Determination of Best Objective Function for Evaluating Geometric Deviations

Laser scanning equipment and coordinate measuring machines are used to sample points from manufactured surfaces for inspection purposes. The sampled points are then used to evaluate the geometric deviations associated with the surface. The evaluation of geometric deviations involves an optimisation step which fits a substitute surface to the measured points, while minimising the error between the substitute surface and the measured points. The geometric deviation is equal to the difference between the maximum and the minimum 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 estimated. This paper presents a procedure for determining the best fitting function. It considers the trade-off between the accuracy of the estimation and the susceptibility to measurements and sampling errors. The proposed procedure has been verified for a number of geometric deviation types. Those results show that adopting a generic form for the fitting objective function may lead to large estimation errors with some geometric deviations, and that the proposed procedure reduces these errors significantly.