used to samp le points from manufactured surfaces for inspection purposes. The sampled p oints are then used to evaluate the geometric deviations associated with th e surface. The evaluation of geometric deviations involves an optimisation step which fits a substitute surface to the measured points, while minimisi ng the error between the substitute surface and the measured points. The ge ometric deviation is equal to the difference between the maximum and the mi nimum normal distances between the fitted surface and the measured surface points. The choice of the objective function used in fitting the substitute surface affects the accuracy by which the geometric deviations are estimat ed. This paper presents a procedure far determining the best fitting functi on. It considers the trade-of between the accuracy of the estimation and th e susceptibility to measurements and sampling errors. The proposed procedur e has been verified for a number of geometric deviation types. Those result s show that adopting a generic form for the fitting objective function may lead to large estimation errors with some geometric deviations, and that th e proposed procedure reduces these en-ors significantly.