Some remarks on comparing microgeometrical profiles and the application of replicas in microgeometrical measurements

First a method for comparing profiles given in the following considerations. The profile comparisons have to be carried out in such position, that their average distance should be the smallest possible. Helmert transform is used for fitting measured points sets to one another in geodesy so that the least square distance of the measured points would be the smallest. However, for Helmert transform corresponding point pairs are to be found, i.e. for each point of one of the profiles has to be found a nearest one on the other profile. Multiple approaches are studied for finding corresponding point to a measured point in a point set. The effectiveness of the Helmert transform and the results of profile comparison are given for profiles of rounded triangle wave shaped regular roughness standards in the most used mechanical roughness range taken by contact stylus and confocal white light optical scanner. As an application, a method for qualifying replica materials is also presented. Our method uses roughness standards of at least three different roughnesses and takes replicas of them. The inverted scanned profiles of the replicas are compared with the scanned profiles of the original surfaces. The comparison uses Helmert transform to fit the two corresponding profiles. The average distance of one of the profile point sets from the other one is calculated by determining the distance of all the points in one profile from the circles given by their three nearest measured points in the other profile. The method is also used for comparing the less noisy stylus scans and the more sensitive optical scans of the original surface in order to determine, whether the noise in the replica scans are due to the replica taking process or to the scanning.